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UBC Theses and Dissertations

A Psychophysics of active kinesthesis as measured by amplitude of movement Reid , Ian Stewart 1970

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THE PSYCHOPHYSICS OF ACTIVE KINESTHESIS AS MEASURED BY AMPLITUDE OF MOVEMENT by IAN STEWART REID B.P.E., U n i v e r s i t y o f M a n i t o b a , 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF PHYSICAL EDUCATION I n t h e S c h o o l o f P h y s i c a l E d u c a t i o n and R e c r e a t i o n We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA AUGUST, 19 70 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Co lumb i a , I a g ree tha t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s tudy . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y pu rpo se s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d tha t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f * p W y s I r AuciCTi' a<rt /\v«L ^e&reATc a ^ The U n i v e r s i t y o f B r i t i s h Co lumbia Vancouver 8, Canada ABSTRACT The purpose o f t h i s s t u d y was t o dete r m i n e whether judgment, o f a m p l i t u d e o f a c t i v e movement was su b s e r v e d by a p r o t h e t i c o r m e t a t h e t i c p r o c e s s . To d i f f e r e n t i a t e b e t -ween t h e s e two p r o c e s s e s s e v e r a l p s y c h o p h y s i c a l methods were employed. F i f t y v o l u n t e e r s u b j e c t s were randomly a s s i g n e d t o one o f f i v e groups o f e q u a l N. Each o f the groups produced movements under one of f i v e e x p e r i m e n t a l c o n d i t i o n s . These c o n d i t i o n s were: R a t i o P r o d u c t i o n , Magnitude P r o d u c t i o n , B i s e c t i o n o f A s c e n d i n g S t i m u l u s S e r i e s , B i s e c t i o n o f Descending S t i m u l u s S e r i e s , and Ca t e g o r y P r o -d u c t i o n . The r e s u l t s o f Group I (R.P.) and Group I I (M.P.) showed t h a t judgments o f a m p l i t u d e o f movement were c o n s t a n t o v e r the movement continuum as used i n t h i s s t u d y . There was a l s o a l a c k o f an h y s t e r e s i s e f f e c t shown i n t h e com-p a r i s o n o f b i s e c t i o n s o f a s c e n d i n g and d e s c e n d i n g s t i m u l u s s e r i e s . The comparison o f the s u b j e c t i v e and p h y s i c a l v a r i a b l e s o f c a t e g o r y p r o d u c t i o n a l s o showed c o n s t a n t sen-s i t i v i t y o v e r the continuum range. Taken as a whole, the f i n d i n g s tended t o s u p p o r t the c o n c l u s i o n t h a t judgments o f a m p l i t u d e o f movement a r e s u b s e r v e d by a m e t a t h e t i c p r o c e s s . ACKNOWLEDGEMENT "The t e a c h e r who wa l k s i n t h e shadow o f the te m p l e , among h i s f o l l o w e r s , g i v e s n o t o f h i s wisdom b u t r a t h e r o f h i s f a i t h and h i s l o v i n g -n e s s . I f he i s i n d e e d w i s e he does n ot b i d you e n t e r the house o f wisdom, b u t r a t h e r l e a d s you t o the t h r e s h o l d o f your own mind." -- The P r o p h e t . I would l i k e t o thank t h e members o f my t h e s i s committee, Dr. W. Davenport, Dr. K. C o u t t s , Mr. N. K o r c h i n s k y , and e s p e c i a l l y my committee c h a i r m a n , Dr. R.G. M a r t e n i u k , f o r t h e i r e x c e l l e n t g u i d a n c e , a s s i s t a n c e and encouragement. A v e r y s p e c i a l thank you t o my f u t u r e w i f e , D i a n e , f o r h e r d e v o t i o n and a s s i s t a n c e . TABLE OF CONTENTS CHAPTER PAGE I STATEMENT OF THE PROBLEM 1 I n t r o d u c t i o n 1 The Problem 9 D e f i n i t i o n o f Terms 9 Working H y p o t h e s i s 11 L i m i t a t i o n s o f t h e Study 12 D e l i m i t a t i o n s o f the Study 12 I I REVIEW OF THE LITERATURE . 14 P s y c h o p h y s i c s P e r t i n e n t t o the Study o f K i n e s t h e s i s 14 Weber's Law 15 Fechner's Law . . . . . . . . . . . . 16 Ste v e n s ' Power F u n c t i o n 18 Two C l a s s e s o f Sensory C o n t i n u a . . . 21 I n d i v i d u a l Power F u n c t i o n s 27 C r o s s - M o d a l i t y S t u d i e s 2 8 N e u r o p h y s i o l o g y o f K i n e s t h e s i s • 31 Musc l e S p i n d l e s 32 G o l g i Tendon Organs . . . . . . . . 37 Cutaneous R e c e p t o r s 38 Motor I n n e r v a t i o n . . 3 9 J o i n t R e c e p t o r s . . . 42 Two C l a s s e s o f J o i n t R e c e p t o r s . 43 E x c i t a t o r y A n g l e s . . . . . . . 45 C o r t i c a l C o n n e c t i o n s . . . . . . 46 CHAPTER PAGE P s y c h o p h y s i c a l C o n c l u s i o n s Based on N e u r o p h y s i o l o g i c a l E v i d e n c e . . . . 50 B e h a v i o u r a l S t u d i e s o f the P s y c h o p h y s i c s o f K i n e s t h e s i s 54 K i n e s t h e t i c I n f o r m a t i o n . . . 58 Does K i n e s t h e t i c I n f o r m a t i o n Reach the C o r t e x ? . 5 8 A t t e n t i o n t o K i n e s t h e t i c I n f o r m -a t i o n 58 I s K i n e s t h e t i c I n f o r m a t i o n Used? . 59 I I I METHODS AND PROCEDURES 61 S u b j e c t s 61 Ap p a r a t u s 61 P r o c e d u r e 63 E x p e r i m e n t a l D e s i g n 6 8 E x p e r i m e n t a l C o n d i t i o n s 69 Group I - R a t i o P r o d u c t i o n . . . . 69 Group I I - Magnitude P r o d u c t i o n . . 69 Group I l l - B i s e c t i o n o f A s c e n d i n g S t i m u l u s V a l u e s 70 Group IV - B i s e c t i o n of Descending S t i m u l u s V a l u e s . . . . . 71 Group V - C a t e g o r y P r o d u c t i o n . . . 71 S t a t i s t i c a l A n a l y s i s 72 CHAPTER PAGE IV RESULTS AND DISCUSSION . . . . . 74 R e s u l t s 74 D i s c u s s i o n 93 K i n e s t h e t i c Cues 99 V SUMMARY AND CONCLUSIONS 102 Recommendations 104 BIBLIOGRAPHY . . . . . 105 APPENDICES A. S t a t i s t i c a l Treatment 114 B. I n d i v i d u a l Score Sheets 124 C. Raw Sc o r e s f o r E x p e r i m e n t a l Groups 131 LIST OF TABLES TABLE PAGE I Comparison o f t h e P h y s i c a l Degrees, S u b j e c t i v e . A r i t h m e t i c Means, and S t a n d a r d D e v i a t i o n s o f the Four F r a c t i o n s o f Group I ( R a t i o P r o d u c t i o n ) 75 I I Comparison of the P h y s i c a l Degrees, S u b j e c t i v e A r i t h m e t i c Means, and S t a n d a r d D e v i a t i o n s o f t h e Four Magnitudes o f Group I I (Magnitude P r o d u c t i o n ) 80 I I I C o r r e l a t i o n s f o r the Three F u n c t i o n s o f Groups I ( R a t i o P r o d u c t i o n ) and I I (Magnitude Produc-t i o n ) and P e r c e n t a g e o f A c c o u n t e d V a r i a n c e . ; 85 IV "Z" T e s t f o r D i f f e r e n c e Between the Three C o r r e l a t i o n s o f Groups I ( R a t i o P r o d u c t i o n ) and I I (Magnitude P r o d u c t i o n ) 86 V Comparison o f t h e P h y s i c a l Degrees, S u b j e c t i v e A r i t h m e t i c Means, and S t a n d a r d D e v i a t i o n s o f the Three B i s e c t i o n s o f Group I I I ( B i s e c t i o n o f a A s c e n d i n g S e r i e s ) and Group IV ( B i s e c t i o n o f a D escending S e r i e s ) 89 VI Comparison o f the P h y s i c a l Degrees, S u b j e c t i v e A r i t h m e t i c Means, and S t a n d a r d D e v i a t i o n s o f the Seven C a t e g o r i e s o f Group V 9 0 LIST OF FIGURES FIGURE PAGE 1 The Ap p a r a t u s 62 2 S u b j e c t i n t h e S t a r t i n g P o s i t i o n 65 3 S u b j e c t B e i n g G i v e n a S t a n d a r d Movement . . . 67 4 R a t i o and C a t e g o r y P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n Log.-Log. C o o r d i n a t e s 76 5 R a t i o P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n L i n e a r - L o g . C o o r d i n a t e s . . . . 77 6 R a t i o P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n L i n e a r - L i n e a r C o o r d i n a t e s . . . 79 7 Magnitude and C a t e g o r y P r o d u c t i o n Judgments of A m p l i t u d e o f Movements i n Log.-Log. C o o r d i n a t e s . . . . . 81 8 Magnitude P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n L i n e a r - L o g . C o o r d i n a t e s . . 82 9 Magnitude P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n L i n e a r - L i n e a r C o o r d i n a t e s . 84 10 Comparison o f t h e F u n c t i o n s o f t h e B i s e c t i o n o f A s c e n d i n g S e r i e s and B i s e c t i o n o f Descending S e r i e s 88 11 C a t e g o r y P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n L i n e a r - L i n e a r C o o r d i n a t e s . . . 92 CHAPTER I STATEMENT OF THE PROBLEM I n t r o d u c t i o n Two p s y c h o p h y s i c a l laws t h a t have been shown to' d e s c r i b e the c h a r a c t e r i s t i c s o f s e v e r a l d i f f e r e n t s e n s o r y m o d a l i t i e s a r e laws by Stevens and Fechner. These laws d e s c r i b e t h e r e l a t i o n s h i p between a p h y s i c a l s t i m u l u s w i t h i n a s e n s o r y continuum and the s u b j e c t i v e i m p r e s s i o n of the s t i m u l u s i n t e n s i t y . F echner's Law (91) proposes t h a t e q u a l s t i m u l u s r a t i o s c o r r e s p o n d t o e q u a l s e n s a t i o n d i f f e r e n c e s , o r i n o t h e r words, the s t r e n g t h o f the s e n s a t i o n (R) v a r i e s d i r e c t l y w i t h the l o g a r i t h m o f the s t i m u l u s ( S ) ; s t a t e d i n a l g e b r a e i c form: R = K l o g S. When t h e l o g a r i t h m o f the s t i m u l u s i n t e n s i t y i s p l o t t e d a g a i n s t l i n e a r d i f f e r e n c e s i n s e n s a t i o n , Fechner's Law p r e d i c t s a s t r a i g h t l i n e . F echner's Law i s s t i l l used i n p s y c h o p h y s i c a l s t u d i e s even though i t has been l a b e l l e d e r r o n e o u s because o f i t s use o f e q u a l j u s t - n o t i c e a b l e d i f f e r e n c e s ( j . n . d . s ) as a u n i t o f s c a l e (90, 20, 32). 2. T h i s same re a s o n has l e d Stevens t o propose an a l t e r n a t e form o f Fechner's Law. S t e v e n s 1 Power F u n c t i o n Law s t a t e s t h a t e q u a l s t i m u l u s r a t i o s produce e q u a l s u b j e c t i v e r a t i o s . A c c o r d i n g t o St e v e n s ' Power F u n c t i o n Law, the s u b j e c t i v e e v a l u a t i o n o f a p h y s i c a l s t i m u l u s i s r e l a t e d t o t h e p h y s i c a l s t i m u l u s by a power f u n c -t i o n o f t h e form: R = K S N ; where R i s t h e s u b j e c t i v e magnitude, K i s a c o n s t a n t whose v a l u e i s d e t e r m i n e d by the u n i t s u s e d , and S i s the p h y s i c a l s t i m u l u s , w i t h N b e i n g the exponent o r the s l o p e o f t h e power f u n c t i o n l i n e on a l o g - l o g p l o t . S tevens (82) has p o s t u l a t e d t h a t s e n s o r y m o d a l i t i e s d i v i d e d t hemselves i n t o two c l a s s e s depending upon c e r t a i n o p e r a t i n g c h a r a c t e r i s t i c s . C l a s s I , o r p r o t h e t i c c o n t i n u a , a r e concerned w i t h "how much", and d i s c r i m i n a t i o n i s me d i a t e d by an a d d i t i v e o r p r o t h e t i c p r o c e s s a t the p h y s i o l o g i c a l l e v e l . The r e c e p t o r s t h a t s u b s e r v e t h i s c l a s s o p e r a t e on a q u a n t i t a t i v e mechanism, 3. adding e x c i t a t i o n t o e x c i t a t i o n . On the other hand, c l a s s I I or m e t a t h e t i c c o n t i n u a are concerned with "where" and "what k i n d " , and d i s c r i m i n a t i o n i s mediated by a m e t a t h e t i c or s u b s t i t u t i v e process a t the p h y s i o l o g i c a l l e v e l . The r e c e p t o r s t h a t subserve t h i s c l a s s operate on a q u a l i t a t i v e mechanism where e x c i t a t i o n i s s u b s t i t u t e d by e x c i t a t i o n along the continuum. There are four c r i t e r i a t h a t Stevens (82) has o u t l i n e d t h a t d i s t i n g u i s h between the above two c l a s s e s : 1. S u b j e c t i v e s i z e of the j u s t n o t i c e a b l e d i f f e r e n c e s . On c l a s s I c o n t i n u a the s u b j e c t s are not a b l e to e q u a l i z e i n t e r v a l s due to the v a r i a b l e s i z e of the j.n.d. along the continuum. However, on c l a s s I I c o n t i n u a , the s u b j e c t has constant s e n s i t i v i t y along the continuum and i s able to produce equal j.n.ds. The- major d i f f e r e n c e between the two c l a s s e s of c o n t i n u a i s a c t u a l l y t h i s constant and non-constant s e n s i t i v i t y along the sensory continuum. Stevens (82) has r e p o r t e d t h a t h i s power f u n c t i o n . h o l d s on c l a s s I sensory c o n t i n u a , and, t h a t F e c h n e r 1 s Law holds on c l a s s I I c o n t i n u a because of the equal j.n.d.s. 2. When a category r a t i n g s c a l e i s p l o t t e d a g a i n s t a r a t i o s c a l e of s u b j e c t i v e magnitude, the f u n c t i o n o b t a i n e d i s n o n l i n e a r f o r c l a s s I c o n t i n u a , and may be l i n e a r on c l a s s I I s e n s o r y c o n t i n u a . A c a t e g o r y r a t i n g s c a l e i s t h e f u n c t i o n o b t a i n e d when a s u b j e c t judges a s e t o f s t i m u l i i n terms o f a s e t o f c a t e g o r i e s . 3. Time o r d e r e r r o r i s a t h i r d c h a r a c t e r i s t i c and r e f e r s t o the f a c t t h a t t h e second o f two e q u a l s t i m u l i tends t o be judged g r e a t e r than the f i r s t . T h i s i s c h a r -a c t e r i s t i c o f c l a s s I c o n t i n u a , b u t not on judgments o f c l a s s I I . 4. H y s t e r e s i s , o r " l a g g i n g b e h i n d " e f f e c t , d e s c r i b e s what happens when the a p p a r e n t sense d i f f e r e n c e s between s u c c e s s i v e s t i m u l i a r e judged i n d i f f e r e n t o r d e r . Judgments o f s t i m u l i i n an a s c e n d i n g s e r i e s a r e u s u a l l y judged h i g h e r i n i n t e n s i t y t h a n judgments o f s t i m u l i i n a d e s c e n d i n g o r d e r . T h i s e f f e c t i s a c h a r a c t e r i s t i c o f c l a s s I c o n t i n u a b u t i s n o t found on c l a s s I I s e n s o r y c o n t i n u a . There has been s t r o n g p s y c h o p h y s i c a l e v i d e n c e i n s u p p o r t o f S t e v e n s ' Power F u n c t i o n Law. Stevens has shown t h a t o f s i x t e e n s e n s o r y c o n t i n u a s t u d i e d , t w e l v e b e l o n ged t o c l a s s I s e n s o r y c o n t i n u a and f o l l o w e d the Power F u n c t i o n Law ( 8 9 ) , and f o u r s e n s o r y c o n t i n u a (90) b e l o n g e d t o 5. c l a s s I I o r m e t a t h e t i c c o n t i n u a . The Power F u n c t i o n Law and t h e d i s t i n c t i o n i t makes between th e two s e n s o r y c o n t i n u a has been shown t o h o l d w i t h o u t e x c e p t i o n (89, 20, 94). These p s y c h o p h y s i c a l f i n d i n g s can be r e l a t e d t o k i n e s -t h e s i s , as k i n e s t h e s i s i s c o n s i d e r e d a s e n s o r y m o d a l i t y . W i l l i a m s (97) , a l o n g w i t h Smith (80) , has d e s c r i b e d the k i n e s t h e t i c r e c e p t o r s i n the j o i n t c a p s u l e as f u n c t i o n i n g as a m e t a t h e t i c s e n s o r y continuum. They have s t a t e d t h a t t h e r e a r e c o u n t l e s s numbers o f r e c e p t o r c e l l s i n t h e - j o i n t w hich a r e s e n s i t i v e t o v a r i o u s p o r t i o n s o f the movement a r c o f a g i v e n j o i n t . Each c e l l i s r e s p o n s i b l e f o r a s p e c i f i c s e c t i o n o f the movement a r c and t h i s e x c i t a t o r y range was r e p o r t e d t o be about f i f t e e n t o twenty degrees of a r c . T h e r e f o r e d i f f e r e n t j o i n t a n g l e s would cause d i f f e r e n t r e c e p t o r s t o d i s c h a r g e , d e s c r i b i n g a m e t a t h e t i c continuum. M o u n t c a s t l e and P o w e l l (63) have a l s o r e p o r t e d t h a t the j o i n t r e c e p t o r s s u b s e r v i n g , k i n e s t h e s i s f u n c t i o n meta-t h e t i c a l l y , i . e . s p e c i f i c r e c e p t o r s d e p i c t s p e c i f i c j o i n t a n g l e s . They a l s o found t h a t c e l l s i n the s e n s o r y c o r t e x t h a t c o r r e s p o n d t o the j o i n t r e c e p t o r s a r e a r r a n g e d i n a t o p o g r a p h i c p a t t e r n , and t h a t t h e p a t t e r n o f n e u r a l a c t i v i t y d e p i c t e d the j o i n t , a n g l e s and changes i n t h o s e a n g l e s . As w e l l as t h i s q u a l i t a t i v e o r m e t a t h e t i c p r o c e s s , t h e y a l s o found a q u a n t i t a t i v e 6. p r o c e s s a t the c o r t i c a l l e v e l . These c o r t i c a l neurons, d i s c h a r g e d a t a f r e q u e n c y t h a t was s p e c i f i c t o a g i v e n p o i n t p o s i t i o n . M o u n t c a s t l e , Poggio and Werner (62) a l s o s u p p o r t e d the c o n t e n t i o n t h a t the j o i n t r e c e p t o r s f u n c t i o n as a m e t a t h e t i c c o n t i n u a . They tho u g h t t h a t t h e f r e q u e n c y o f d i s c h a r g e o f t h e s e r e c e p t o r s was not s u i t a b l e f o r d e p i c t i n g p o s i t i o n , as p o s i t i o n must be d e p i c t e d by w h i c h s p e c i f i c groups o f r e -c e p t o r s a r e b e i n g d i s c h a r g e d . Y e t i n measuring the a c t i v i t y o f t h e t h i r d o r d e r r e l a y o f j o i n t r e c e p t o r s i n the v e n t r o -b a s a l complex o f the t h a l a m u s , t h e y found the o p p o s i t e : h e r e , the f r e q u e n c y o f d i s c h a r g e d i d d e p i c t the degree o f movement and j o i n t p o s i t i o n . I n o t h e r words, a m e t a t h e t i c p r o c e s s a t the f i r s t o r d e r a f f e r e n t s had been t r a n s f o r m e d i n t o a p r o t h e t i c p r o c e s s i n t h e thalamus. In a d d i t i o n t o t h e s e f i n d i n g s , Wood (98) i n a beha-v i o r a l s t u d y has shown t h a t speed, one a s p e c t o f k i n e s t h e s i s , o p e r a t e d a s a p r o t h e t i c c o n t i n u a . She found t h a t the s u b j e c t i v e i m p r e s s i o n o f speed from a s e l f - i n i t i a t e d s h o u l d e r movement was r e l a t e d t o the a c t u a l speed o f movement by a power f u n c t i o n , and t h a t o t h e r c h a r a c t e r i s t i c s o f p r o t h e t i c s e n s o r y c o n t i n u a , such as h y s t e r e s i s , were met. I n i n t e r p r e t i n g Wood's r e s u l t s and the n e u r o p h y s i o l o -g i c a l e v i d e n c e o f M o u n t c a s t l e , Poggio and Werner (62) i t 7. might be s u g g e s t e d t h a t the s u b j e c t i v e i m p r e s s i o n of some a s p e c t s o f k i n e s t h e s i s a r e formed as e a r l y as t h e t h i r d o r d e r a f f e r e n t r e l a y o f the j o i n t r e c e p t o r s i n t h e thalamus/ and t h a t a p r o t h e t i c mechanism i s the f i n a l t r a n s l a t i o n i n t o s u b j e c t i v e i m p r e s s i o n . The knowledge of wh i c h r e c e p t o r s a r e r e s p o n s i b l e f o r k i n e s t h e s i s and the o p e r a t i n g c h a r a c t e r i s t i c s o f t h e s e r e c e p t o r s , i s i n v a l u a b l e i n s t u d y i n g the p s y c h o p h y s i c s o f a c t i v e k i n e s t h e s i s , as i t h e l p s t o e x p l a i n t h e o b s e r v e d r e l a t i o n s h i p between p h y s i c a l s t i m u l u s and s u b j e c t i v e sen-s a t i o n . The j o i n t r e c e p t o r s , w h i c h i n c l u d e t h e s p r a y o r r u f f i n i t y p e endings and the p a c i n i a n c o r p u s c l e s i n t h e c o n n e c t i v e t i s s u e s o f the j o i n t c a p s u l e , a l o n g w i t h the f r e e ( G o l g i -type). endings i n t h e l i g a m e n t s , a r e c o n s i d e r e d by many t o p l a y the major r o l e i n k i n e s t h e t i c d i s c r i m i n a t i o n (3, 9, 79, 7 5 ) . These r e c e p t o r s have been shown t o have d i r e c t c o n n e c t i o n s t o the s e n s o r y a r e a s o f the c o r t e x t h a t s u b s e r v e p e r c e p t i o n , and t h e r e f o r e a r e d i r e c t l y r e s p o n s i b l e f o r sub-j e c t i v e i m p r e s s i o n o f k i n e s t h e s i s (62, 7 9 ) . The o t h e r r e c e p t o r s t h a t a r e c o n s i d e r e d t o p l a y a r o l e i n k i n e s t h e s i s a r e the muscle s p i n d l e r e c e p t o r s found i n muscle f i b e r s . Such s t u d i e s as P a i l l a r d and Brouchon (69) and Browne, Lee and R i n g ( 1 0 ) , have s t a t e d t h a t the muscle 8. s p i n d l e s p r o v i d e i m p o r t a n t i n f o r m a t i o n t o the k i n e s t h e t i c sense. F u r t h e r s u p p o r t f o r t h i s i s g i v e n by O s c a r s s o n and Rosen (68) and A l b e - F i s s a r d and L i e b e s k i n d ( 1 1 ) , who d i s -c o v e r e d t h a t the s p i n d l e s have c o n n e c t i o n s t o the s e n s o r y c o r t e x i n c a t s and monkeys, which would mean t h a t i n f o r m -a t i o n from muscle s p i n d l e s c o u l d be used i n the s u b j e c t i v e e v a l u a t i o n o f j o i n t movement and p o s i t i o n . Y e t t h e r e has been put f o r t h e v i d e n c e t h a t opposes t h i s r o l e o f muscle s p i n d l e s i n k i n e s t h e s i s . S t u d i e s by H o l m q v i s t , Lundberg and O s c a r s s o n ( 3 5 ) , L a p o r t e and Lund-b e r g ( 4 1 ) , and O s c a r s s o n (66) have shown t h a t the muscle s p i n d l e a f f e r e n t s do not p r o j e c t t o t h e c o r t e x , b u t t o the c e r e b e l l u m , w h i c h means t h a t i n f o r m a t i o n ; f r o m t h e s e r e -c e p t o r s c o u l d n o t be used i n s u b j e c t i v e i m p r e s s i o n o f j o i n t a c t i o n . F u r t h e r t o t h i s , M erton ( 5 4 ) , Rose and M o u n t c a s t l e (75) and M o u n t c a s t l e and P o w e l l (63) have s t a t e d t h a t because of s p i n d l e dependence on muscle s t r e t c h i t c o u l d n o t p o s s i b l y p e r f o r m as a d e t e c t o r o f j o i n t p o s i t i o n . Other s o u r c e s o f i n f o r m a t i o n such as t h a t a r i s i n g from G o l g i tendon o r g a n s , cutaneous r e c e p t o r s , and p a t t e r n o f motor i n n e r v a t i o n , have a l s o been suggested t o c o n t r i b u t e t o the k i n e s t h e t i c sense. 9 . The Problem As S t e v e n s ' Power F u n c t i o n Law (82), which d i s t i n g u i s h e s two c l a s s e s o f s e n s o r y c o n t i n u a and p r e d i c t s a power f u n c t i o n r e l a t i o n s h i p between the p h y s i c a l s t i m u l u s and i t s s u b j e c t i v e i m p r e s s i o n , has been g e n e r a l l y a c c e p t e d as t h e p s y c h o p h y s i c a l law g o v e r n i n g s u b j e c t i v e i m p r e s s i o n on s e n s o r y m o d a l i t i e s , t h i s s t u d y endeavored t o i n v e s t i g a t e the p s y c h o p h y s i c s o f t h e a m p l i t u d e o f movement, a s p e c t o f a c t i v e k i n e s t h e s i s . I n e s s e n c e , the probelm i n v e s t i g a t e d the q u e s t i o n o f whether the a m p l i t u d e o f a s e l f - i n i t i a t e d arm movement, l a t e r a l f l e x i o n o f the human s h o u l d e r , was a p r o t h e t i c o r m e t a t h e t i c continuum and whether the s u b j e c t i v e i m p r e s s i o n of the movement was r e l a t e d t o t h e a c t u a l p h y s i c a l movement by a p o w e r - f u n c t i o n o f the form; R = K S N o r Fechner's Law: R = C l o g S. D e f i n i t i o n o f Terms Continuum - r e f e r s t o a c l o s e l y graded s e r i e s o f s t i m u l i , one s t e p merging i m p e r c e p t i b l y i n t o the n e x t ; the i n f o r m a t i o n forms a s t r a i g h t . l i n e s i g n i f y i n g changes i n a s i n g l e d i r e c t i o n (32). 10. M e t a t h e t i c C o n t i n u a P r o t h e t i c C o n t i n u a K i n e s t h e s i s -r e f e r s t o s t i m u l u s d i s c r i m i n a t i o n s t h a t a r e based on "what k i n d " , "where" and q u a l i t y ; d i s c r i m i n a t i o n i s m e d i a t e d by a s u b s t i t u t i v e p r o c e s s a t the p h y s i o l o g i c a l l e v e l ( 82). r e f e r s t o s t i m u l u s d i s c r i m i n a t i o n s t h a t a r e based on q u a n t i t y , "how much"; d i s c r i m i n a t i o n i s mediated by an a d d i t i v e p r o c e s s a t the p h y s i o -l o g i c a l l e v e l ( 82). d i s c r i m i n a t i o n o f the p o s i t i o n s and movements o f t h e body p a r t s based on i n f o r m a t i o n o t h e r than v i s u a l , a u d i -t o r y , t a c t u a l , o r - v e r b a l . . The d i s c r i m -i n a t i o n i s based on s t i m u l i t h a t a r i s e from the t e n s i o n , l e n g t h , and d i s t o r t i o n o f body p a r t s , i n r e l a t i o n t o each o t h e r and g r a v i t y . A c t i v e k i n e s t h e s i s i n t h i s s t u d y was d e f i n e d as the s e n s a t i o n s (o-t h e r than v i s u a l , a u d i t o r y , t a c t u a l , and v e r b a l ) t h a t a r i s e from s e l f - i n i t i a t e d l a t e r a l f l e x i o n o f the p r e f e r r e d s h o u l d e r . 11. Sensory M o d a l i t y - d e f i n e d as a s u b j e c t i v e l y d i s t i n c t i v e r e sponse w i t h i n the c e n t r a l nervous system t o t h e s t i m u l a t i o n o f a group o f s p e c i f i c r e c e p t o r s (80). Working H y p o t h e s i s Based on t h e s t u d i e s by Wood (98) and by M o u n t c a s t l e , P o g g i o and Werner (62) i t was h y p o t h e s i z e d t h a t the a m p l i t u d e o f movement a s p e c t o f k i n e s t h e s i s w i l l f u n c t i o n as a p r o t h e t i c s e n s o r y continuum. I t was a l s o h y p o t h e s i z e d t h a t t h e s u b j e c t -i v e i m p r e s s i o n o f a m p l i t u d e o f movement was r e l a t e d t o the phy-s i c a l degree o f movement by a power f u n c t i o n , as d e s c r i b e d by Stevens (82). I n e s s e n c e , t h e h y p o t h e s i s s t a t e d t h a t a m p l i t u d e o f movement s h o u l d show t h r e e c h a r a c t e r i s t i c s o f a p r o t h e t i c c o n t i n u a : . 1. the s u b j e c t i v e i m p r e s s i o n of a m p l i t u d e o f movement s h o u l d b e ' r e l a t e d t o the a c t u a l amount of movement by a power f u n c t i o n o f the form: R = K S N . T h i s power f u n c t i o n s h o u l d p l o t a s t r a i g h t l i n e when the l o g a r i t h m o f s u b j e c t i v e magnitude i s p l o t t e d a g a i n s t t h e l o g a r i t h m o f the p h y s i c a l s t i m u l u s , i . e . , degrees moved; 2. a h y s t e r e s i s e f f e c t ; 3. a n o n l i n e a r p l o t when the r e s u l t s o f a c a t e g o r y p r o d u c t i o n method a r e p l o t t e d a g a i n s t the power f u n c t i o n . These e x p e c t e d c h a r a c t e r i s t i c s a r e a l l due t o one r e a son: t h e s u b j e c t ' s i n a b i l i t y t o e q u a l i z e i n t e r v a l s o v e r continuum, o r i n o t h e r words, the n o n c o n s t a n t s e n s i t i v i t y a l o n g the continuum. L i m i t a t i o n s o f t h e Study 1. The sample s i z e o f t e n s u b j e c t s f o r each o f f i v e e x p e r i m e n t a l groups. 2. D i r e c t i o n s t o the s u b j e c t s were g i v e n v e r b a l l y by. the e x p e r i m e n t e r . 3. The d i s t i n c t i o n by S.S. Stevens (82) between c l a s s I and c l a s s I I s e n s o r y c o n t i n u a . D e l i m i n a t i o n s o f the Study 1. The ty p e o f movement used i n t h e e x p e r i m e n t a l t a s k 13. i . e . , a c t i v e l a t e r a l f l e x i o n o f t h e human s h o u l d e r j o i n t . 2. The i n v e s t i g a t i o n o f a m p l i t u d e o f movement wh i c h i s o n l y one a s p e c t o f k i n e s t h e s i s . : 3. The a n a l y s i s o f d a t a t h r o u g h S t e v e n s ' Power F u n c t i o n Law. CHAPTER I I REVIEW OF THE LITERATURE The l i t e r a t u r e has been r e v i e w e d under the f o l l o w i n g f o u r major h e a d i n g s : 1) P s y c h o p h y s i c s P e r t i n e n t t o t h e Study o f K i n e s t h e s i s ; 2) N e u r o p h y s i o l o g y o f K i n e s t h e s i s ; 3) B e h a v i o r a l S t u d i e s on the P s y c h o p h y s i c s o f K i n e s t h e s i s ; 4) K i n e s t h e t i c I n f o r m a t i o n . T h i s r e v i e w c o n t a i n s some l i t e r a t u r e t h a t i s o n l y p e r i -p h e r a l l y r e l a t e d t o t h e p r e s e n t problem s i n c e emphasis, f o r t h i s s e c t i o n o f t h e p r e s e n t s t u d y , w a s , p l a c e d on an i n - d e p t h s t u d y o f k i n e s t h e s i s . However, because o f the e x h a u s t i v e n a t u r e o f t h i s r e v i e w not a l l s t u d i e s w i l l be used i n the d i s c u s s i o n o f the r e s u l t s o f the p r e s e n t s t u d y . P s y c h o p h y s i c s P e r t i n e n t t o t h e Study o f K i n e s t h e s i s To i n v e s t i g a t e t h e n a t u r e o f any s e n s o r y system and i t s r e c e p t o r s , one must b e g i n w i t h p s y c h o p h y s i c s . Founded by F e c h n e r , p s y c h o p h y s i c s i s a s c i e n c e o f the f u n c t i o n a l r e l a t i o n s between body and mind. P s y c h o p h y s i c s s t u d i e s sens-a t i o n s , t h e i r r e l a t i o n s h i p w i t h i n a g i v e n s e n s o r y m o d a l i t y , 15. and the s t i m u l i t h a t cause them. The main o b j e c t i v e o f t h i s s c i e n c e i s t o i n v e s t i g a t e and o b s e r ve q u a n t i t a t i v e r e l a t i o n s h i p s between p h y s i c a l s t i m u l i and s u b j e c t i v e magnitude. To i l l u s t r a t e p s y c h o p h y s i c a l f u n c t i o n s , luminance and e l e c t r i c shock can be used. When the luminance o f a s p o t o f l i g h t i s d o u b l e d i n a dark f i e l d the a p p a r e n t sub-j e c t i v e b r i g h t n e s s i s l i t t l e a f f e c t e d . To a t y p i c a l o b s e r v e r the a p p a r e n t i n c r e a s e i n b r i g h t n e s s i s about t w e n t y - f i v e per c e n t . Y e t d o u b l i n g the c u r r e n t o f a s i x t y c y c l e c u r r e n t p a s s i n g t h r o u g h t h e f i n g e r s makes the s e n s a t i o n o f shock seem about t e n t i m e s as s t r o n g . I t i s a p p a r e n t t h a t the p s y c h o p h y s i c a l f u n c t i o n between t h e s e two examples i s c l e a r l y d i f f e r e n t ( 9 0 ) . Weber's Law. A l t h o u g h t h e r e have been many psycho-p h y s i c a l l a w s , t h e f i r s t one t h a t showed any r e l e v a n c e was Weber's. I t s t a t e d t h a t i n o r d e r f o r the second of two s t i m u l i t o be d i s c r i m i n a t e d from the f i r s t > t h e r e must be a j u s t n o t i c e a b l e d i f f e r e n c e ( j . n . d . ) . The i n c r e m e n t o r j . n . d . , between the two s t i m u l i must be a c o n s t a n t f r a c t i o n o f the o r i g i n a l s t i m u l u s (78). To a good a p p r o x i m a t i o n Weber's Law h o l d s i n s e n s o r y 16. c o n t i n u a , Stevens (86) has s t a t e d t h a t the Weber f r a c t i o n i s c o n s t a n t on about 99 per c e n t o f the u s e a b l e range o f s t i m u l u s i n t e n s i t y . G u i l f o r d (32) has s t a t e d t h a t Weber's Law cannot be r e g a r d e d as a u n i v e r s a l law o f d i f f e r e n t i a l s e n s i t i v i t y , f o r i t r e l a t e s two p h y s i c a l measurements, s t i m u l u s i n c r e m e n t w i t h t h e s t i m u l u s , and does n o t r e l a t e , as i t s h o u l d t o be a t r u e p s y c h o p h y s i c a l law, measurements on response t o t h o s e o f the s t i m u l u s . T h e r e f o r e i t s h o u l d not be e x p e c t e d t o a p p l y c o n s t a n t l y . A l l measurements a r e made on t h e s t i m u l u s s c a l e , c o r r e s p o n d i n g t o c e r t a i n landmarks on the r e s ponse continuum. The landmarks a r e s t a t i s t i c a l l y d e r i v e d a t p o i n t s o f e q u a l l i k e l i h o o d o f two d i f f e r e n t judgments. I n f a c t , the o n l y t h i n g p s y c h o p h y s i c a l about Weber's Law i s t h a t t h e s t i -mulus i n c r e m e n t s t a n d s f o r a presumably c o n s t a n t p s y c h o l o g i c a l i n c r e m e n t measured on the s t i m u l u s s c a l e . F e chner's Law. I t was Fechner who f i r s t s u g g e s t e d i n v e s t -i g a t i n g t h e r e l a t i o n s h i p between a s u b j e c t i v e i n t e n s i t y and the i n t e n s i t y o f the p h y s i c a l s t i m u l a t i o n e v o k i n g t h a t s u b j e c t i v e r e s p o n s e . On t h e b a s i s o f Weber's Law and the a ssumption t h a t j . n . d . s . a r e e q u a l , Fechner d e r i v e d h i s l o g a r i t h m i c law (20). I t s p r o c e d u r e was t o measure j.n.d.s a l o n g the continuum and t o use t h e s e measures as e q u a l u n i t s on a s c a l e o f s e n s a t i o n ( 8 5 ) . Because the i n c r e m e n t s i n l o g a r i t h m s a r e c o n s t a n t , Fechner thought t h a t t h e i r use i n a s c a l e o f i n t e n s i t y would be more c o n v e n i e n t , r a t h e r than t h e d i f f e r e n c e l i m e n , f o r a c c o r d i n g t o Weber's Law, t h e d i f f e r e n c e l i m e n i s a c o n s t a n t f r a c t i o n o f the s t a n d a r d s t i m u l u s and t h e r e f o r e must g e t b i g g e r as we go up the s c a l e . Fechner's Law (91) p r oposed t h a t e q u a l s t i m u l u s r a t i o s c o r r e s p o n d t o e q u a l s e n s a t i o n d i f f e r e n c e s , o r i n o t h e r words, the s t r e n g t h o f the s e n s a t i o n (R) v a r i e s d i r e c t l y as the l o g a r i t h m o f the s t i m u l u s ( S ) . The a l g e b r a i c form o f Fechner's Law i s . : R = K l o g S. I f Fechner's Law h o l d s , i t would produce a s t r a i g h t . l i n e f u n c -t i o n when e q u a l s e n s o r y u n i t s are p l o t t e d a g a i n s t l o g a r i t h m i c p h y s i c a l u n i t s . Stevens (90) has l a b e l l e d F echner's Law as b e i n g e r r o n e o u s . S t e v e n s ' argument a g a i n s t a c c e p t a n c e of Fechner's Law was t h a t i t was b u i l t on t h e m i s c o n c e p t i o n t h a t e r r o r i t s e l f p r o v i d e s a u n i t o f measurement o r the j . n . d . Under most c i r c u m s t a n c e s the j . n . d . , i s a s t a t i s t i c a l c o n c e p t , a measure o f the d i s -p e r s i o n o r v a r i a b i l i t y o f a d i s c r i m i n a t o r y r e s p o n s e ; i n s h o r t , a measure o f e r r o r . Fechner made d i s p e r s i o n among judgments, 18. n o r m a l l y a n u i s a n c e t o s c i e n c e , i n t o a j . n . d . , and used i t as h i s u n i t o f s c a l e (89). I n d e r i v i n g h i s law, Fechner made the er r o n e o u s assumption t h a t e r r o r ( j . n . d . ) i s c o n s t a n t up and down th e p s y c h o p h y s i c a l s c a l e . Does a s t i m u l u s f o r t y j.n.d.s above t h r e s h o l d seem t w i c e as g r e a t as a s t i m u l u s twenty j.n.d.s above t h r e s h o l d ? Stevens (85) has s t a t e d t h a t t h i s does not h o l d t r u e on t h e m a j o r i t y o f s e n s o r y con-t i n u a . S t e v e n s ' Power F u n c t i o n . An a l t e r n a t e form, the power f u n c t i o n , was s u g g e s t e d e a r l y as a s u b s t i t u t e t o Fechner's Law. Proposed by P l a t e a u (89); i t was b r i e f l y debated and then was f o r g o t t e n u n t i l Stevens d e v e l o p e d "the method o f magnitude e s t i m a t i o n " and d i s c o v e r e d t h a t i t , n o t Fechner's Law, was c o n s i s t e n t w i t h h i s d a t a . Stevens e x p l o r e d the use o f f r a c t i o n a t i o n and m u l t i p l i -c a t i o n i n an e f f o r t t o improve t h e p s y c h o p h y s i c a l s c a l i n g p r o c e d u r e s used by Fechner. The g e n e r a l p r o c e d u r e i n St e v e n s ' method was: a s t i m u l u s was p r e s e n t e d and the s u b j e c t was asked t o a d j u s t a v a r i a b l e s t i m u l u s t o a v a l u e t h a t was e i t h e r h a l f o r t w i c e as g r e a t . The i m p o r t a n t a s s u m p t i o n o f t h i s method i s the way i n wh i c h the terms " o n e - h a l f " and " t w i c e " [ i n the i n s t r u c t i o n s a r e assumed t o be used by t h e s u b j e c t i n a r r i v i n g a t h i s judgments. I n S t e v e n s ' "method o f magnitude e s t i m a t i o n " , t h e s u b j e c t i s i n s t r u c t e d t o a s s i g n a number t o each s t i m u l u s p r e s e n t a t i o n so t h a t the numbers a r e p r o p o r t i o n e d t o t h e s u b j e c t i v e magnitude produced by t h e s t i m u l i . Other methods used by Stevens t h a t g i v e e s s e n t i a l l y i d e n t i c a l r e s u l t s , and t h a t were v a r i a t i o n s o f t h e magnitude e s t i m a t i o n method, have been d e s c r i b e d by Stevens ( 8 3 ) , Luce and G a l a n t e r ( 4 8 ) , G u i l f o r d ( 3 2 ) , Stevens ( 8 5 ) , and Stevens and G a l a n t e r (94). Stevens (82) has shown t h a t t h e r e i s a p s y c h o p h y s i c a l law r e l a t i n g s u b j e c t i v e magnitude t o s t i m u l u s magnitude and the law s i m p l y s t a t e d , " e q u a l s t i m u l u s r a t i o s produce e q u a l s u b j e c t i v e r a t i o s " . A c c o r d i n g t o S t e v e n s , r a t i o s c a l e s o f s u b j e c t i v e magnitudes a r e r e l a t e d t o t h e s t i m u l u s by a power f u n c t i o n , and not Fechner's l o g a r i t h m i c f u n c t i o n . A l g e b r a i c -a l l y , S t e v e n s ' power...function i s e x p r e s s e d : R = K S N . The s u b j e c t i v e i m p r e s s i o n i s "R", and "S" i s t h e p h y s i c a l s t i m u l u s . The c o n s t a n t "K" i s d e t e r m i n e d by the c h o i c e o f u n i t s , and i t s v a l u e can be found where t h e power f u n c t i o n l i n e produced by r a t i o o r magnitude p r o d u c t i o n c r o s s e s the o r d i n a t e on a l o g . - l o g . p l o t . "K" can a l s o be found a l -g e b r a i c a l l y by: l o g K = l o g R - N l o g S. Stevens (90) has shown t h a t h i s power f u n c t i o n can be c o n v e r t e d i n t o a l i n e a r e q u a t i o n : 20. l o g R = l o g K + N • S, whi c h has a c e r t a i n p r a c t i c a l use, f o r the f u n c t i o n can be r e p r e s e n t e d by a s t r a i g h t l i n e on l o g . - l o g . c o o r d i n a t e s . The s l o p e o f t h i s s t r a i g h t l i n e i s e q u a l t o the v a l u e o f the exponent (N) o f t h e power f u n c t i o n . Stevens (60) has g i v e n a f o r m u l a f o r "N" wh i c h i s : Y - Y N _ l o g S _ s e n s a t i o n r a t i o _ _2 1. ~ l o g r ~ s t i m u l u s r a t i o x 2 - x^ * Stevens (91) has a l s o s t a t e d t h a t t h e exponent "N" v a r i e s w i t h each m o d a l i t y , w i t h each m o d a l i t y h a v i n g i t s own c h a r a c t e r -i s t i c exponent. I n l a t e r p u b l i c a t i o n s Stevens (90 and 91) r e v i s e d t h i s power f u n c t i o n t o : R = K (S - S ) N , o where S q i s an added c o n s t a n t v a l u e t o c o r r e s p o n d t o t h e t h r e s h o l d . T h i s a d d i t i v e c o n s t a n t was used t o b r i n g the z e r o of the p h y s i c a l s c a l e i n t o c o i n c i d e n c e w i t h the ze r o o f the p s y c h o l o g i c a l s c a l e . F o r ranges o f s t i m u l i w e l l above the minimum d e t e c t a b l e l e v e l , the v a l u e o f S q i s u s u a l l y ne-g l i g i b l e , b u t i t assumes l a r g e r p r o p o r t i o n s when s u b j e c t i v e s c a l e s a r e extended downward toward v e r y low v a l u e s . 21. Two C l a s s e s of Sensory Continua. Stevens (82) has r e p o r t e d t h a t p e r c e p t u a l c o n t i n u a d i v i d e themselves i n t o two g e n e r a l c l a s s e s . Two c o n t i n u a which i l l u s t r a t e t h i s f a c t are loudness and p i t c h . The j.n.d., f o r p i t c h remains constant whereas those of the loudness continuum are un-equal. T h i s f a c t suggests t h a t there may be two b a s i c me-chanisms of d i s c r i m i n a t i o n u n d e r l y i n g these two sensory c o n t i n u a . The uniform s e n s i t i v i t y on the p i t c h continuum and the non-uniformity on. the loudness continuum a l s o serve to e x p l a i n s e v e r a l other f u n c t i o n a l d i f f e r e n c e s between the two types of sensory c o n t i n u a . The p r o t h e t i c c o n t i n u a or c l a s s I (ex. loudness) are concerned w i t h "how much", whereas m e t a t h e t i c c o n t i n u a or c l a s s I I (ex. p i t c h ) are concerned w i t h "what k i n d " , or "where". There are two b a s i c p h y s i o l o g i c a l mechanisms t h a t correspond to the two c l a s s e s of c o n t i n u a . In c l a s s I con-t i n u a d i s c r i m i n a t i o n i s mediated by an a d d i t i v e or p r o t h e t i c process a t the p h y s i o l o g i c a l l e v e l . T h i s c l a s s r e q u i r e s a q u a n t i t a t i v e r e c e p t o r mechanism. Receptors mediating a prothe-t i c c o n t i n u a respond i n i n c r e a s i n g numbers or frequency as the stimulus i n t e n s i t y i s i n c r e a s e d . On loudness, an example of c l a s s I, we progress along the continuum by adding e x c i t -a t i o n to e x c i t a t i o n (82) . D i s c r i m i n a t i o n on c l a s s I I continua i s mediated by a s u b s t i t u t i v e o r m e t a t h e t i c process a t - t h e p h y s i o l o g i c a l l e v e l . T h i s c l a s s r e q u i r e s a q u a l i t a t i v e r e c e p t o r me-chanism. A stimulus change on t h i s c l a s s would cause a d i f f e r e n t p o p u l a t i o n of r e c e p t o r s t o be a c t i v a t e d w i t h no i n c r e a s e i n the number of r e c e p t o r s responding. An example i s p i t c h , where we proceed along the continuum by s u b s t i -t u t i n g e x c i t a t i o n f o r e x c i t a t i o n , i . e . , by changing the focus of e x c i t a t i o n . Stevens (82) has o u t l i n e d f o u r f u n c t i o n a l c r i t e r i a t h a t are r e l e v a n t to the d i s t i n c t i o n between the two c l a s s e s of sensory c o n t i n u a : 1. S u b j e c t i v e s i z e of the j u s t n o t i c e a b l e d i f f e r e n c e s . On c l a s s I c o n t i n u a the j.n.d.s. are not equal i n s u b j e c t i v e s i z e . In ot h e r words, a stimulus f o r t y j.n.d.s above t h r e s h o l d w i l l not be twice as gr e a t as a stimulus only twenty j.n.d.s. above t h r e s h o l d . On m e t a t h e t i c c o n t i n u a the stimulus f o r t y j.n.d.s above t h r e s h o l d would seem twice as g r e a t , f o r on c o n t i n u a of c l a s s I I the j.n.d.s t u r n out to be approximately equal i n s u b j e c t i v e s i z e . Thus a c r u c i a l d i f f e r e n c e between these two c l a s s e s of c o n t i n u a i s t h a t i n me t a t h e t i c c o n t i n u a the j.n.d.s are s u b j e c t i v e l y equal over the continuum, whereas i n the p r o t h e t i c c o n t i n u a , the j.n.d.s grow r a p i d l y l a r g e r i n s u b j e c t i v e s i z e as the upper end of t h e continuum i s re a c h e d . Stevens (82) has s t a t e d t h a t i n c l a s s I o r p r o t h e t i c c o n t i n u a h i s power f u n c t i o n i s t h e form o f the r e l a t i o n -s h i p between s u b j e c t i v e magnitude and p h y s i c a l s t i m u l u s i n t e n s i t y , b u t not on m e t a t h e t i c c o n t i n u a . On m e t a t h e t i c c o n t i n u a Fechner's l o g a r i t h m i c f u n c t i o n would be t h e form o f the r e l a t i o n s h i p , f o r F e c h n e r 1 s s c a l e i s based on e q u a l j .n.d.s a l o n g the continuum, and the j.n.d.s on m e t a t h e t i c c o n t i n u a a r e e q u a l . 2. C a t e g o r y r a t i n g s c a l e s . A c a t e g o r y r a t i n g s c a l e i s t he f u n c t i o n o b t a i n e d when a s u b j e c t judges a s e t o f s t i m u l i i n terms o f a s e t o f c a t e g o r i e s l a b e l l e d e i t h e r by numbers o r a d j e c t i v e s ' . The form t h a t t h e s e s c a l e s t a k e when p l o t t e d a g a i n s t a r a t i o s c a l e o f s u b j e c t i v e magnitude i s d i f f e r e n t ' o n t h e two c l a s s e s o f s e n s o r y c o n t i n u a . On c l a s s I the r e l a t i o n s h i p between the two s c a l e s i s n o n l i n e a r , whereas on c l a s s I I the form may be l i n e a r , when so p l o t t e d (82) . On most p r o t h e t i c c o n t i n u a i n v e s t i g a t e d t o d a t e , the form o f the n o n - l i n e a r r e l a t i o n s h i p has been concave down-ward (82, 90, 9 5 ) . Concave upward p l o t s have a l s o been found f o r p r o t h e t i c c o n t i n u a ( 95). The r e a s o n f o r the n o n l i n e a r c u r v e i n p r o t h e t i c c o n t i n u a has been d i s c u s s e d as b e i n g the r e s u l t o f un-e q u a l j . n . d . s . , o r n o n c o n s t a n t s e n s i t i v i t y o v e r the e n t i r e continuum ( 8 2 ) . A g i v e n d i f f e r e n c e may seem l a r g e and o b v i o u s i n the lower p a r t o f the continuum, bu t the same - a b s o l u t e d i f f e r e n c e i s much l e s s i m p r e s s i v e i n the upper p a r t o f t h e continuum. T h i s asymmetry i n - t h e o b s e r v e r ' s s e n s i t i v i t y t o d i f f e r e n c e s r e s u l t s i n a non-u n i f o r m i t y i n t h e w i d t h o f t h e c a t e g o r i e s . Near the lower end o f the continuum the c a t e g o r i e s t e n d t o be narrow and thus the s l o p e o f the f u n c t i o n i s s t e e p . Near the upper end the c a t e g o r i e s broaden and the s l o p e o f the f u n c t i o n d e c l i n e s , f o r m i n g a concave downward p l o t . I f t h e n o n c o n s t a n t s e n s i t i v i t y was r e v e r s e d the p l o t formed would be concave upward (82) . On c l a s s I I o r m e t a t h e t i c c o n t i n u a , the j . n . d . s . , a r e e q u a l and the s e n s i t i v i t y o r d i s c r i m i n a t i o n tends t o be c o n s t a n t o v e r t h e e n t i r e continuum. T h i s r e s u l t s i n a l i n e a r p l o t between c a t e g o r y and r a t i o s c a l e s . 3. Time-order e r r o r . T h i s r e f e r s t o t h e f a c t t h a t the second o f two e q u a l s t i m u l i tends t o be judged g r e a t e r than t h e f i r s t . Stevens (82) s t a t e d t h a t t i m e - o r d e r e r r o r i s c h a r a c t e r i s t i c o f judgments on c l a s s I c o n t i n u a but not o f judgments on c l a s s I I . The cause of the t i m e - o r d e r e r r o r i s , as i t was f o r n o n l i n e a r i t y o f c a t e g o r y p l o t s , the asym-metry o f s e n s i t i v i t y o v e r the s e n s o r y continuum. 4. H y s t e r e s i s , o r " l a g g i n g b e h i n d " e f f e c t , d e s c r i b e s what happens when s u c c e s s i v e s t i m u l i a r e judged i n d i f f e r e n t o r d e r s . T h i s e f f e c t has been found most c l e a r l y i n psycho-p h y s i c a l b i s e c t i o n o r e q u i p a r t i t i o n e x p e r i m e n t s . I f a c e r t a i n range o f a continuum i s p o r t i o n e d i n e q u a l i n t e r v a l s by a s u b j e c t , the p o s i t i o n o f t h e d i v i s i o n s o b t a i n e d w i l l depend on whether t h e s t i m u l i a r e p r e s e n t e d . i n an a s c e n d i n g o r d e s c e n d i n g o r d e r (82). I n an ex p e r i m e n t on lo u d n e s s by Stevens ( 8 2 ) , the average s u b j e c t i v e response o f the b i s e c t i n g l e v e l was s e t some f i v e t o e i g h t dbs. h i g h e r i n the a s c e n d i n g o r d e r than i n t h e d e s c e n d i n g o r d e r . I t appeared t h a t t h e lou d n e s s the s u b j e c t h e a r d l a g g e d b e h i n d what he s h o u l d have h e a r d as he went up o r down t h e s c a l e . H y s t e r e s i s has been shown f o r s u b j e c t i v e l o u d n e s s , b r i g h t n e s s and l i f t e d w e i g h t s , (82) , w h i c h a re a l l p r o t h e t i c c o n t i n u a , b u t has n o t been found i n t y p i c a l m e t a t h e t i c con-t i n u a . Stevens (82) has s t a t e d t h a t the e v i d e n c e f o r h y s t e r -e s i s i n c l a s s I c o n t i n u a and not i n c l a s s I I i s s u g g e s t i v e , b u t n ot y e t c o n c l u s i v e . E i s l e r and O t t a n d e r ' s (19) r e s e a r c h found t h a t t h e h y s t e r e s i s e f f e c t i n p r o t h e t i c c o n t i n u a i s m o s t l y , i f not s o l e l y due t o d i f f e r e n t " s u b j e c t i v e z e r o s " o r "S " i n t h e p s y c h o p h y s i c a l power f u n c t i o n s : R = K (S - S ) N o f o r a s c e n d i n g and d e s c e n d i n g s e r i e s . A c c o r d i n g t o E i s l e r and O t t a n d e r ( 1 9 ) , p r e c i s e knowledge o f the z e r o p o i n t (S Q) would p r e v e n t h y s t e r e s i s , and t h a t seemed t o be the case i n c e r t a i n m e t a t h e t i c c o n t i n u a such as p o s i t i o n . Stevens (82) has s t a t e d i n a t t e m p t i n g t o e x p l a i n t h e h y s t e r e s i s ' e f f e c t : ... i n c a l l i n g t h i s phenomenon h y s t e r e s i s I am t r y i n g t o des-c r i b e i t , n o t e x p l a i n i t . I am n o t s u r e I know how t o e x p l a i n i t . As d i s c u s s e d e a r l i e r , Stevens (82) has s t a t e d t h a t the power f u n c t i o n a p p l i e d t o p r o t h e t i c c o n t i n u a , b u t n o t t o m e t a t h e t i c c o n t i n u a . The number o f p r o t h e t i c c o n t i n u a on w h i c h the power f u n c t i o n has been shown t o h o l d now exceeds two dozen (Stevens 89) . Stevens (89) has s t a t e d t h a t as y e t no e x c e p t i o n t o the Power F u n c t i o n Law has been e n c o u n t e r e d . Ekman (20) has s u p p o r t e d t h i s i d e a o f no e x c e p t i o n t o the Power F u n c t i o n Law a l o n g w i t h Stevens and G a l a n t e r (94); M o u n t c a s t l e , P o g g i o and Werner (62); Luce and G a l a n t e r (48); and M i l l a r , Pederson and Sheldon (56). S t e v e n s 1 Power F u n c t i o n Law s t a t e s t h a t on m e t a t h e t i c c o n t i n u a the j.n.d.s a r e e q u a l , and t h e r e f o r e Fechner's f u n c t i o n would form the r e l a t i o n s h i p between s u b j e c t i v e magnitude and s t i m u l u s i n t e n s i t y , n ot t h e power f u n c t i o n . T h i s p a r t o f the Power F u n c t i o n Law was s u p p o r t e d by Stevens (90) and Stevens and G a l a n t e r (94) who have shown the c o n t i n u a : p i t c h , a p p a r e n t v i s u a l p o s i t i o n (azemuth), p r o p o r t i o n , and apparent i n c l i n a t i o n t o b e l o n g t o t h e • m e t a t h e t i c c o n t i n u a c l a s s . I n d i v i d u a l Power F u n c t i o n s . A l l o f the exponents of p r o t h e t i c c o n t i n u a r e s u l t e d from a p r o c e d u r e where the average o f the judgments from a group o f o b s e r v e r s was c a l c u l a t e d and used i n d e v e l o p i n g the exponent. T h i s p r o c e d u r e was j u s t -i f i e d because o f the i n t e r e s t i n t h e average exponent i n f o r m i n g a g e n e r a l law. Marks and Stevens (52) have shown t h a t the p s y c h o p h y s i c a l power f u n c t i o n a l s o h o l d s f o r the i n d i v i d u a l p e r c e i v e r . They showed t h a t 150 p s y c h o p h y s i c a l f u n c t i o n s o f s e p a r a t e o b s e r v e r s h e l d t o the power f u n c t i o n , and they c o n c l u d e d t h a t t h e power f u n c t i o n t h e r e f o r e cannot be an a r t i f a c t o f a v e r a g i n g . Stevens (90) has shown t h a t on t h i r t y -n i n e i n d i v i d u a l f u n c t i o n s t h a t r e l a t e d the magnitude o f sub-j e c t i v e e f f o r t t o the f o r c e e x e r t e d on a p r e c i s i o n hand dyna-mometer, good a p p r o x i m a t i o n s t o power f u n c t i o n s were a c h i e v e d . I n a d d i t i o n , t w e n t y - t h r e e s e p a r a t e l o u d n e s s f u n c t i o n s a l l 28. obeyed the Power F u n c t i o n Law i n a s t u d y on vowel l o u d n e s s by C r o s s and Lane ( 1 7 ) . C r o s s - M o d a l i t y S t u d i e s . Ekman and S j o b e r g (21) , as w e l l as Luce and G a l a n t e r (48) have p o i n t e d o u t t h a t d e s p i t e the massive e v i d e n c e i n f a v o r o f the Power F u n c t i o n Law, q u e s t i o n s a r i s e , because i n i t i a l developments o f t h e power f u n c t i o n r e s t e d m a i n l y on methods t h a t i n v o l v e d n u m e r i c a l e s t i m a t i o n s by the s u b j e c t s . Any q u e s t i o n s about the power f u n c t i o n due t o t h e n u m e r i c a l e s t i m a t i o n have been s i l e n c e d by t h e r e s u l t s o f a method i n wh i c h the o b s e r v e r equates t h e apparent s t r e n g t h s o f t h e s e n s a t i o n s produced i n two d i f f e r e n t s e n s o r y m o d a l i t i e s , By means o f such c r o s s - m o d a l i t y matches made a t v a r i o u s l e v e l s o f s t i m u l u s i n t e n s i t y , an " e q u a l - s e n s a t i o n f u n c t i o n " can be mapped o u t , and i t s form can be compared w i t h t h e form p r e -d i c t e d by the magnitude s c a l e s f o r the two m o d a l i t i e s i n v o l v e d , Stevens (90) has shown t h a t i f , g i v e n an a p p r o p r i a t e c h o i c e o f u n i t s , two m o d a l i t i e s a r e governed by t h e e q u a t i o n s : R 1 = K S N ' R 2 = K S N and i f the s u b j e c t i v e v a l u e s R^ and R^ are equated by a s k i n g t h e o b s e r v e r t o make the one s e n s a t i o n seem as s t r o n g as the o t h e r a t v a r i o u s l e v e l s , t h e n the r e s u l t i n g e q u a l sens-a t i o n f u n c t i o n w i l l be g i v e n by: N N KS 1 = KS 2 In terms o f l o g a r i t h m s : l o g KS = N 2/N 1 l o g KS I n l o g - l o g c o o r d i n a t e s , t h e r e f o r e , t h e e q u a l s e n s a t i o n f u n c -t i o n s h o u l d be a s t r a i g h t l i n e w i t h a s l o p e e q u a l t o the r a t i o o f t h e two exponents. T h i s p r e d i c t i o n was n i c e l y borne out by a s e r i e s o f c r o s s - m o d a l i t y matches between t h e s u b j e c t i v e s c a l e s o f l o u d n e s s , o f e l e c t r i c shock, and o f v i b r a t i o n (84). C r o s s -m o d a l i t y matches have been made between l o u d n e s s and t e n o t h e r c o n t i n u a (93). The m a t c h i n g f u n c t i o n s were a l l power f u n c t i o n s . When t h e exponent v a l u e s o f the matching f u n c -t i o n s were d i v i d e d by t h e exponent v a l u e s p r e v i o u s l y determ-i n e d f o r the v a r i o u s c o n t i n u a , the q u o t i e n t s p r e d i c t e d v a -l u e s f o r the lo u d n e s s exponent. The mat c h i n g f u n c t i o n s b e t -ween f o r c e o f handgrip, and n i n e o t h e r c o n t i n u a were a l l shown t o approximate power f u n c t i o n s - s t r a i g h t l i n e s on l o g . l o g . c o o r d i n a t e s ( 90). 30. The a b i l i t y t o s p e c i f y the power f u n c t i o n s r e l a t i v e • t o o t h e r s e n s o r y c o n t i n u a , i n s t e a d of numbers, seems t o c o n t r a d i c t the o b j e c t i o n s r a i s e d by Ekman and S j o b e r g (21) and by Luce and G a l a n t e r (48) t h a t t h e power f u n c t i o n was based e n t i r e l y on n u m e r i c a l e s t i m a t i o n s . . W i t h o u t r e s o r t t o numer-i c a l e s t i m a t i o n methods' i t has been shown t h a t the o v e r - a l l t r a n s f e r f u n c t i o n o f s e v e r a l s e n s o r y m o d a l i t y were r e l a t e d t o one a n o t h e r as a f a m i l y o f power f u n c t i o n s (93). Stevens (92) has recommended t h a t i f one continuum was' t o be used as a v a l i d a t i o n i t s h o u l d be judgment o f apparent l e n g t h o f l i n e s w i t h an "N" o f 1.0. N e u r o p h y s i o l o g y o f K i n e s t h e s i s The main g o a l o f p s y c h o p h y s i c a l r e s e a r c h i s t o d i s c o v e r t h e q u a n t i t a t i v e r e l a t i o n s h i p between s t i m u l u s i n p u t and s u b j e c t i v e o u t p u t , and a l s o t o d i s c o v e r - the o p e r a t i n g c h a r -a c t e r i s t i c s o f t h e r e c e p t o r s and the e n t i r e s e n s o r y system o f t h a t p a r t i c u l a r s e n s o r y m o d a l i t y . Stevens (8.4) has s t a t e d t h a t t h e power f u n c t i o n r e l a -t i o n s h i p o f a g i v e n s e n s o r y continuum can r e l a t e some i n -f o r m a t i o n as t o the o p e r a t i n g c h a r a c t e r i s t i c s o f the r e c e p t o r s and the e n t i r e n e u r a l c h a i n between s t i m u l u s and s u b j e c t i v e response.. A c o n v e r s e r e l a t i o n s h i p c o u l d e x i s t as w e l l — t h e known o p e r a t i n g c h a r a c t e r i s t i c s o f the r e c e p t o r s and se n s o r y system o f a g i v e n s e n s o r y m o d a l i t y c o u l d s u p p l y i m p o r t a n t i n f o r m a t i o n about t h e p s y c h o p h y s i c a l r e l a t i o n -s h i p between s t i m u l u s i n p u t and s u b j e c t i v e o u t p u t . One such s e n s o r y m o d a l i t y i n wh i c h the n e u r o p h y s i o l o g y o f the r e c e p t o r s and o f the n e u r a l c h a i n c o u l d s u p p l y i n -f o r m a t i o n on the p s y c h o p h y s i c a l r e l a t i o n s h i p , i s k i n e s -t h e s i s . K i n e s t h e s i s i s the s e n s o r y m o d a l i t y t h a t i s concerned w i t h the d i s c r i m i n a t i o n o f p o s i t i o n and movement o f body p a r t s , b o t h a c t i v e l y and p a s s i v e l y produced, and i s based on i n f o r m a t i o n o t h e r than v i s u a l , a u d i t o r y o r t a c t i l e (36). The r e c e p t o r s g i v i n g r i s e t o k i n e s t h e t i c i n f o r m a t i o n a r e unique as t o t h e i r a n a t o m i c a l l o c a t i o n and t h e i r r e s p o n s i -veness t o a p a r t i c u l a r form o f energy. They a r e mechano-r e c e p t o r s , e x c i t e d by t h e d e f o r m a t i o n o f t h e i r e ndings p r o -duced by t h e s t r e t c h i n g o r c o m p r e s s i o n o f the s t r u c t u r e s i n whi c h they a r e embedded. K i n e s t h e t i c d i s c r i m i n a t i o n i s based on unique s t i m u l i t h a t a r i s e from changes i n l e n g t h , t e n s i o n , movement and the d i s t o r t i o n o f body p a r t s i n r e -l a t i o n t o each o t h e r and g r a v i t y . The r e c e p t o r s a re i n v o l v e d i n awareness o f : 1) o n s e t and d u r a t i o n o f movement, 2) d i r e c t i o n o f movement, 3) v e l o c i t y and a c c e l e r a t i o n o f movement, 4) range o f movement, 5) s t a t i c p o s i t i o n i n g o f j o i n t segments p r i o r t o and a f t e r movement'(36). Which p e r i p h e r a l r e c e p t o r s a r e r e s p o n s i b l e f o r k i n -e s t h e s i s and t h e i r f u n c t i o n a l c h a r a c t e r i s t i c s c o u l d t e l l us a g r e a t d e a l about the mechanisms w h i c h u n d e r l i e the s u b j e c t i v e f o r m a t i o n o f k i n e s t h e s i s . The r e c e p t o r s t h a t have been thought t o be i n v o l v e d i n k i n e s t h e t i c p e r c e p t i o n a r e : t h e muscle s p i n d l e s found i n o r d i n a r y muscle f i b r e ; the g o l g i tendon organs w h i c h a r e found i n muscle tendons; and the s p r a y on R u f f i n i t y p e endin g s and t h e p a c i m i a n c o r p u s c l e s found i n t h e c o n n e c t i v e t i s s u e o f a r t i c u l a r j o i n t c a p s u l e s . The cutaneous r e c e p t o r s i n t h e s k i n and the p a t t e r n o f motor i n n e r v a t i o n have a l s o been s u g g e s t e d a s ' c o n t r i b u t i n g t o k i n e s t h e s i s . These j o i n t r e c e p t o r s and muscle s p i n d l e s have been l o c a t e d and i d e n t i -f i e d by Gardner ( 2 7 ) , Boyd ( 8 1 ) , Skoglund ( 7 9 ) , Andrew (2) and by Howard and Templeton (36). M u s c l e S p i n d l e s . M u s c l e s p i n d l e s c o n t a i n c o n t r a c t i l e elements and two t y p e s o f s e n s o r y elements which respond t o changes i n t h e l e n g t h and t e n s i o n i n the s p i n d l e . The two t y p e s o f s e n s o r y e n d i n g s a r e commonly known as p r i m a r y and secondary e n d i n g s . When a muscle i s s t r e t c h e d , the p r i m a r y e n d i n g s s i g n a l b o t h the i n s t a n t a n e o u s l e n g t h o f the muscle and r a t e o f s t r e t c h i n g , w h i l e secondary e n d i n g s s i g n a l m a i n l y i n s t a n t -aneous l e n g t h . When a muscle c o n t r a c t s , the t e n s i o n on t h e s p i n d l e i s r e l e a s e d , and i t s s e n s o r y end organs cease f i r i n g u n t i l t h e s l a c k i n t h e s p i n d l e i s t a k e n up by t h e c o n t r a c t i o n o f i n t r a f u s a l muscle f i b r e s i n s i d e t h e s p i n d l e . The d i s c h a r g e r a t e o f the s p i n d l e s i s a v e r y s e n s i t i v e i n d i c a t o r o f changes of muscle t e n s i o n . The d i s c h a r g e o f p r i m a r y s p i n d l e e n d i n g s i s a p p r o x i m a t e l y p r o p o r t i o n a l t o the l o g a r i t h m o f the l o a d o r amount o f s t r e t c h a p p l i e d t o the p a s s i v e m u scle, b u t adapt-a t i o n i s r a p i d , t h e r e f o r e t h e maximum d i s c h a r g e r e a c h e d w i l l depend as much on the r a t e a t which t h e muscle i s s t r e t c h e d as on t h e a b s o l u t e t e n s i o n (53). I n two e x p e r i m e n t s i n w h i c h the amount o f e r r o r was measured when one hand, p a s s i v e l y o r a c t i v e l y d i s p l a c e d , was l o c a t e d by t h e o t h e r hand, P a i l l a r d and Brouchon (69) showed t h a t a c t i v e movement was s i g n i f i c a n t l y b e t t e r i n p r e c i s i o n t h a n p a s s i v e movement, and t h e r e was no s i g n i f i c a n t d i f f e r e n c e between a c t i v e and p a s s i v e maintenance o f t h e f i n a l p o s i t i o n . They a l s o found t h a t the d i s p e r s i o n o f e r r o r s i n c r e a s e d as a f u n c t i o n o f t e m p o r a l i n t e r v a l . They c o n c l u d e d t h a t t h e r e must have been more k i n e s t h e t i c i n f o r m a t i o n a v a i l -a b l e from a c t i v e movement, and t h a t t h e r e must have been an i n f o r m a t i o n d e f i c i t d u r i n g p a s s i v e movement. S i n c e t h e y f e l t t h a t the amount o f i n f o r m a t i o n from the j o i n t r e c e p -t o r s was the same under a c t i v e and p a s s i v e movement, they e x c l u d e d the j o i n t r e c e p t o r s as b e i n g r e s p o n s i b l e f o r t h e i r r e s u l t s . What t h e y d i d c o n c l u d e was t h a t t h e i n f o r m -a t i o n a r i s i n g from t h e muscle s p i n d l e a f f e r e n t s p r o v i d e d i m p o r t a n t i n f o r m a t i o n t h a t a c c o u n t e d f o r the s u p e r i o r a c c u r a o f a c t i v e movement. An o t h e r e x p e r i m e n t has r e a c h e d s i m i l a r r e s u l t s and c o n c l u s i o n s . Browne, Lee and R i n g (10) i n j e c t e d p r o c a i n e i n t o c e r t a i n j o i n t s , t h e r e b y a n a e s t h e t i z i n g t h e j o i n t r e -c e p t o r s . A l t h o u g h b l i n d f o l d e d , s u b j e c t s were not a b l e t o p e r c e i v e p a s s i v e movement, y e t t h e y were a b l e t o move l i m b s v o l u n t a r i l y t o s p e c i f i e d p o s i t i o n s . These a u t h o r s (10) sug-g e s t e d t h a t p a s s i v e movement was' me d i a t e d by j o i n t r e c e p t o r s w h i l e a c t i v e movement was mediated by r e c e p t o r s w i t h i n the muscles - and tendons. Y e t Merton ( 5 4 ) , and Rose and M o u n t c a s t l e (75) have s t a t e d t h a t the r e c e p t o r s w i t h i n t h e muscles and tendons are 35. n o t c a p a b l e o f p r o v i d i n g k i n e s t h e t i c i n f o r m a t i o n . A c c o r d i n g t o t h e s e a u t h o r s , muscle s p i n d l e s respond t o changes i n muscle l e n g t h , i . e . , measure r e l a t i v e l e n g t h , b u t w i t h t h e i r c o n t r a c t i l e ends t h e y would o b v i o u s l y be u n s a t i s f a c t o r y i n s -truments f o r making a b s o l u t e l e n g t h measurements. Mount-c a s t l e and P o w e l l (63) have s t a t e d t h a t s i n c e muscle s p i n d l e s do not v a r y f r e q u e n c y o f d i s c h a r g e i n a l i n e a r , o r any o t h e r s o r t o f c o n s t a n t r e l a t i o n t o muscle l e n g t h , t h e y c o u l d not p e r f o r m as d e t e c t o r s o f j o i n t p o s i t i o n . Both G o l d s c h e i d e r (29) and A n g i e r (4) i n t h e i r e x p e r i m e n t s on j o i n t s e n s i t i v i t y con-c l u d e d t h a t the muscle s p i n d l e s p l a y an u n i m p o r t a n t r o l e i n p o s i t i o n sense. P a i l l a r d and Brouchon (69) have s t a t e d t h a t what Merton (54) and Rose and M o u n t c a s t l e (75) have a l l e g e d about s p i n d l e s not b e i n g a b l e t o s u p p l y k i n e s t h e t i c i n f o r m a t i o n would be t r u e f o r f i x e d p o s i t i o n s o f t h e l i m b . They (69) went on ... b u t i f , as we a r e a b l e t o show, v e l o c i t y d e t e c t i o n w i t h i t s c h a r a c t e r -i s t i c decay i n t i m e may appear t o p r o -v i d e p o t e n t c a l i b r a t i n g i n f o r m a t i o n about th e f i n a l p o s i t i o n o f the l i m b a t t h e end o f a movement, then the s p i n d l e becomes a n o t - t o - b e i g n o r e d c a n d i d a t e f o r such a f u n c t i o n . One argument advanced i n s u p p o r t o f t h e u n i m p o r t a n t r o l e p l a y e d by muscle s p i n d l e s i n k i n e s t h e s i s i s t h a t s p i n d l e a f f e r e n t s do not have a d i r e c t c o n n e c t i o n t o t h e s e n s o r y a r e a s o f the c o r t e x , b u t p r o j e c t i n s t e a d t o the c e r e b e l l u m . (31, 35, 41, 42, 43, 46, 50, 66, 75). Much of t h i s e v i d e n c e was a r e -s u l t o f work on c a t s . Y e t O s c a r s s o n and Rosen (68) have s t a t e d t h a t the mus-c l e s p i n d l e a f f e r e n t s from the f o r e l i m b o f the c a t do, i n f a c t , p r o j e c t t o t h e somatosensory a r e a s o f the c o r t e x une-q u i v o c a l l y . T h i s has a l s o been c o n f i r m e d i n monkeys by A l b e -F i s s a r d and L i e b e s k i n d ( 1 ) . Matthews (53) has shown t h a t the muscle s p i n d l e s and tendon organs b o t h respond d i r e c t l y t o the amount of e x t e r n a l s t r e t c h a p p l i e d t o the muscle and tendon. F u l t o n and P i - S u n e r (25) i n d i c a t e d t h a t s i n c e one o f the f a c t o r s which i n f l u e n c e the e x t e r n a l s t r e t c h of a muscle and tendon i s movement and p o s i t i o n o f the bones t o w h i c h t h e y a r e a t t a c h e d , i t f o l l o w s t h a t t h e muscle s p i n d l e s can f u n c t i o n , a t l e a s t t o some degree, as m o v e m e n t - p o s i t i o n r e c e p t o r s . S koglund (79) a l s o s u p p o r t e d a minor r o l e i n k i n e s t h e s i s f o r the muscle s p i n d l e a f f e r e n t i n f o r m a t i o n w i t h t h i s argument. I n an e x p e r i m e n t by Cohen (15) i n which he measured the c o n t r i b u t i o n s o f t a c t i l e , m u s c u l o - t e n d i n o u s and j o i n t mechanisms t o p o s i t i o n sense i n the human s h o u l d e r , the r e s u l t s showed t h a t the muscle s p i n d l e s and tendon r e c e p t o r s b o t h made a s m a l l b u t s i g n i f i c a n t c o n t r i b u t i o n t o k i n e s t h e s i s . G o l g i Tendon Organs. Howard and Templeton (36) have d e s c r i b e d the tendon organs as h a v i n g a h i g h e r t r e s h o l d t o e x t e r n a l s t r e t c h t h a n t h e muscle s p i n d l e s ; t h e r e f o r e a t low t e n s i o n s t h e r e w i l l be a p r o p o r t i o n a t e l y g r e a t e r d i s c h a r g e from the s p i n d l e s ; as the t e n s i o n i n c r e a s e s , more and more tendon organs w i l l d i s c h a r g e . Tendon organs respond t o t e n s i o n e i t h e r a c t i v e l y o r p a s s i v e l y produced. M o u n t c a s t l e and P o w e l l (63) mentioned t h a t t h e t e n s i o n t o which t h e s e r e -c e p t o r s f i r e depends on muscle l e n g t h , i . e . , upon j o i n t a n g l e and upon the f o r c e e x e r t e d . They c o n c l u d e d t h a t a number o f g o l g i organs and t h e i r r a t e s o f d i s c h a r g e a r e not v a r i a b l e s dependent s o l e l y upon t h e a n g l e o f the j o i n t a c r o s s w h i c h th e muscle works; they c a n n o t , t h e r e f o r e , i n f o r m j o i n t p o s i t i o n . F u r t h e r t o t h i s , P a i l l a r d and Brouchon (69) have s t a t e d t h a t t h e g o l g i tendon o r g a n s , w i t h t h e i r h i g h t h r e s -h o l d t o s t r e t c h , a r e not s u i t e d t o g i v e k i n e s t h e t i c i n f o r m a t i o n i n r e s t i n g and p a s s i v e movement c o n d i t i o n s because o f the low t e n s i o n s . But on a c t i v e movement they s h o u l d g i v e i m p o r t a n t k i n e s t h e t i c i n f o r m a t i o n due t o h i g h e r t e n s i o n . Y e t Weber and D a l l e n b a c h ' (95) have shown t h a t l o a d i n g o f a moving l i m b , w h i c h s h o u l d i n c r e a s e t e n s i o n and t h e r e f o r e i n f o r m a t i o n from 38. the g o l g i tendon o r g a n s , has no c o n s i s t e n t e f f e c t on a c c u r -acy o f p o s i t i o n sense. Browne, Lee and R i n g ( 1 0 ) , i n t h e i r e x periment on the s e n s i t i v i t y o f a n a e s t h e t i z e d j o i n t s , c o n c l u d e d t h a t the muscle s p i n d l e s and the tendon.organs p l a y e d an i m p o r t a n t r o l e i n k i n e s t h e s i s . I t has been demo n s t r a t e d , however, t h a t t h e r e c e p t o r s w i t h i n the muscles and tendons a r e not c a p a b l e o f p r o v i d i n g k i n e s t h e t i c i n f o r m a t i o n (54,75). To d e t e c t p o s i t i o n and movement, t h e y would have t o i n d i c a t e the a b s o l u t e l e n g t h and t e n s i o n o f the muscle and tendon i n w h i c h they are embedded, n e i t h e r the g o l g i tendon organ nor the s p i n d l e can. The most c o n c l u s i v e e v i d e n c e r e f u t i n g a r o l e f o r g o l g i tendon organs i n k i n e s t h e s i s i s t h a t w h i c h i n d i c a t e s t hey do not have a d i r e c t c o n n e c t i o n t o the c l a s s i c i a l s e n s o r y are a s o f t h e c o r t e x , b u t a r e c o n n e c t e d t o the c e r e b e l l u m , and a r e t h e r e f o r e used i n motor i n t e g r a t i o n . T h i s i s sup-p o r t e d by Merton ( 5 4 ) , Rose and M o u n t c a s t l e ( 7 5 ) , O s c a r s s o n (66) and O s c a r s s o n ( 6 7 ) . Y e t Cohen (15) c o n c l u d e d t h a t t h e m u s c u l o - t e n d i n o u s r e -c e p t o r s made a s m a l l b u t s i g n i f i c a n t c o n t r i b u t i o n t o p o s i t i o n sense i n t h e human s h o u l d e r . Cutaneous R e c e p t o r s . These r e c e p t o r s have been shown t o f i r e i n response t o d e f o r m a t i o n o f t h e skin-, so t h a t t h e y c o u l d s e r v e t o i n d i c a t e c h a n g i n g s k i n t e n s i o n r e s u l t i n g from changes i n the p o s i t i o n o f the l i m b . Y et S h e r r i n g t o n ( 7 7 ) , and Lee and R i n g (44) r e p o r t e d t h a t i n t e r f e r e n c e w i t h the s k i n s e n s a t i o n around a j o i n t does n ot a f f e c t p o s i t i o n sense. T h i s s t a t e m e n t i s a l s o s u p p o r t e d by G o l d s c h e i d e r (29) who a n a e s t h e t i z e d the s k i n o f the f i n g e r and found no l o s s i n t h e s e n s i t i v i t y o f k i n e s t h e s i s . Cohen (15) c o n c l u d e d t h a t t h e cutaneous r e c e p t o r s , a l o n g w i t h t h e m u s c l o - t e n d i n o u s r e -c e p t o r s , made a s m a l l b u t s i g n i f i c a n t c o n t r i b u t i o n t o k i n e s -t h e s i s . Cohen s t a t e d t h a t s i n c e t h e l i m b i s r a r e l y s t a t i c , t h e t a c t i l e r e c e p t o r s must u s u a l l y c o n t r i b u t e u s e f u l i n f o r m -a t i o n i n r e g a r d t o k i n e s t h e s i s , b u t t h e i r b a s i c s t i m u l u s must be movement r a t h e r than p o s i t i o n . Motor I n n e r v a t i o n . I n t h e i r d i s c u s s i o n on k i n e s t h e s i s , H o w a r d and Templeton (36) s t a t e d t h a t t h e p a t t e r n o f motor i n n e r v a t i o n must be a n . a v a i l a b l e s o u r c e o f k i n e s t h e t i c i n f o r m a t i o n . Y e t K e e l e (37) d e p a r t e d from t h i s by not i n c l u d i n g motor i n n e r v a t i o n as a p a r t o f k i n e s t h e s i s . The r e a s o n he gave f o r t h i s was t h a t a l l t h e o t h e r s o u r c e s o f k i n e s t h e s i s a r e a f f e r e n t and o f p e r i p h e r a l o r i g i n , whereas motor i n n e r v a t i o n i s o f c e n t r a l o r i g i n , and may have q u i t e d i f f e r e n t consequences f o r movement 40 . c o n t r o l . I t has been shown i n a t l e a s t two e x p e r i m e n t s t h a t a c t i v e movement p o s i t i o n i n g was s u p e r i o r i n a c c u r a c y t o p a s s i v e movement p l a c i n g ; L l o y d and C a l d w e l l (45) showed t h i s i n t h e human l e g and P a i l l a r d and Brouchon (69) showed t h i s i n t h e human arm. Many reas o n s have been g i v e n t o a c c o u n t f o r the more a c c u r a t e a c t i v e movement i n c l u d i n g the p a t t e r n o f motor i n n e r v a t i o n . S i n c e p a s s i v e movements don't have a p a t t e r n o f motor i n n e r v a t i o n and a c t i v e move-ments do, t h i s c o u l d p o s s i b l y a c c o u n t f o r some o f the d i f -f e r e n c e between t h e two. P a i l l a r d and Brouchon (69) have i n f e r r e d two p o s s i b l e ways t h a t t h e p a t t e r n o f motor i n n e r v a t i o n may e x p l a i n t h e d i f f e r e n c e between a c t i v e and p a s s i v e movements: F i r s t , t h e y p roposed an i n t e r n a l m o n i t o r i n g system, a system t h a t s e r v e s . k i n e s t h e s i s by t h e "motor o u t f l o w " . T h i s concept c o v e r s t h e i d e a t h a t some a f f e r e n t c o n t r o l s i g n a l goes t o the mu s c l e , and a l s o t o some comparator o r c o r r e l a t o r s t r u c t u r e i n t h e . n e r v o u s system. T h i s system must have o t h e r i n f o r m a t i o n such as t h e s t a r t i n g p o s i t i o n i n o r d e r t o be u s e f u l t o k i n e s t h e t i c judgments, f o r i t can o n l y s i g n a l movement o f d e s i r e d a m p l i t u d e i n a g i v e n d i r e c t i o n . The system was p r o -posed by P a i l l a r d and Brouchon t o be c a p a b l e o f e n g r a v i n g c e r t a i n movements t o b u i l d up s p a t i a l s t a n d a r d s as r e -f e r e n c e s . Once engrammed, such s t a n d a r d s would be a b l e t o o p e r a t e t h e programming o f adjustment r e a c t i o n s which b e l o n g t o the u s u a l modes o f r e a c t i o n o f the i n d i v i d u a l . Suprasystems o f c o n t r o l s would emerge from t h i s p r o g r e s s i v e o r g a n i z a t i o n t h a t would be a b l e t o t a k e charge o f some r e -o r g a n i z a t i o n s of t h e i r own. S e c o n d l y , P a i l l a r d and Brouchon (69) proposed t h a t t h e p a t t e r n o f motor- i n n e r v a t i o n c o u l d be a l t e r e d by p e r i p h e r a l methods. They proposed t h a t e v e r y motor command a c t i n g on the a l p h a motorneurons i s pr e c e d e d , accompanied, and f o l l o w e d by a p a t t e r n o f i n n e r v a t i o n o f gamma motor-neurons which b i a s e s the s p i n d l e r e c e p t o r s o f the muscle so as t o i n i t i a t e , s u s t a i n , and modulate the a l p h a d i s c h a r g e a c c o r d i n g t o the aim o f the d e s i r e d a c t i o n . They went on t o s t a t e t h a t t h i s double motor system p r e d i s p o s e s t h e p r i m a r y endings i n the s p i n d l e s t o a c t as speed d e t e c t o r s (gamma dynamic) and a l s o t o a c t as s t a t i c p o s i t i o n r e c e p t o r s (gamma s t a t i c ) . P a i l l a r d and Brouchon (69) , a c c r e d i t e d the gamma dynamic system w i t h i t s decay o v e r t i m e , as b e i n g r e s p o n s i b l e f o r t h e i r r e s u l t s o f a c t i v e movement b e i n g more a c c u r a t e than p a s s i v e movements. P a i l l a r d and Brouchon t e r m i n a t e d t h e i r d i s c u s s i o n by w a r n i n g t h a t t h e s e two t h e o r i e s o f motor i n n e r v a t i o n f u n c t i o n i were pure c o n j e c t u r e . J o i n t R e c e p t o r s . The j o i n t r e c e p t o r s i n c l u d e n ot o n l y the s p r a y o r R u f f i n i t y p e e n d i n g s and the p a c i n i a n c o r p u s c l e s found i n t h e c o n n e c t i v e t i s s u e o f the a r t i c u l a t e j o i n t c a p s u l e , b u t a l s o t h e f r e e ( G o l g i - t y p e ) e n d i n g s found i n the l i g a m e n t s around j o i n t c a p s u l e s . G e n e r a l l y , two e x p e r i m e n t a l methods have been used t o i n v e s t i g a t e the r o l e p l a y e d by t h e s e j o i n t r e c e p t o r s i n k i n e s t h e s i s : one method i n c l u d e s a n a e s t h e t i z i n g the j o i n t c a p s u l e w i t h p r o c a i n e and then measuring p o s i t i o n and move-ment sense; the o t h e r method c o n s i s t s o f r e c o r d i n g the p o t e n t i a l s o f j o i n t neurons d i r e c t l y d u r i n g a c t u a l l i m b movements and p o s i t i o n s . The f i r s t method has g e n e r a l l y shown t h a t a l l sense o f p o s i t i o n and p a s s i v e movement o f the j o i n t a n a e s t h e t i z e d was l o s t . The second method u s u a l l y showed t h a t when t e n s i o n was a p p l i e d t o the j o i n t , s l o w l y a d a p t i n g d i s c h a r g e s were r e c o r d e d , and o f t e n an i n i t i a l d e c l i n e i n response f r e q u e n c y d u r i n g the f i r s t few seconds. These neurons d i s c h a r g e d s t e a d i l y f o r the whole p e r i o d w h i l e s t e a d y t e n s i o n was a p p l i e d . The o v e r a l l c o n c l u s i o n drawn from e x p e r i m e n t s u s i n g e i t h e r method was t h a t the r e c e p t o r organs o f the j o i n t cap-s u l e p l a y e d a major r o l e i n p o s i t i o n and movement sense o r k i n e s t h e s i s . T h i s c o n c l u s i o n i s s u p p o r t e d by s t u d i e s u s i n g the c a t (2, 3, 9, 14, 26, 58, 63, 75, 79). The same c o n c l u s i o n was r e a c h e d i n s t u d i e s w i t h humans (15, 30, 54, 74) . Cohen (15) went on t o s t a t e t h a t t h e r e was.no e v i d e n c e p r e s e n t i n h i s s t u d y on t h e human s h o u l d e r t o i n d i c a t e the r e l a t i v e ' r o l e o f each of the j o i n t r e c e p t o r s i n k i n e s t h e t i c s ; y e t Rose and M o u n t c a s t l e (75).have s t a t e d t h a t the m a j o r i t y o f k i n e s t h e t i c r e c e p t o r s i n t h e j o i n t , c a p s u l e appear t o be o f a slow a d a p t i n g v a r i e t y . O t her e v i d e n c e t h a t s u p p o r t s t h e major r o l e p l a y e d by t h e j o i n t . r e c e p t o r s i n k i n e s t h e s i s i s t h a t t h e a f f e r e n t p r o -j e c t i o n s o f t h e j o i n t r e c e p t o r s have d i r e c t c o n n e c t i o n t o the somatosensory are a s of the c o r t e x , w h i c h means c o n s c i o u s p e r c e p t i o n o f s t i m u l i . E x p e r i m e n t s have shown u n e q u i v o c a l l y t h a t t h e s e j o i n t r e c e p t o r a f f e r e n t s p r o j e c t t o the v e n t r o b a s a l n u c l e a r complex o f the thalamus; t o the c o n t r a l a t e r a l s e n s o r y a r e a s , SMI and SMII; and t o the i p s i l a t e r a l s e n s o r y a r e a SMII o f t h e c o r t e x . T h i s has been shown i n monkeys by M o u n t c a s t l e (60) and M o u n t c a s t l e and P o w e l l (63); a n d . a l s o i n c a t s (28, 36, 58, 59, 61, -62 , 73, 79) . Two C l a s s e s o f J o i n t R e c e p t o r s . The a r t i c u l a t e j o i n t r e c e p t o r s r e s p o n s i b l e f o r k i n e s t h e s i s c o u l d be d i v i d e d i n t o two c l a s s e s : f a s t o r slow a d a p t i n g (3,,9, 27, 63, 66, 80, 97) . The slow a d a p t i n g r e c e p t o r s have been shown t o be s u b s e r v e d by t h e s p r a y o r r u f f i n i t y p e e n d i n g s i n the j o i n t c a p s u l e and the f r e e ( G o l g i - t y p e ) endings i n t h e l i g a m e n t s . Smith (80) has o u t l i n e d the o p e r a t i n g c h a r a c t e r i s t i c s ' o f t h e s e slow a d a p t i n g r e c e p t o r s . 1) R e c e p t o r s f i r e a t d i f f e r e n t f r e q u e n c i e s f o r a s p e c i f i c j o i n t a n g l e r e g a r d l e s s o f the speed o r d i r e c t i o n o f w h i c h th e p o s i t i o n was approached. 2) R e c e p t o r s adapt s l o w l y and o f t e n a s i n g l e u n i t has a d i f f e r e n t a d a p t a t i o n r a t e f o r each j o i n t a n g l e . 3) More r e c e p t o r s a r e r e s p o n s i b l e t o a l i m i t e d range o f the t o t a l j o i n t a c t i o n , i . e . , t h e r e i s a f r a c t i o n a t i o n o f t h e p h y s i o l o g i c a l range of m o t i o n . T h e r e f o r e , t h e s l o w - a d a p t i n g r e c e p t o r s a r e dependent on j o i n t a n g l e , b u t independent o f movement d i r e c t i o n and speed. On t h e o t h e r hand, Smith (80) has r e p o r t e d t h a t f a s t a d a p t i n g r e c e p t o r s a r e independent o f j o i n t a n g l e b u t de-pendent upon v e l o c i t y a c c e l e r a t i o n and d i r e c t i o n o f l i m b movement. She went on t o o u t l i n e t h e c h a r a c t e r i s t i c s o f t h e s e f a s t a d a p t i n g receptors'. 45: 1) R e c e p t o r s adapt r a p i d l y t o s t a t i c p o s i t i o n i n g o f the limbs'. 2) Many r e c e p t o r s a r e u n i d i r e c t i o n a l — t h e y respond t o o n l y one d i r e c t i o n o f movement. 3) The m a j o r i t y o f - r e c e p t o r s a r e s e n s i t i v e t o move-ment v e l o c i t y ; i . e : , t h e i r o v e r a l l d i s c h a r g e f r e q u e n c y i n -c r e a s e s as v e l o c i t y i n c r e a s e s . 4) U n i t s have a r a p i d o n s e t o f f i r i n g and low v e l o c i t y t h r e s h o l d ; however, the v e l o c i t y t h r e s h o l d s d i f f e r f o r groups o f r e c e p t o r s . The p a c i n i a n c o r p u s c l e s found i n the j o i n t c a p s u l e a r e b e l i e v e d t o f u n c t i o n as t h e f a s t a d a p t i n g r e c e p t o r s , and a r e b e l i e v e d t o be l e s s numerous th a n the slow a d a p t i n g r e -c e p t o r s (97) . E x c i t a t o r y A n g l e . As w e l l a s . t h e above r e c e p t o r c h a r a c t e r -i s t i c s , M o u n t c a s t l e and P o w e l l (63) r e p o r t e d t h a t the s l o w a d a p t i n g r e c e p t o r s responded t o movements i n t h e i r e x c i t a t o r y a n g l e s w i t h h i g h f r e q u e n c y d i s c h a r g e , and t h a t i f t h i s movement came t o a h a l t w i t h i n t h i s e x c i t a t o r y range, the f i r i n g r a t e adapted t o a lo w e r s t e a d y r a t e i n a few seconds. The i m p o r t a n t f a c t here was t h a t t h e s t e a d y adapted r a t e o f d i s c h a r g e i s a v a r i a b l e i n f l u e n c e d o n l y by t h e j o i n t a n g l e — t h e y f u n c t i o n as a b s o l u t e d e t e c t o r s o f a n g l e . They a l s o s t a t e d t h a t t h i s adapted r a t e f o r any a n g l e was not a f f e c t e d by the speed o r d i r e c t i o n o f movement b e f o r e t h e , s t e a d y p o s i t i o n and does not v a r y o v e r t i m e . M o u n t c a s t l e and P o w e l l (63) have a l s o s t a t e d t h a t t h e e x c i t a t o r y a n g l e o f j o i n t r e c e p t o r s i s about f i f t e e n t o twenty degrees o f a r c . These e x c i t a t o r y a n g l e s l i e i n a continuum a l o n g the a r c o f j o i n t movement, and many showed maximal s t e a d y d i s c h a r g e r a t e s a t f u l l f l e x i o n , o t h e r s a t f u l l e x t e n s i o n , and o t h e r s a t a n g l e s between f l e x i o n and e x t e n s i o n (5, 9, 63, 80, 9 7 ) . Movement o f a j o i n t would t r a v e r s e the o v e r l a p p i n g ranges o f s u c c e s s i v e r e c e p t o r s . The p r o f i l e o f w h i c h r e c e p t o r s were a c t i v e and the s t e a d y f i r i n g r a t e would p i c t u r e t h e j o i n t a n g l e s and movement. D i r e c t i o n and speed o f movement would be d e p i c t e d by w h i c h group of r e -c e p t o r s i n c r e a s e d o r d e c r e a s e d i n f r e q u e n c y o f > d i s c h a r g e and t h e e x t e n t o f such changes (63, 80, 9 7 ) . C o r t i c a l C o n n e c t i o n s . P e r i p h e r a l j o i n t r e c e p t o r s have been shown t o be c o n n e c t e d t o c e r t a i n c o r t i c a l c e l l s i n t h e s e n s o r y a r e a s , t h e r e f o r e t h e s e c o r t i c a l c e l l s must be d r i v e n by c o n n e c t i n g j o i n t r e c e p t o r s . T h e r e l a t i o n s h i p between j o i n t r e c e p t o r d i s c h a r g e and the c o n n e c t i n g c o r t i c a l c e l l p o t e n t i a l s a r e o f prime i m p o r t a n c e t o the u n d e r s t a n d i n g o f s u b j e c t i v e p e r c e p t i o n o f j o i n t movement and p o s i t i o n . M o u n t c a s t l e and P o w e l l (63) have i d e n t i f i e d j o i n t movement as the s t i m u l u s f o r a c t i v a t i n g c e r t a i n c e l l s i n the p o s t c e n t r a l g y r u s . These c o r t i c a l r e c e p t o r c e l l s appear t o be grouped i n t o r e c e p t i v e f i e l d s w h i c h , when f i t t e d t o g e t h e r , form a c o r t i c a l p r o j e c t i o n p a t t e r n o f the body. With such a t o p o g r a p h i c p a t t e r n t h e s t e a d y a n g l e s o f the body j o i n t s and changes i n t h o s e a n g l e s a re d e p i c t e d by the p a t t e r n o f a c t i v i t y o f the c o r t i c a l c e l l s . These a u t h o r s (63) c o n c l u d e d t h a t b o t h t h e p l a c e o f occu r e n c e o f n e u r a l a c t i v i t y and t e m p o r a l p a t t e r n o f n e u r a l d i s c h a r g e a re used t o d e p i c t the p l a c e , i n t e n s i t y , and t e m p o r a l cadence o f se n s o r y e v e n t s ; and t h a t t h i s mechanism p r o v i d e s a w e l l -d e f i n e d a n a t o m i c a l n u c l e u s f o r f i n e ; k i n e s t h e t i c d i f f e r e n t -a t i o n between j o i n t movements and p o s i t i o n s . M o u n t c a s t l e and P o w e l l (63) have a l s o d i s c u s s e d t h e s e n s i t i v i t y r e l a t i o n s h i p s between c o n n e c t i n g c o r t i c a l and j o i n t r e c e p t o r s . Most c o r t i c a l c e l l s r espond t o movement o v e r a s i x t y t o n i n e t y degree range which i s c o n s i d e r a b l y w i d e r than t h e j o i n t r e c e p t o r ' s range o f f i f t e e n t o twenty degrees o f a r c . T h i s s i t u a t i o n s u g g e s t s t h a t a c o r t i c a l 48. neuron i s " d r i v e n " by i n p u t from a number o f p e r i p h e r a l r e c e p t o r s whose narrower e x c i t a t o r y ranges o v e r l a p one an o t h e r i n o r d e r t o c o v e r the n i n e t y degrees o f a r c o f the c o r t i c a l neurons. Smith (80) s t a t e d t h a t t h e s e r e p o r t s t e n d t o suggest t h a t d e t a i l e d k i n e s t h e t i c i n f o r m a t i o n made a v a i l a b l e by t h e j o i n t r e c e p t o r s does n ot r e a c h the c o r t i c a l c e n t r e s t h a t s u b s e r v e p e r c e p t i o n ; i n s t e a d , o n l y a summary o f t h i s i n f o r m a t i o n r e a c h e s t h e s e c e n t r e s . M o u n t c a s t l e and P o w e l l (63) a l o n g w i t h M o u n t c a s t l e , C o v a i n and H a r r i s o n (61) have shown a r e c i p r o c a l i n h i b i t i o n i n a d j a c e n t c o r t i c a l c e l l s . These a u t h o r s r e p o r t e d t h a t some p a i r s o f s p a t i a l l y r e l a t e d c o r t i c a l c e l l s a r e r e c i p r o c -a l l y r e l a t e d , one c e l l b e i n g a c t i v e , a s t h e j o i n t moves i n one d i r e c t i o n , and the o t h e r i n h i b i t i n g i t s d i s c h a r g e r a t e and v i c e v e r s a . These p r o c e s s e s a re b e l i e v e d t o r e s u l t i n a s h a r p e n i n g o f i n c o m i n g n e u r a l k i n e s t h e t i c i n f o r m a t i o n . The response p a t t e r n o f the c o r t i c a l neurons have been shown t o be s i m i l a r and a l s o o p p o s i t e t o the response p a t -t e r n s o f t h e j o i n t r e c e p t o r s . M o u n t c a s t l e and P o w e l l (63) have o b s e r v e d t h a t the q u i c k a d a p t i n g c o r t i c a l neurons a r e much l e s s common tha n the slow a d a p t i n g ones, and t h a t the slow a d a p t i n g c o r t i c a l neurons show r a p i d o n s e t , d e c l i n i n g t o a s t e a d y adapted r a t e d u r i n g s t e a d y j o i n t p o s i t i o n i n g --two c h a r a c t e r i s t i c s s i m i l a r t o t h o s e of t h e j o i n t r e c e p t o r s . These a u t h o r s have l i s t e d the c h a r a c t e r i s t i c response p a t -t e r n s o f the c o r t i c a l neurons t o j o i n t movement: 1) c o r t i c a l c e l l s b e g i n t o d i s c h a r g e a t an a b s o l u t e v a l u e o f a n g u l a r d i s p l a c e m e n t . 2) t h e speed w i t h w h i c h the j o i n t i s moved i n t o t h e e x c i t a t o r y a n g l e d e t e r m i n e s t h e f r e q u e n c y o f the on s e t t r a n s i e n t d i s c h a r g e o f the neuron. 3) the f i n a l s t e a d y adapted r a t e o f d i s c h a r g e depends on j o i n t a n g l e . 4) d u r i n g m a i n t a i n e d j o i n t p o s i t i o n t h e r a t e o f n e u r a l d i s c h a r g e assumes a lo w e r s t e a d y s t a t e . Some o f t h e s e o p e r a t i n g c h a r a c t e r i s t i c s a r e s i m i l a r t o tho s e o f j o i n t r e c e p t o r s t o w h i c h t h e y a r e c o n n e c t e d . M o u n t c a s t l e , P o g g i o and Werner (62) have shown t h a t t h e response p a t t e r n o f the j o i n t r e c e p t o r s d i f f e r from t h o s e o f the c o r t i c a l c e l l s . R e c o r d i n g from the t h i r d o r d e r r e l a y of, j o i n t r e c e p t o r a f f e r e n t p r o j e c t i o n s i n the v e n t r o b a s a l n e u r a l c o m p l e x o f the thalamus, t h e y found t h a t the c o r t i c a l c e l l s s i g n a l l e d " i n t e n s i v e l y " , by the i n c r e a s e d r a t e o f d i s -c harge i n t h e r e l e v a n t groups o f c e l l s , t he degree o f move-ment a t the j o i n t . Y-et t h e y c o n c l u d e d t h a t a t t h e l e v e l o f the f i r s t o r d e r a f f e r e n t s a t the j o i n t r e c e p t o r s , r a t e o f d i s c h a r g e c o u l d not s i g n a l p o s i t i o n ; p o s i t i o n c o u l d o n l y be s i g n a l l e d e x t e n s i v e l y , i . e . , by d e t e r m i n i n g which f i b e r s cf the t o t a l p o p u l a t i o n were a c t i v e . These p o i n t s s uggest t h a t an i m p o r t a n t t r a n s f o r m a t i o n has o c c u r r e d , i n the n e u r a l c h a i n t h a t s u b s e r v e s k i n e s t h e s i s as e a r l y as t h e t h i r d o r d e r a f f e r e n t r e l a y . T h e i r r e s u l t s a l s o i n d i c a t e d t h a t a power f u n c t i o n o f the form: R = K S N a d e q u a t e l y d e s c r i b e d the r e l a t i o n s h i p between j o i n t p o s i t i o n and the response o f the t h a l a m i c c e l l s . The s u b j e c t i v e i m p r e s s i o n o f j o i n t movement and p o s i t i o n i s o n l y formed a f t e r a l a r g e , d e l i c a t e s e r i e s o f n e u r a l e v e n t s i n t h e c e n t r a l nervous system. The- e v i d e n c e p r e s e n t e d above s h o u l d a s s i s t i n f o r m u l a t i n g a t h e o r y which reproduces. t h i s n e u r a l c h a i n between the p h y s i c a l and s u b j e c t i v e e x p e r i e n c e s . P s y c h o p h y s i c a l C o n c l u s i o n s Based on N e u r o p h y s i o l o g i c a l  E v i d e n c e . The n e u r o p h y s i o l o g i c a l o p e r a t i n g c h a r a c t e r i s t i c s o f t h e k i n e s t h e t i c r e c e p t o r s p r e s e n t e d above have d e p i c t e d k i n e s -t h e s i s as f u n c t i o n i n g on b o t h a m e t a t h e t i c and p r o t h e t i c b a s i s . M o u n t c a s t l e and P o w e l l ( 6 3 ) , Boyd and R o b e r t s ( 9 ) , Smith (80) , and W i l l i a m s (97) have a l l i n d i c a t e d t h a t the j o i n t r e c e p t o r s , w h i c h are m a i n l y r e s p o n s i b l e f o r k i n e s t h e s i s , f u n c t i o n on a m e t a t h e t i c b a s i s . These a u t h o r s s t a t e d t h a t d i f f e r e n t j o i n t a n g l e s caused d i f f e r e n t groups o f t h e t o t a l p o p u l a t i o n o f j o i n t r e c e p t o r s t o f i r e . Some f i r e d a t complete f l e x i o n , o t h e r s a t complete e x t e n s i o n , and o t h e r s between f l e x i o n and e x t e n s i o n . J o i n t . p o s i t i o n would be d e t e r m i n e d by t h e d i s c h a r g e r a t e o f a s p e c i f i c group o f r e c e p t o r s , w h i l e j o i n t movement would be d e t e r m i n e d by the o v e r l a p p i n g o f e x c i t a t o r y a n g l e s o f a s u c c e s s i o n o f j o i n t . r e c e p t o r s . These a u t h o r s have a l s o i n d i c a t e d t h a t a p r o t h e t i c p r o -c e s s may be i n v o l v e d i n t h e s u b j e c t i v e i m p r e s s i o n o f j o i n t p o s i t i o n . They have s t a t e d t h a t i f a movement s t o p s i n t h e e x c i t a t o r y a n g l e o f a group of j o i n t r e c e p t o r s , the r a t e o f d i s c h a r g e o f t h e s e r e c e p t o r s adapts t o a l o w e r , s t e a d i e r s t a t e w i t h i n a few seconds, and t h a t t h i s f i n a l l o w e r , s t e a d y s t a t e i s a v a r i a b l e i n f l u e n c e d o n l y by t h e j o i n t a n g l e . I n o t h e r words, a s p e c i f i c j o i n t a n g l e would have a s p e c i f i c l o w e r s t e a d y r a t e o f d i s c h a r g e t h a t was s p e c i f i c t o t h a t a n g l e . Such a q u a n t i t a t i v e p r o c e s s i n d i c a t e s t h a t a p r o t h e t i c me-chanism may a s s i s t i n s u b s e r v i n g j o i n t p o s i t i o n and movement a l o n g w i t h a m e t a t h e t i c p r o c e s s . M o u n t c a s t l e and P o w e l l (63) c o n c l u d e d t h a t t h e c e n t r a l nervous system u t i l i z e s b o t h t h e p l a c e o f o c c u r r e n c e ( m e t a t h e t i c p r o c e s s ) and the t e m p o r a l p a t t e r n o f n e u r a l a c t i v i t y ( p r o t h e t i c p r o c e s s ) t o d e p i c t p o s i t i o n and movement o f t h e body l i m b s . S m i t h (80) and W i l l i a m s (97) have s u g g e s t e d t h a t the s u b j e c t i v e i m p r e s s i o n o f d i r e c t i o n o f movement was sub-s e r v e d by a m e t a t h e t i c mechanism. They s t a t e d t h a t d i r e c t i o n o f j o i n t movement was r e p r e s e n t e d by a p r o f i l e of which j o i n t r e c e p t o r c e l l s showed t r a n s i e n t i n c r e a s e s i n r a t e o f d i s c h a r g e , and wh i c h d e c r e a s e d i n a c t i v i t y . The same a u t h o r s (80, .97) have a l s o d e p i c t e d t h a t speed o f j o i n t movement must o p e r a t e a l o n g a p r o t h e t i c continuum, f o r th e y s t a t e d t h a t speed o f movement was i n d i c a t e d by the r a t e o r e x t e n t o f t r a n s i e n t d i s c h a r g e o f the j o i n t r e c e p t o r s t o movement.. The f a s t e r the movement, the g r e a t e r the d i s c h a r g e r a t e o f t h e j o i n t r e c e p t o r s ; t h e r e f o r e speed o f j o i n t movement was coded q u a n t i t a t i v e l y by f r e q u e n c y o f j o i n t r e c e p t o r d i s c h a r g e . I n s t u d y i n g the n e u r a l a c t i v i t y o f the c e l l s i n t h e p o s t c e n t r a l g y r u s , M o u n t c a s t l e and P o w e l l (63) have found t h a t c e l l s w h i c h were a c t i v a t e d by j o i n t r e c e p t o r s were a r r a n g e d i n t o p o g r a p h i c p a t t e r n s and t h a t the n e u r a l p a t t e r n o f a c t i v i t y q u a l i t a t i v e l y d e p i c t e d j o i n t a n g l e s and changes i n t h e s e a n g l e s . T h i s s u g g e s t s t h a t j o i n t p o s i t i o n and movement might be. s u b s e r v e d by a q u a l i t a t i v e o r m e t a t h e t i c p r o c e s s a t the c o r t i c a l l e v e l . A c c o r d i n g t o M o u n t c a s t l e , P o ggio and Werner ( 6 2 ) , the j o i n t r e c e p t o r s must s i g n a l j o i n t p o s i t i o n and move-ment m e t a t h e t i c a l l y , f o r th e y have s t a t e d t h a t j o i n t p o s i -t i o n and movement cannot be d e p i c t e d by f r e q u e n c y o f j o i n t r e c e p t o r d i s c h a r g e , o r i n o t h e r words, q u a n t i t a t i v e l y . P o s i t i o n must be s i g n a l l e d q u a l i t a t i v e l y -- by a s p e c i f i c group o f j o i n t r e c e p t o r s d i s c h a r g i n g . Y et th e y (62) found t h a t a t the t h i r d o r d e r r e l a y o f j o i n t r e c e p t o r a f f e r e n t p r o j e c t i o n s i n t h e v e n t r o b a s a l . n e u r a l complex o f the t h a -lamus, j o i n t p o s i t i o n and movement were s i g n a l l e d q u a n t i -t a t i v e l y o r p r o t h e t i c a l l y by t h e i n c r e a s e d r a t e o f d i s c h a r g e They c o n c l u d e d t h a t between the j o i n t r e c e p t o r s , w h i c h s i g n a l j o i n t movement and p o s i t i o n m e t a t h e t i c a l l y , and the t h a l a m i c t h i r d o r d e r r e l a y c e l l s , w h i c h s i g n a l j o i n t p o s i -t i o n and movement p r o t h e t i c a l l y , a n e u r a l t r a n s f o r m a t i o n must o c c u r . These a u t h o r s (62) a l s o found t h a t the r e l a -t i o n s h i p between j o i n t p o s i t i o n and d i s c h a r g e o f t h a l a m i c c e l l s f o l l o w e d a power f u n c t i o n o f the form: N R = KS , whi c h i s a p r o t h e t i c c h a r a c t e r i s t i c . T h i s n e u r o p h y s i o l o g i c a l evidence tends to i n d i c a t e t h a t the a r t i c u l a r j o i n t r e c e p t o r s , which are mainly r e s -p o n s i b l e f o r k i n e s t h e s i s , s i g n a l j o i n t p o s i t i o n and move-ment m e t a t h e t i c a l l y , and t h a t t h i s q u a l i t a t i v e i n f o r m a t i o n process i s transformed by the j o i n t r e c e p t o r t h i r d order a f f e r e n t s i n the thalamus i n t o a q u a n t i t a t i v e i n f o r m a t i o n , or p r o t h e t i c p r o c e s s . The presented n e u r o p h y s i o l o g i c a l evidence can only l e a d to suggestions about the psychophysics of k i n e s t h e s i s . In order to d i s c o v e r the p s y c h o p h y s i c a l r e l a t i o n s h i p between stimulus i n p u t and s u b j e c t i v e output on k i n e s t h e s i s i s to q u a n t i t a t i v e l y measure.these v a r i a b l e s through b e h a v i o r a l s t u d i e s . B e h a v i o u r a l S t u d i e s on the Psychophysics of K i n e s t h e s i s A very l i m i t e d amount of b e h a v i o u r a l r e s e a r c h has been done i n k i n e s t h e s i s u s i n g p s y c h o p h y s i c a l s c a l i n g methods or r e l a t i n g k i n e s t h e s i s to Stevens' Power F u n c t i o n Law. G o l d s c h e i l d e r . (29) s t u d i e d the s e n s i t i v i t y of nine body j o i n t s u s i n g p a s s i v e movements and found t h a t the s e n s i t i v i t y was d i r e c t l y r e l a t e d to the p r o x i m i t y of the limb to the trunk. In o t h e r words, these r e s u l t s of G o l d s c h e i l d e r i n -d i c a t e d t h a t when a body limb was i n complete f l e x i o n , which i s the p o s i t i o n most approximate t o the t r u n k , the sens-i t i v i t y t o p a s s i v e movement s h o u l d be maximal. T h e r e f o r e i t c o u l d be s t a t e d t h a t s e n s i t i v i t y t o p a s s i v e movement i s g r e a t e r a t the one l i m i t o f movement, i n . t h i s c a s e , complete f l e x i o n . C l e g h o r n and Darcus (13) have fou n d , i n t h e i r e x p e r i m e n t on s e n s i t i v i t y t o p a s s i v e movements, t h a t as t h e l i m b ' s degree o f d i s p l a c e m e n t from the body t r u n k i n c r e a s e d , the s e n s i t i v i t y a l s o i n c r e a s e d . These r e -s u l t s would suggest t h a t a t complete e x t e n s i o n o f a body l i m b t h e r e s h o u l d be the g r e a t e s t amount o f s e n s i t i v i t y t o p a s s i v e movements. These two s t u d i e s , G o l d s c h e i l d e r (29) and C l e g h o r n and Darcus (13) , i n d i c a t e t h a t a t t h e two extremes o f j o i n t movement'the k i n e s t h e t i c s e n s t i v i t y s h o u l d be maximal. One s u g g e s t i o n t h a t c o u l d account f o r the g r e a t e r k i n e s t h e t i c s e n s i t i v i t y a t the l i m i t s o f the j o i n t movement i s t h a t t h e j o i n t r e c e p t o r s must be d i s -c h a r g i n g a t a h i g h e r r a t e , o r more r e c e p t o r s a r e d i s c h a r g i n g , w h i c h would s u p p l y g r e a t e r amounts o f k i n e s t h e t i c i n f o r m -a t i o n . T h i s s u g g e s t i o n i s g i v e n f u r t h e r s u p p o r t by Mount-c a s t l e , P o g g i o and Werner (62) who found t h a t i n a c t i v e movement the j o i n t r e c e p t o r s were m a x i m a l l y a c t i v a t e d a t the extremes o f the range of j o i n t movement. The i m p o r t a n t f a c t s here a r e t h a t t h e j o i n t neurons f i r e m a x i m a l l y a t t h e extreme'range o f movement, and t h a t t h e s e n s i t i v i t y seems t o be the g r e a t e s t a t t h e s e p o i n t s . T h i s k i n d o f b e h a v i o u r s u g g e s t s t h a t sense o f movement may o p e r a t e on a q u a n t i t a t i v e , o r p r o t h e t i c mechanism. Wood (98) has shown t h a t the s u b j e c t i v e i m p r e s s i o n o f the r a t e o r speed o f s e l f - i n i t i a t e d arm movement was r e l a t e d t o t h e a c t u a l speed by a power f u n c t i o n . O ther r e s u l t s ob-t a i n e d a f t e r p u t t i n g f i f t y s u b j e c t s t h r o u g h a speed p r o d u c -t i o n t a s k , u s i n g a c t i v e s h o u l d e r l a t e r a l f l e x i o n , showed h y s t e r e s i s and a n o n l i n e a r p l o t f o r c a t e g o r y p r o d u c t i o n , w h i c h l e d h e r t o c o n c l u d e t h a t k i n e s t h e s i s was a p r o t h e t i c continuum. A c t u a l l y , she s h o u l d have c o n c l u d e d t h a t t h e sense o f r a t e a s p e c t o f k i n e s t h e s i s o p e r a t e d on a q u a n t i t a t i v e p r o c e s s , f o r as t h e above d i s c u s s i o n shows, t h e r e may be many d i f f e r e n t a s p e c t s o f k i n e s t h e s i s : p o s i t i o n s e n s e , d i s c r i m i n a t i o n o f a m p l i t u d e o f movement, d i r e c t i o n o f movement and a c c e l e r a t i o n s ense, and t h a t t h e y may a l l f u n c t i o n d i f f e r e n t l y . I n f a c t , the q u e s t i o n o f whether th e s e a s p e c t s a r e i n d e e d d i f f e r e n t p a r t s o f k i n e s t h e s i s , o r s e p a r a t e senses i n t h e m s e l v e s , has never been answered. F o r c e o f h a n d g r i p and judgments o f h e a v i n e s s , two moda-l i t i e s t h a t a re s i m i l a r t o k i n e s t h e s i s , and p r o b a b l y use k i n -e s t h e t i c i n f o r m a t i o n , have been found t o o p e r a t e a l o n g a p r o -t h e t i c continuum. F o r c e o f h a n d g r i p has been shown by Stevens 57. and Mack (81) t o h o l d t o S t e v e n s ' Power F u n c t i o n Law (N = 1.7). U s i n g a hand dynamometer the s u b j e c t e x e r t e d f o r c e s t h a t seemed t o him p r o p o r t i o n a l t o numbers named i n i r r e g u l a r o r d e r by t h e e x p e r i m e n t e r . F o r c e of hand-g r i p has a l s o been used i n c r o s s - m o d a l i t y s t u d i e s w i t h n i n e o t h e r c o n t i n u a , (68) and a l l the f u n c t i o n s a p p r o x i m a t e d p o w e r . f u n c t i o n s . Judgments of h e a v i n e s s u s i n g l i f t e d w e i g h t s have a l s o been shown t o o p e r a t e p r o t h e t i c a l l y and t o f o l l o w S t e v e n s ' Power F u n c t i o n Law (N= 1.45). (94). I t - c o u l d be c o n c l u d e d t h a t a t t h e j o i n t r e c e p t o r f i r s t o r d e r a f f e r e n t s , p o s i t i o n and movement sense o p e r a t e by a m e t a t h e t i c p r o c e s s . Y e t a t t h e t h i r d o r d e r a f f e r e n t r e l a y o f t h e t h a l a m u s , and b e h a v i o u r a l l y , some a s p e c t s o f k i n -e s t h e s i s have been shown t o o p e r a t e p r o t h e t i c a l l y . I n o r d e r t o answer the q u e s t i o n s about th e p s y c h o p h y s i c a l p r o -p e r t i e s o f k i n e s t h e s i s , each d i f f e r e n t a s p e c t must be mea-' s u r e d and s t u d i e d i n d e p e n d e n t l y . To a s s i s t our u n d e r s t a n d i n g o f how the s u b j e c t i v e im-p r e s s i o n o f j o i n t movement o r k i n e s t h e s i s i s formed, i t would be u s e f u l t o d i s c u s s the q u e s t i o n s and problems t h a t have a r i s e n i n r e g a r d 'to the use and u s e f u l n e s s o f k i n e s t h e t i c i n f o r m a t i o n from the j o i n t r e c e p t o r s . 58. K i n e s t h e t i c I n f o r m a t i o n Does K i n e s t h e t i c I n f o r m a t i o n Reach t h e C o r t e x ? E v i d e n c e has shown t h a t the a f f e r e n t f i b r e s of t h e j o i n t r e c e p t o r s , and p o s s i b l y t h o s e o f the muscle s p i n d l e s do, i n f a c t , have d i r e c t c o n n e c t i o n s t o t h e s e n s o r y a r e a s o f the c o r t e x (1, 28, 36, 58, 6 8 ) . Yet i t i s a n o t h e r q u e s t i o n whether i n f o r m -a t i o n from the k i n e s t h e t i c r e c e p t o r s r e a c h e s t h e c o r t e x . I t i s a w e l l known f a c t t h a t t h e c e n t r a l nervous s y s -tem s e l e c t i v e l y p e r m i t s s e n s o r y s t i m u l a t i o n t o e n t e r c e n t e r s s u b s e r v i n g p e r c e p t i o n , thus i t i s p o s s i b l e t h a t k i n e s t h e t i c i n f o r m a t i o n , o r a p a r t o f i t , i s i n h i b i t e d from r e a c h i n g the p e r c e p t u a l s e n s o r y a r e a s . I t has been shown (62, 63) t h a t some of the k i n e s t h e t i c i n f o r m a t i o n does r e a c h t h e c o r t e x . Y e t Smith (80) has s u g g e s t e d t h a t o n l y a summary o f the k i n e s t h e t i c i n f o r m a t i o n produced by t h e k i n e s t h e t i c r e c e p t o r s r e a c h e s the s e n s o r y a r e a s of t h e c o r t e x . The amount and q u a l i t y o f k i n e s t h e t i c i n f o r m a t i o n r e a c h i n g the c o r t i c a l a r e a s t h a t s u b s e r v e k i n e s t h e s i s i s an i m p o r t a n t a r e a t o the t o t a l u n d e r s t a n d i n g o f k i n e s t h e s i s and must be c o n s i d e r e d a p r i m a r y i t e m f o r f u r t h e r r e s e a r c h . A t t e n t i o n t o K i n e s t h e t i c I n f o r m a t i o n . Even i f k i n e s t h e t i c i n f o r m a t i o n does r e a c h t h e c o r t i c a l s e n s o r y a r e a s , i t must be 59 . a t t e n d e d t o i n o r d e r t o be u s e f u l . K e e l e and Posner (38) have shown t h a t a t t e n t i o n t o k i n e s t h e t i c feedback was g r e a t e s t a t t h e b e g i n n i n g o f a movement, d e c r e a s e d t o a low v a l u e i n the m i d d l e range o f movement, and then showed a s l i g h t i n c r e a s e as t h e end o f the movement approached. I f we do a t t e n d more t o in c o m i n g i n f o r m a t i o n a t the b e g i n n i n g and end o f a movement, s h o u l d n o t our s e n s i t i v i t y be g r e a t e r i n t h e s e a r e a s ? E v i d e n c e p r e s e n t e d above showed t h a t j o i n t and c o r t i c a l neurons f i r e d m a x i m a l l y a t extreme j o i n t range (5, 62, 63) and s e n s i t i v i t y was g r e a t e r a t t h e s e p o i n t s (13, 29 ) . C o u l d t h i s be a r e s u l t o f g r e a t e r a t t e n t i o n ? Smith's (80) s u g g e s t i o n o f a summary o f k i n e s t h e t i c i n f o r m a t i o n r e a c h i n g the c o r t e x , c o u l d be a r e s u l t of l a c k o f a t t e n t i o n t o t h e i n c o m i n g i n f o r m a t i o n . The a t t e n t i o n t o k i n e s t h e t i c i n f o r m a t i o n r e a c h i n g t h e c o r t e x must a l s o be i n v e s t i g a t e d t h r o u g h f u r t h e r r e s e a r c h . I s K i n e s t h e t i c I n f o r m a t i o n Used? I f k i n e s t h e t i c i n f o r m -a t i o n r e a c h i n g t h e c o r t e x i s a t t e n d e d t o , i s i t u s e f u l i n f o r m -a t i o n ? Notterman and Page (15) and F l e i s h m a n and R i c h (24) have shown i n t h e i r r e s p e c t i v e s t u d i e s t h a t k i n e s t h e t i c i n f o r m a t i o n i s used. Both s t u d i e s showed t h a t the s u b j e c t s 60. who were a l l o w e d t o use k i n e s t h e t i c feedback improved t h e i r performance over those s u b j e c t s who were not a l l o w e d use o f k i n e s t h e t i c i n f o r m a t i o n . P a i l l a r d and Brouchon (69) have suggested t h a t we b u i l d up a known system o f s p a t i a l r e l a t i o n s h i p s among the d i f f e r e n t m o b i l e p a r t s o f the body, and a method of c o n t i -n u o u s l y e v a l u a t i n g t h e i r r e l a t i v e p o s i t i o n s . T h i s e x e c u t i v e program would be b u i l t up i n p a r t by k i n e s t h e s i s , and would p r o v i d e a comparator mechanism t o w h i c h • i n c o m i n g i n f o r m a t i o n c o u l d be r e f e r r e d ; such a mechanism would p r o v i d e us w i t h u s e f u l k i n e s t h e t i c i n f o r m a t i o n . These a u t h o r s (69) s t a t e d t h a t the u s e f u l i n f o r m a t i o n about j o i n t p o s i t i o n comes from the f i n a l dynamic phase o f the movement, and n o t the f i n a l p o s i t i o n . The i n f o r m a t i o n as w e l l as t h e methods by w h i c h i t i s coded and used w i l l a l s o be an i m p o r t a n t t o p i c o f f u r t h e r k i n e s t h e t i c r e s e a r c h . CHAPTER I I I METHODS AND PROCEDURES S u b j e c t s F i f t y v o l u n t e e r s u b j e c t s , b o t h male and f e m a l e , r i g h t and l e f t - h a n d e d , were used i n t h e s t u d y . A l l the s u b j e c t s were u n d e r g r a d u a t e s between the ages o f e i g h t e e n and t w e n t y - f i v e y e a r s a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a i n the 1969-1970 academic y e a r . The s u b j e c t s were u n a c q u a i n t e d w i t h t h e a p p a r a t u s used i n the s t u d y and u n f a m i l i a r w i t h the movement under-s t u d y . A p p a r a t u s The a p p a r a t u s used i n t h e s t u d y c o n s i s t e d o f a f l a t p i e c e o f w h i t e c a r d b o a r d c u t i n an a r c o f one hundred degrees and a f f i x e d t o a t a b l e t o p t w e n t y - n i n e i n c h e s h i g h . An a r c o f one hundred degrees was drawn on t h e p i e c e o f c a r d b o a r d , and e v e r y h a l f degree was marked ( F i g u r e 1 ) . The l e n g t h o f t h e one hundred degree a r c was one hundred c e n t i m e t e r s o r one c e n t i m e t e r p e r degree; the r a d i u s o f the a r c was 57.3 c e n t i m e t e r s . The c e n t e r p o i n t o f t h i s a r c 62. THE APPARATUS protruded over the s u b j e c t ' s s i d e of the t a b l e approximately f i v e c e n t i m e t e r s . There were two a d j u s t a b l e wooden stopper b a r s , one a t each end of the s e m i c i r c l e , t h a t served as s t a r t i n g b l o c k s ; p l u s a p o r t a b l e wooden stopper b l o c k used by the experimenter i n p r e s e n t i n g standard movements and i n measuring the s u b j e c t ' s responses. Procedure The standard procedures f o r a l l s u b j e c t s were as f o l l o w s : as each s u b j e c t entered the t e s t i n g s t a t i o n the apparatus was completely covered. Each male s u b j e c t was asked to remove h i s s h i r t and u n d e r s h i r t , ' a n d each female changed i n t o a s l e e v e l e s s j e r s e y p r o v i d e d by the experimenter. T h i s j e r s e y was' c o n s t r u c t e d i n such a manner t h a t i t d i d not i n t e r f e r e w i t h movement of the shoulder j o i n t . Each s u b j e c t was asked to remove any jewelry from h i s neck, p r e f e r r e d hand, or arm. Each s u b j e c t was asked to s i t i n a c h a i r with both f e e t f l a t on the f l o o r and to s i t e r e c t so t h a t h i s back d i d not touch the back of the c h a i r . The s u b j e c t a d j u s t e d the c h a i r p o s i t i o n under d i r e c t i o n s from the experimenter so t h a t he was f a c i n g one of the stoppers a t e i t h e r end of the apparatus w i t h h i s f r o n t a l plane at an angle' of approximately f o r t y - f i v e de-grees to the t a b l e . Right-handed s u b j e c t s faced the l e f t s t opper, and l e f t - h a n d e d s u b j e c t s s a t f a c i n g the r i g h t stopper. A t t h i s p o i n t i n t h e p r o c e d u r e t h e s u b j e c t was b l i n d -f o l d e d and the a p p a r a t u s uncovered. The s u b j e c t was asked t o e x t e n d h i s p r e f e r r e d arm o v e r the a p p a r a t u s , w i t h t h e elbow s t r a i g h t ; t h e f i n g e r s and thumb were p o i n t e d and t o -g e t h e r w i t h t h e palm down. The n o n - p r e f e r r e d arm r e s t e d on t h e s u b j e c t ' s l a p . The s u b j e c t was i n s t r u c t e d t o move, w i t h the e x p e r i m e n t e r ' s g u i d a n c e , h i s p r e f e r r e d s h o u l d e r o v e r t h i s e xtended c e n t e r p o i n t o f the a r c . The s u b j e c t was i n s t r u c t e d t o r e a d j u s t t h e c h a i r i n o r d e r t o move the s h o u l d e r j o i n t o v e r t h i s p o i n t and not t o l e a n - f r o m the body-e r e c t p o s i t i o n . I n e s s e n c e , t h i s c e n t e r p o i n t o f the a r c c l o s e l y s i m u l a t e d the c e n t e r o f r o t a t i o n o f the s h o u l d e r j o i n t , and thus the arm was analogous t o the a r c ' s r a d i u s . The s u b j e c t was t o l d t h a t t h i s p o s i t i o n must be m a i n t a i n e d a t a l l t i m e s d u r i n g the e x p e r i m e n t a l s e s s i o n . The s u b j e c t ' s extended arm was g u i d e d by the e x p e r i -menter's i n s t r u c t i o n s t o the c o r r e s p o n d i n g s t o p p e r , and he was t o l d t h a t t h i s was the s t a r t i n g p o s i t i o n f o r each move-ment and t o r e t u r n t o t h i s p o s i t i o n a f t e r e v e r y movement. The s t o p p e r was a d j u s t e d so t h a t t h e m e d i a l s i d e o f the ex-tended hand was a t the z e r o degree mark ( F i g u r e 2 ) . When th e s u b j e c t had h i s extended arm and hand a t the z e r o degree s t a r t i n g p o s i t i o n , t h e s h o u l d e r a n g l e was 180 d e g r e e s . A t the end o f t h e movement a r c , when the extended 65. SUBJECT IN THE STARTING POSITION arm and hand were a t t h e one hundred degree mark, the s h o u l d e r a n g l e was a p p r o x i m a t e l y e i g h t y degrees. The s u b j e c t was asked t o swing h i s extended arm i n a h o r i z o n t a l p l a n e , k e e p i n g his. hand and arm about one . i n c h above th e a p p a r a t u s a t a l l t i m e s . The s u b j e c t was asked t o swing h i s extended arm i n t h i s manner a t a v e l o c i t y t h a t c o r r e s p o n d e d t o a v e l o c i t y o f a p p r o x i m a t e l y one second f o r e v e r y twenty degrees o f movement and t o keep h i s v e l o c i t y c o n s t a n t f o r a l l movements o f d i f f e r e n t l e n g t h s . B e f o r e the e x p e r i m e n t a l t r i a l s began, the s u b j e c t was a l l o w e d a few p r a c t i c e arm swings t o a c q u a i n t h i m s e l f w i t h the r e q u i r e d movement v e l o c i t y . Throughout th e expe-r i m e n t a l t r i a l s and s t a n d a r d movements the e x p e r i m e n t e r c o r r e c t e d any d e v i a t i o n s from t h i s v e l o c i t y . I n each e x p e r i m e n t a l group t h e r e were one o r two s t a n d a r d movements wh i c h were g i v e n t o the s u b j e c t on each e x p e r i m e n t a l t r i a l . The s t a n d a r d movement was g i v e n t o the s u b j e c t by the e x p e r i m e n t e r i n t h e f o l l o w i n g manner: the e x p e r i m e n t e r h e l d a b l o c k o f wood a t t h e p r e s c r i b e d s t a n d a r d (measured i n degrees) and the s u b j e c t swung h i s extended arm and hand u n t i l t h e m e d i a l • s i d e o f the i n d e x f i n g e r touched t h e wooden b l o c k ( F i g u r e 3 ) . Each s u b j e c t was a l l o w e d t e n s t a n d a r d t r i a l s b e f o r e the e x p e r i m e n t a l t r i a l s began i n o r d e r t o become a c q u a i n t e d w i t h the s t a n d a r d movement, t h a t was b e i n g F i g u r e 3 SUBJECT BEING GIVEN A STANDARD MOVEMENT 68. used. Depending upon which group the s u b j e c t was i n , he was.asked to produce c e r t a i n f r a c t i o n s , magnitudes, and b i s e c t i o n s of the standard movement. Each movement gi v e n as a response by the s u b j e c t was measured i n the f o l l o w i n g manner: the s u b j e c t swung h i s extended hand and arm over the apparatus and h e l d i t over the apparatus f o r about -two seconds at the amplitude which he f e l t corresponded to the requested movement. The experimenter moved a wooden b l o c k ( r i g h t - a n g l e d ) f l u s h with the s u b j e c t ' s medial s i d e of the index f i n g e r of the extended hand without a p p l y i n g p r e s s u r e ; the bottom edge of the b l o c k marked the p o s i t i o n of the s u b j e c t ' s hand on the apparatus. The experimenter recorded t h i s p o s i t i o n t o the n e a r e s t h a l f degree of movement. The s u b j e c t was allowed to r e s t ' a t any time d u r i n g the experiment but was r e q u i r e d to r e s t a t the s t a r t i n g p o s i t i o n and not f o r longer than one minute. The time between t r i a l s was approximately two seconds. Experimental Design The f i f t y s u b j e c t s were randomly a s s i g n e d to one of f i v e experimental groups w i t h the r e s t r i c t i o n s t h a t two r i g h t -handed females, two l e f t - h a n d e d males, and s i x right-handed males appear i n each group t o make a t o t a l o f t e n s u b j e c t s p e r group. The f i v e groups were l a b e l l e d : 1. R a t i o P r o d u c t i o n (R.P.); 2. Magnitude P r o d u c t i o n (M.P.); 3. B i s e c t i o n o f an A s c e n d i n g S e r i e s (B.A.S.); 4. B i s e c t i o n o f a Descending S e r i e s (B.D.S.); 5. C a t e g o r y P r o d u c t i o n (C.P.). E x p e r i m e n t a l C o n d i t i o n s Group I - R a t i o P r o d u c t i o n . Each o f the t e n s u b j e c t s was' g i v e n a s t a n d a r d movement o f one hundred degrees and r e p e a t e d i t u n t i l he became a c q u a i n t e d w i t h i t . The s u b j e c t was t h e n asked t o move t o some f r a c t i o n o f the s t a n d a r d movement — e i t h e r 3/4, 1/2, 1/4, o r 1/3. Each o f the f o u r f r a c t i o n s was p r e s e n t e d f o u r t i m e s each i n random o r d e r so t h a t each s u b j e c t r e c e i v e d s i x t e e n e x p e r i m e n t a l t r i a l s . Each e x p e r -i m e n t a l t r i a l was preceded by t h e s t a n d a r d movement. Group I I - Magnitude P r o d u c t i o n . Each o f the t e n sub-j e c t s was g i v e n a s t a n d a r d movement o f f i f t y d e g r e e s , c a l l e d one hundred, and r e p e a t e d i t u n t i l he was a c q u a i n t e d w i t h i t . The s u b j e c t was th e n asked t o produce movements t h a t c o r r e s p o n d e d t o f i f t y , s e v e n t y - f i v e , one hundred and t w e n t y - f i v e , and one hundred and f i f t y i n r e s p e c t t o the s t a n d a r d o f one hundred. Each o f the f o u r magnitudes was r e p e a t e d f o u r t i m e s , w i t h t h e s t a n d a r d between each t r i a l f o r s i x t e e n e x p e r i m e n t a l t r i a l s p e r s u b j e c t . Group I I I - B i s e c t i o n o f A s c e n d i n g S t i m u l u s V a l u e s . Each o f the t e n s u b j e c t s was g i v e n a s t a n d a r d move-ment o f 6.25 d e g r e e s , and r e p e a t e d i t u n t i l he was a c q u a i n t e d w i t h i t . The s u b j e c t was t h e n asked t o produce a movement t h a t was " t w i c e as g r e a t as the s t a n d a r d " , t h e n a movement t h a t w a s . " t w i c e as g r e a t as t h a t second movement", then a movement t h a t was " t w i c e as g r e a t as t h a t t h i r d movement." I n t h i s manner t h e s u b j e c t i n c r e a s e d h i s movements by d o u b l i n g t h e p r e c e d i n g movement. He produced movements t h a t were 8/1, 4/1, and 2/1 o f the s t a n d a r d 1. The s t a n d a r d , f o l l o w e d by t h e t h r e e movements was r e p e a t e d s i x ti m e s f o r e i g h t e e n e x p e r i m e n t a l t r i a l s p e r s u b j e c t . 71. Group IV - B i s e c t i o n o f Descending S t i m u l u s V a l u e s . Each o f the t e n s u b j e c t s was g i v e n a s t a n d a r d move-ment o f one hundred degrees and r e p e a t e d i t u n t i l he was a c q u a i n t e d w i t h i t . The s u b j e c t was th e n asked t o produce a movement t h a t was " o n e - h a l f o f t h a t movement", then a n o t h e r movement t h a t was " o n e - h a l f t h e second movement", th e n a n o t h e r movement t h a t was " o n e - h a l f the t h i r d movement".- I n t h i s manner the s u b j e c t reduced each movement by o n e - h a l f o f the p r e c e d i n g movement. He produced movements t h a t were 1/2, 1/4, and 1/8 o f the s t a n d a r d f o r they b i s e c t e d t h r e e s u c c e s s i v e movements. The s t a n d a r d f o l l o w e d by t h e t h r e e movements was r e p e a t e d s i x times f o r e i g h t e e n e x p e r i m e n t a l t r i a l s p e r s u b j e c t . Group V - C a t e g o r y P r o d u c t i o n . Each o f the t e n sub-j e c t s was g i v e n two s t a n d a r d movements. One was t h i r t e e n degrees and c a l l e d C a t e g o r y 1; the o t h e r was a movement o f n i n e t y degrees and c a l l e d C a t e g o r y 7. The s t a n d a r d s were r e p e a t e d u n t i l the s u b j e c t was a c q u a i n t e d w i t h them b o t h . The s u b j e c t was th e n t o l d t h a t t h e r e were seven c a t e g o r i e s , each one e q u i d i s t a n t from one a n o t h e r . Then each s u b j e c t was asked t o produce movements t h a t c o r r e s p o n d e d t o the c a t e g o r i e s between 1 and 7 i n c l u s i v e . Both s t a n d a r d s were g i v e n i n s u c c e s s i o n between e x p e r i m e n t a l t r i a l s , and each of the seven c a t e g o r i e s was' g i v e n f i v e times, each i n random o r d e r f o r t h i r t y - f i v e e x p e r i m e n t a l t r i a l p e r s u b j e c t . S t a t i s t i c a l A n a l y s i s Group g e o m e t r i c and a r i t h m e t i c means were c a l c u l a t e d f o r a l l judgments o f r a t i o , magnitude, b i s e c t i o n s and c a t e -gory p r o d u c t i o n groups. These v a l u e s were t r a n s f o r m e d i n t o common l o g a r i t h m v a l u e s . S i n c e the d i f f e r e n c e s between the g e o m e t r i c and a r i t h m e t i c means were s m a l l , the a r i t h m e t i c mean was used as t h e measure o f the s u b j e c t i v e i m p r e s s i o n be cause o f i t s t h e o r e t i c a l r e l a t i o n t o o t h e r c a l c u l a t i o n s . The s t a n d a r d d e v i a t i o n s o f i n d i v i d u a l judgments about the group a r i t h m e t i c mean were c a l c u l a t e d f o r each o f the f i v e groups. The s t a t i s t i c a l a n a l y s i s i n c l u d e d f o u r g r a p h i c p r o c e -dures : 1. The l o g a r i t h m i c v a l u e s o f the s u b j e c t i v e magnitude were p l o t t e d a g a i n s t the l o g a r i t h m i c v a l u e s o f the p h y s i c a l s t i m u l u s f o r Group I (R.P.) and Group I I (M.P.) i n o r d e r t o t e s t f o r S t e v e n s 1 power f u n c t i o n . 73. 2. The l i n e a r v a l u e s ' o f the s u b j e c t i v e i m p r e s s i o n were p l o t t e d a g a i n s t the l o g a r i t h m i c v a l u e s o f the phy-s i c a l s t i m u l u s f o r Group I (R.P.) and Group I I (M.P.) i n o r d e r t o t e s t f o r Fechner's s t r a i g h t l i n e f u n c t i o n . 3. U s i n g t h e r e s u l t s o f the B i s e c t i o n o f A s c e n d i n g and D e s c e n d i n g g r o u p s , t h e two o r d e r s o f p r e s e n t a t i o n were p l o t t e d a g a i n s t each o t h e r o v e r the p h y s i c a l s t i m u l i i n o r d e r t o t e s t f o r h y s t e r e s i s . 4. R e s u l t s o f the C a t e g o r y P r o d u c t i o n group were p l o t t e d a g a i n s t the r a t i o s c a l e o f s u b j e c t i v e magnitude o f a m p l i t u d e o f movement ( i . e . , t h e power f u n c t i o n ) on, b o t h the r a t i o and magnitude p r o d u c t i o n groups. The l i n e s o f b e s t . f i t were c a l c u l a t e d f o r the f u n c t i o n s on the l o g - l o g and l i n e a r - l i n e a r p l o t s f o r Group I (R.P.) and Group I I (M.P.). The q u a d r a t i c c u r v e s o f b e s t f i t were c a l c u l a t e d and p l o t t e d f o r the f u n c t i o n s o f B i s e c t i o n o f A s c e n d i n g and B i s e c t i o n o f Descending S t i m u l u s S e r i e s . The q u a d r a t i c c u r v e s were c a l c u l a t e d and p l o t t e d f o r the C a t e g o r y P r o d u c t i o n (Group V) r e s u l t s a g a i n s t the r a t i o s c a l e o f sub-j e c t i v e magnitude o b t a i n e d from Group I (R.P.) and Group I I (M.P.). The l i n e s and q u a d r a t i c c u r v e s o f b e s t f i t were c a l c u l a t e d by r e g r e s s i o n a n a l y s i s u s i n g the method o f l e a s t s q u a r e s . CHAPTER IV RESULTS AND DISCUSSION R e s u l t s Comparison o f the S u b j e c t i v e I m p r e s s i o n and the  P h y s i c a l S t i m u l u s on Group I (R.P.). The a r i t h m e t i c means, s t a n d a r d d e v i a t i o n s and t h e i r l o g a r i t h m i c v a l u e s , f o r each o f the f o u r judgment f r a c t i o n s ' o f Group I (R.P.) ar e l i s t e d i n T a b l e I . I n o r d e r t o t e s t t h e r e l a t i o n s h i p between the sub-j e c t i v e and p h y s i c a l s c o r e s f o r S t e v e n s ' Power F u n c t i o n , t h e l o g a r i t h m i c mean o f t h e s u b j e c t i v e i m p r e s s i o n was p l o t t e d a g a i n s t t h e l o g a r i t h m o f the p h y s i c a l movement i n degrees ( F i g u r e 4 ) . The f u n c t i o n o b t a i n e d was a s t r a i g h t l i n e o f b e s t f i t , c a l c u l a t e d by r e g r e s s i o n a n a l y s i s u s i n g t h e method o f l e a s t s q u a r e s . The c o r r e l a t i o n between the two v a r i a b l e s was r = .846 (P <.05, d f = 39) (Table I I I ) . To t e s t f o r Fechner's f u n c t i o n between t h e s u b j e c t i v e and p h y s i c a l v a r i a b l e s o f Group I (R.P.), the l o g a r i t h m o f t h e p h y s i c a l s t i m u l u s was p l o t t e d a g a i n s t t h e a r i t h m e t i c means o f the f o u r f r a c t i o n s ( F i g u r e 5 ) . U s i n g a r e g r e s s i o n TABLE I COMPARISON OF THE PHYSICAL DEGREES, SUBJECTIVE ARITHMETIC MEANS, AND STANDARD DEVIATIONS OF THE FOUR FRACTIONS OF GROUP I ( RATIO PRODUCTION) F r a c -t i o n P h y s i c a l Degrees Log. o f P h y s i c a l Degrees S u b j e c t i v e A r i t h m e t i c Log. o f S u b j . A r i t h , Means Stand. Dev. Log. o f S. D. 1/4 25.00 1. 398 40.10 1.592 9.73 .10 1/3 33.34 1.523 50.00 1.689 10.39 .09 1/2 50.00 1.698 67.73 1.828 8.33 .05 3/4 75.00 1. 875 83.40 1.920 6.61 . 03 76. w <L> <u Q > •H -P O (D - n .Q W O t-3 1.0 1.1 1.2 1.3 1.4 1 . 5 1 . 6 1.7 1.8 Log. P h y s i c a l Degrees 1.9 2.0 -e-L i n e o f B e s t F i t R a t i o P r o d u c t i o n .Curve o f B e s t F i t C a t . P r o d u c t i o n .Observed R a t i o P r o d . V a l u e s +S.D. i A (Values + S.D. FIGURE 4 R a t i o and C a t e g o r y P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n Log.-Log. C o o r d i n a t e s 77. FIGURE 5 R a t i o P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n L i n e a r - L o g . C o o r d i n a t e s 78 . a n a l y s i s as above, th e f u n c t i o n o b t a i n e d was a b e s t f i t s t r a i g h t l i n e . The c o r r e l a t i o n between th e two v a r i a b l e s was r = .883 (P < .05, df = 39) (Table I I I ) . S i n c e t h e r e was r e l a t i v e l y l i t t l e d i f f e r e n c e i n the way S t e v e n s ' Power F u n c t i o n o r Fechner's Law d e s c r i b e d t h e s e d a t a , i t was d e c i d e d t o f u r t h e r c l a r i f y t h e r e l a t i o n -s h i p between the s u b j e c t i v e and p h y s i c a l v a r i a b l e s f o r Group I (R.P.) by p l o t t i n g them on l i n e a r - l i n e a r c o o r d i n -a t e s . A g a i n u s i n g the same r e g r e s s i o n a n a l y s i s t h e f u n c -t i o n o b t a i n e d was a s t r a i g h t l i n e ( F i g u r e 6 ) . The c o r r e l a t i o n between th e two v a r i a b l e s was r= .8 82 (P < .05, df = 39) (Table I I I ) . Comparison o f the S u b j e c t i v e I m p r e s s i o n and t h e P h y s i c a l  S t i m u l u s on Group I I (M.P.)- The a r i t h m e t i c means, s t a n d a r d d e v i a t i o n s and the l o g a r i t h m i c v a l u e s f o r each o f t h e f o u r judgment magnitudes of Group I I (M.P.) a r e l i s t e d i n T a b l e I I . A n a l y s i s of t h e s e d a t a was done i n an i d e n t i c a l manner t o t h a t completed on Group I (R.P.). The r e s u l t s were v e r y s i m i l a r , i n t h a t the b e s t f i t s t r a i g h t l i n e t h a t t e s t e d S t e v e n s ' Power F u n c t i o n ( F i g u r e 7) had a h i g h c o r r e l a t i o n (r = .956, P <.05, d f = 3 9 ) . (Table I I I ) , w h i l e a t e s t f o r F echner's Law ( F i g u r e 8) a l s o produced a b e s t f i t s t r a i g h t l i n e w i t h a c o r r e l a t i o n o f r = .945 (P <.05,df=39)(Table I I I ) . 79. R a t i o P r o d u c t i o n Judgments of* A m p l i t u d e o f Movement i n L i n e a r - L i n e a r C o o r d i n a t e s 80 TABLE I I COMPARISON OF THE PHYSICAL DEGREES, SUBJECTIVE ARITHMETIC MEANS AND STANDARD DEVIATIONS OF THE FOUR MAGNITUDES OF GROUP I I (MAGNITUDE PRODUCTION) Magni-tude 50 75 125 150 P h y s i c a l Degrees 25.00 37.50 62.50 75.00 Log. Phy. Degrees 1. 398 1.574 1.796 1. 875 Subj . A r i t h , Log. A r i t h , Means Means Standard D e v i a t i o n Log, S.D, 30.99 40.81 72.20 80 . 05 1.486 1.609 1.857 1.901 5.29 3.88 6.27 9 . 22 .07 04 .04 05 81. 2.0 r -w <P 0) U Cn CD Q <D > O (U •t—i X! CO o o '.0 1.1 1.2 1 . 3 1 . 4 1.5 .1.6 1.7 1.8 1.9 2.0 Log. o f P h y s i c a l Degrees L i n e o f B e s t F i t Magnitude P r o d u c t i o n Curve o f B e s t F i t C a t e g o r y P r o d u c t i o n •A-Observed Magnitude P r o d . V a l u e s + S.D. — Observed C a t e g o r y P r o d u c t i o n V a l u e s + S.D, FIGURE 7 Magnitude and C a t e g o r y P r o d u c t i o n Judgments Am-p l i t u d e o f Movement i n Log.-Log. C o o r d i n a t e s 82. Magnitude P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n L i n e a r - L o g . C o o r d i n a t e s 83. As i n the a n a l y s i s o f Group I , t h e s e d a t a were then p l o t t e d on l i n e a r - l i n e a r c o o r d i n a t e s ( F i g u r e 9 ) , and the r e s u l t i n g f u n c t i o n was a b e s t f i t s t r a i g h t l i n e w i t h a c o r r e l a t i o n o f r = .953 (P <.05, d f - 39) (Table I I I ) . Comparison o f t h e C o r r e l a t i o n s f o r the F u n c t i o n s b e t - ween t h e S u b j e c t i v e and P h y s i c a l V a r i a b l e s f o r Groups I  (R.P.) and I I (M.P.) I n o r d e r t o d e t e r m i n e i f S t e v e n s ' Power F u n c t i o n , F echner's Law, and t h e l i n e a r - l i n e a r f u n c -t i o n s f i t t e d t he d a t a o f Groups I (R.P.) and I I (M.P.) e q u a l l y w e l l , a "Z" t e s t (101) was computed t o d e t e r m i n e i f the c o r r e l a t i o n s were s i g n i f i c a n t l y d i f f e r e n t . f r o m each o t h e r . The- c o r r e l a t i o n f o r each o f the t h r e e f u n c t i o n s o f Groups I (R.P.) and I I (M.P.) a r e l i s t e d i n T a b l e I I I . I n comparing the t h r e e c o r r e l a t i o n s o f Group I (R.P.), no s i g n i f i c a n t d i f f e r e n c e s were found (Table IV) u s i n g the .05 l e v e l o f s i g n i f i c a n c e . I n comparing the t h r e e c o r r e l a t i o n s o f Group I I (M.P.), no d i f f e r e n c e between any two c o r r e l a t i o n s r e a c h e d s i g n i f i c -ance . When t a k e n c o l l e c t i v e l y , the r e s u l t s i n d i c a t e t h a t t h e s e t h r e e s t r a i g h t l i n e f u n c t i o n s , t h a t were f i t t o the d a t a o f 84. P h y s i c a l Degrees Observed V a l u e s + S.D. — L i n e o f B e s t F i t FIGURE 9 Magnitude P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n L i n e a r - L i n e a r C o o r d i n a t e s 85. TABLE I I I CORRELATIONS FOR THE THREE FUNCTIONS OF GROUPS I (RATIO PRODUCTION) AND I I (MAGNITUDE PRODUCTION) AND PERCENT-AGE OF ACCOUNTED VARIANCE No, F u n c t i o n Group I(R.P.) r % Acc. V a r . Group II(M.P.) % Acc. V a r . 1. 3. Stevens 1 Power Func-t i o n (Log^Log) Fechner's Law ( l i n e a r -l o g . ) L i n e a r - L i n e a r • .846 883 882 71. 51 .956 77.97 945 77.78 953 91.46 89.23 90.78 86. TABLE I V 11 z ii TEST FOR D I F F E R E N C E BETWEEN THE THREE CORRELATIONS OF GROUPS-I (RATIO PRODUCTION) AND I I (MAGNITUDE PRODUCTION)* Group I (R.P.) Group I I (M.P.) •r —r r — T r — T 689 593 094 r — r T — T r — r 1 2 1 3 2 3 443 232 .210 F o r t w o - t a i l e d t e s t , P=.05, "Z" r e q u i r e d was 1.9 5 b o t h Groups I (R.P.) and I I ( M . P . ) , f i t the r e l a t i o n s h i p between t h e s u b j e c t i v e and p h y s i c a l v a r i a b l e s o f b o t h groups e q u a l l y w e l l . Comparison o f t h e S u b j e c t i v e and P h y s i c a l S c o r e s o f the  B i s e c t i o n o f A s c e n d i n g S e r i e s (Group I I I ) w i t h t h o s e o f  B i s e c t i o n o f Descending S e r i e s (Group I V ) . I n o r d e r t o t e s t f o r an h y s t e r e s i s e f f e c t , b o t h t h e B i s e c t i o n o f A s c e n d i n g 87. and Descending s t i m u l u s s e r i e s were p l o t t e d a g a i n s t de-grees o f movement ( F i g u r e 10) so t h a t the same s t i m u l i t h a t appeared i n b o t h s e r i e s c o u l d be compared. The phy-s i c a l s t i m u l u s , s u b j e c t i v e a r i t h m e t i c means, and s t a n d a r d d e v i a t i o n s o f the t h r e e b i s e c t i o n s ' o f Group I I I (B i . A s . ) and Group IV (Bi.Des.) a r e l i s t e d i n T a b l e V. The q u a d r a t i c c u r v e s o f b e s t f i t , as c a l c u l a t e d by r e g r e s s i o n a n a l y s i s u s i n g the method o f l e a s t s q u a r e s , d i d n o t show a h y s t e r e s i s l o o p ( F i g u r e 10). The p e r c e n t a g e o f t o t a l v a r i a n c e a c c o u n t e d f o r by the c u r v e o f b e s t f i t f o r Group I I I (B i . A s . ) was 99.98, and 99.90 f o r Group IV ( B i . Des.) . Comparison o f t h e S u b j e c t i v e Scores o f Ca t e g o r y P r o d u c t i o n  (Group V) w i t h t h e R a t i o S c a l e o f S u b j e c t i v e Magnitude Ob- t a i n e d from R a t i o P r o d u c t i o n (R.P.). The p h y s i c a l s t i m u l u s , s u b j e c t i v e a r i t h m e t i c means, s t a n d a r d d e v i a t i o n s , and t h e i r l o g a r i t h m i c v a l u e s f o r t h e seven c a t e g o r i e s o f Ca t e g o r y P r o -d u c t i o n (Group V ) , a r e . l i s t e d i n T a b l e V I . To t e s t f o r t h e c h a r a c t e r i s t i c n o n l i n e a r f u n c t i o n o f a p r o t h e t i c continuum when c a t e g o r y p r o d u c t i o n i s employed, the s u b j e c t i v e a r i t h m e t i c means o f each o f the seven c a t e g o r i e s o f Group V(C.P.) were p l o t t e d a g a i n s t the r a t i o s c a l e o f 88. CO <D •H U <U CO CO e 4-> 10 C •H •O CJ <U o CO 100 (S) 3T5 3T3 5TJ 515—71 Degrees o f Movement Curves o f B e s t F i t D e s c e n d i n g Curves o f B e s t F i t A s c e n d i n g i - @ 1 Observed Desc. Sub j . V a l u e s + S.D. - i Observed A s c . Sub j . V a l u e s + S.D. 50 25 12 TuO D E S C E N D I N G S T I M U L U S S 5 s R I E S FIGURE 10 Comparison o f t h e F u n c t i o n s o f t h e B i s e c t i o n o f A s c e n d i n g S e r i e s and B i s e c t i o n o f D e s c e n d i n g S e r i e s 89. TABLE V COMPARISON OF THE PHYSICAL DEGREES,SUBJECTIVE ARITHMETIC MEANS, AND STANDARD DEVIATIONS'OF THE THREE BISECTIONS OF GROUP I I I (BISECTION OF A ASCENDING SERIES) AND GROUP IV (BISECTION OF A DESCENDING SERIES). B i s e c t i o n Phys. Deg. S u b j . A r i t h . Mean S t a n d a r d D e v i a t i o n Group I I I t w i c e as g r e a t 12.50 19 .50 3.68 (B i . A s . ) t w i c e as g r e a t 25.00 40.57 8.55 s t a n d a r d t w i c e as g r e a t 50.00 64.43 15.19 = 6.259 Group IV 1/2 l e s s 50. 00 65.87 7.40 (Bi.Des.) 1/2 l e s s 25. 00 41.88 11. 26 s t a n d a r d 1 / 2 . l e s s 12.50 24.36 11.36 = lOOo TABLE VI COMPARISON OF THE PHYSICAL DEGREES, SUBJECTIVE ARITHMETIC MEANS, AND STANDARD DEVIATIONS OF THE SEVEN CATEGORIES OF GROUP V Phys. Log. o f A r i t h . Log. o f S t a n d a r d Log. o f Ca t . Deg. Phy. Deg. Mean A r i t h . Mean D e v i a t i o n S.D. 1 13.0 1.114 16.18 1.209 4.12 0.615 2 26.0 1. 415 34.09 1.532 6.77 0.830 3 39.0 1.591 46.04 1,663 8.96 0.952 4 52.0 1.716 60.38 1. 780 7.87 0.896 5 65.0 1.813 72.91 1.862 4.84 0.684 6 78.0 1.892 81.26 1. 909 2.92 0. 465 7 90.0 1.954 93 . 79 1.972 3.09 0.489 s u b j e c t i v e magnitude ( i . e . , t h e power f u n c t i o n ) o b t a i n e d from Group I (R.P.). The f u n c t i o n o b t a i n e d was a q u a d r a t i c c u r v e , c a l c u l a t e d by r e g r e s s i o n a n a l y s i s u s i n g the method of l e a s t s q u a r e s , w h i c h was concave upward ( F i g u r e 4 ) . 91. Comparison o f t h e S u b j e c t i v e S c o r e s o f C a t e g o r y Produc-t i o n (Group V) w i t h t h e R a t i o S c a l e o f S u b j e c t i v e Magnitude  O b t a i n e d from Magnitude P r o d u c t i o n (M.P.). As i n t h e im-m e d i a t e l y p r e c e d i n g a n a l y s i s , the s u b j e c t i v e a r i t h m e t i c means o f each o f t h e seven c a t e g o r i e s o f Group V ( C P . ) (Table VI) were p l o t t e d a g a i n s t the r a t i o s c a l e o f s u b j e c t i v e magnitude o b t a i n e d from Group I I (M.P.). U s i n g the same r e g r e s s i o n a n a l y s i s , the f u n c t i o n o b t a i n e d was a q u a d r a t i c c u r v e w h i c h was concave upward ( F i g u r e 7 ) . Comparison o f the S u b j e c t i v e A r i t h m e t i c Means and  P h y s i c a l S t i m u l i o f t h e Seven C a t e g o r i e s o f Group V ( C P . ) . S i n c e the d a t a o f Groups I (R.P.), and I I (M.P.) were d e s c r i b e d e q u a l l y w e l l by t h r e e f u n c t i o n s , ( i . e . , S t e v e n s ' Power F u n c t i o n , Fechner's Law, and a l i n e a r - l i n e a r p l o t ) i t seemed i n a p p r o p r i a t e t o p l o t the d a t a o b t a i n e d from c a t e g o r y p r o d u c t i o n (Group V) a g a i n s t the s o - c a l l e d power f u n c t i o n d a t a . T h e r e f o r e , t o a n a l y z e the c a t e g o r y p r o d u c t i o n d a t a t o a g r e a t e r e x t e n t , t h e s e d a t a were p l o t t e d a g a i n s t t h e l i n e a r v a l u e s o f t h e p h y s i c a l s t i m u l i . U s i n g r e g r e s s i o n a n a l y s i s by t h e method o f l e a s t s q u a r e s , the f u n c t i o n ob-t a i n e d was a b e s t f i t s t r a i g h t l i n e ( F i g u r e 11) w i t h a c o r -r e l a t i o n o f r = .970 (P <.05, d f = 39). 92. 0 10 20 30 40 50 60 70 80 90 100 S u j b j e c t i v e Degrees o f Movement i ^ 1 Observed V a l u e s + S.D. ________ L i n e o f B e s t F i t FIGURE 11 C a t e g o r y P r o d u c t i o n Judgments o f A m p l i t u d e o f Movement i n L i n e a r - L i n e a r C o o r d i n a t e s D i s c u s s i o n S t e v e n s ' power f u n c t i o n , a c h a r a c t e r i s t i c o f p r o t h e t i c c o n t i n u a , and Fechner's f u n c t i o n , a c h a r a c t e r i s t i c o f meta-t h e t i c c o n t i n u a , b o t h appeared t o d e s c r i b e the r e l a t i o n s h i p between th e s u b j e c t i v e and p h y s i c a l v a r i a b l e s o f Groups I (R.P.) and I I (M.P.) e q u a l l y w e l l , as t h e c o r r e l a t i o n s r e -p r e s e n t i n g each f u n c t i o n were n o t s i g n i f i c a n t l y d i f f e r e n t from each o t h e r (Table I V ) . One e x p l a n a t i o n t h a t would account, f o r t h i s i s the p o s s i b i l i t y t h a t t h e r e i s a power f u n c t i o n r e l a t i o n s h i p i n w h i c h t h e exponent i s e q u a l t o one.-Such a f u n c t i o n . w o u l d f i t S t e v e n s 1 power f u n c t i o n and a l s o p l o t as a s t r a i g h t l i n e on l i n e a r - l i n e a r c o o r d i n a t e s . S i n c e the d a t a o f Groups I (R.P.) and I I (M.P.) b o t h p l o t t e d as s t r a i g h t l i n e s on l i n e a r - l i n e a r c o o r d i n a t e s ( F i g u r e s 6 and 9 ) , t h e e v i d e n c e from t h i s p a r t i c u l a r a n a l y s i s would suggest t h a t the k i n e s t h e s i s o f a m p l i t u d e o f movement i s s u b s e r v e d by a p r o t h e t i c p r o c e s s . N e v e r t h e l e s s , t h e s e r e s u l t s by them-s e l v e s a r e not u n e q u i v o c a l and f u r t h e r i n t e r p r e t a t i o n o f the d a t a from the t o t a l e x periment must be made b e f o r e any c o n c r e t e c o n c l u s i o n s can be r e a c h e d . I n c o n t r a d i c t i o n t o the above r e s u l t s , s u p p o r t f o r the f a c t t h a t t h e movement under s t u d y i n . t h i s e x p e r i m e n t was s u b s e r v e d by a m e t a t h e t i c p r o c e s s came from the l a c k o f a h y s t e r e s i s e f f e c t ( F i g u r e 1 0 ) . I n f a c t , t h e q u a d r a t i c c u r v e r e l a t i n g s u b j e c t i v e magnitudes o f t h e a s c e n d i n g b i s e c t i o n s a l m o s t o v e r l a p p e d the q u a d r a t i c c u r v e r e l a t i n g s u b j e c t i v e magnitudes of the d e s c e n d i n g b i s e c t i o n s . T h i s l a c k o f h y s -t h e r e s i s i s a c h a r a c t e r i s t i c o f c o n s t a n t s e n s i t i v i t y and m e t a t h e t i c p r o c e s s e s . Thus a g i v e n s t i m u l u s would appear the same b o t h i n an a s c e n d i n g and d e s c e n d i n g o r d e r . E i s l e r and O t t a n d e r (19) have s t a t e d the " h y s t e r e s i s l o o p " e f f e c t found on p r o t h e t i c c o n t i n u a i s m o s t l y due t o the " s u b j e c t i v e z e r o " o r t h e s u b j e c t i v e i m p r e s s i o n o f the z e r o p o i n t not b e i n g c o n s t a n t . These a u t h o r s (19) have s t a t e d t h a t i n me-t a t h e t i c c o n t i n u a h y s t e r e s i s was p r e v e n t e d by the p r e c i s e knowledge o f the s u b j e c t i v e z e r o . T h i s f a c t c o u l d p o s s i b l y e x p l a i n the l a c k o f h y s t e r e s i s i n the p r e s e n t e x p e r i m e n t s i n c e the s u b j e c t i v e z e r o , o r s t a r t i n g p o i n t , w a s . c o n s t a n t and known t o the s u b j e c t . C o n f l i c t i n g r e s u l t s , i n terms of d i s c r i m i n a t i n g between a p r o t h e t i c o r m e t a t h e t i c p r o c e s s , were o b t a i n e d f o r the c a t e g o r y p r o d u c t i o n d a t a of Group V. F i g u r e s 4 and 7 show a concave upward f u n c t i o n when the c a t e g o r y d a t a a r e p l o t t e d a g a i n s t the power f u n c t i o n s d e r i v e d from r a t i o and magnitude p r o d u c t i o n . The f a c t t h a t a concave f u n c t i o n was o b t a i n e d i n d i c a t e s n o n - c o n s t a n t s e n s i t i v i t y o v e r the range of move-ment, and thus t h e s e r e s u l t s i n f e r a p r o t h e t i c p r o c e s s under-l y i n g a m p l i t u d e o f movement. However, some doubt about the meaning o f t h e s e r e s u l t s i s r a i s e d by t h e f a c t t h a t Stevens (82, 90) r e p o r t s t h a t on t h e v a s t m a j o r i t y o f p r o t h e t i c c o n t i n u a , the f u n c t i o n r e l a t i n g c a t e g o r y p r o d u c t i o n t o t h e power f u n c t i o n was concave downward. F u r t h e r t o t h i s , as i t has been p r e v i o u s l y e s t a b l i s h e d i n the p r e s e n t d i s c u s s i o n t h a t the r e s u l t s t o t h i s p o i n t a r e a t b e s t a m b i g u o u s , • i t was d e c i d e d t o f u r t h e r a n a l y z e , the c a t e g o r y p r o d u c t i o n d a t a . S i n c e t h e r e was some doubt as t o whether a power f u n c t i o n was t h e b e s t way t o d e s c r i b e t h e r e l a t i o n s h i p between a m p l i t u d e o f movement and the s u b j e c t i v e judgment o f a m p l i t u d e , i t was" reasoned t h a t t h e p l o t o f c a t e g o r y p r o d u c t i o n d a t a a g a i n s t t h e o b t a i n e d power f u n c t i o n s may have been m e a n i n g l e s s . That i s , i t may be m e a n i n g l e s s i n t h a t the c a t e g o r y p r o d u c t i o n da-t a were p l o t t e d a g a i n s t a f u n c t i o n ( i . e . , t he power f u n c t i o n ) t h a t d i d not a c c u r a t e l y d e s c r i b e the d a t a . I n f u r t h e r a n a l y z -i n g t h e c a t e g o r y p r o d u c t i o n d a t a , a l i n e a r f u n c t i o n was found when t h e mean c a t e g o r y r e s p o n s e s were p l o t t e d a g a i n s t t h e a c t u a l c a t e g o r y v a l u e s ( F i g u r e 1 1 ) . These r e s u l t s s u g g e s t e d t h a t t h e r e i s c o n s t a n t s e n s i t i v i t y o v e r the range o f movement which c h a r a c t e r i z e s a s e n s o r y system s u b s e r v e d by a m e t a t h e t i c p r o c e s s . T h i s r e s u l t adds w e i g h t t o t h e s u g g e s t i o n t h a t t h e concave upward f u n c t i o n s o f Group V do - not i m p l y an under-l y i n g p r o t h e t i c continuum. I f a m p l i t u d e o f movement was sub-s e r v e d by a p r o t h e t i c continuum, t h e f u n c t i o n on the l i n e a r -l i n e a r - c o o r d i n a t e s s h o u l d have been n o n l i n e a r , due t o the no n c o n s t a n t s e n s i t i v i t y a l o n g the continuum. Thus when the e x p e r i m e n t a l r e s u l t s a r e t a k e n as a whole, the f i n d i n g s tended t o s u p p o r t the c o n c l u s i o n t h a t a m p l i t u d e o f movement i s s u b s e r v e d by a m e t a t h e t i c p r o c e s s . T h i s agrees w i t h a g r e a t d e a l o f the p h y s i o l o g i c a l e v i d e n c e d e a l i n g w i t h t h e r o l e and f u n c t i o n o f the r e c e p t o r s , which a r e c o n s i d e r e d r e s p o n s i b l e f o r k i n e s t h e s i s . A c c o r d i n g t o Stevens ( 8 2 ) , d i s c r i m i n a t i o n on a m e t a t h e t i c continuum i s media t e d by a s u b s t i t u t i v e p r o c e s s a t the p h y s i o l o g i c a l l e v e l , and would r e q u i r e a q u a l i t a t i v e r e c e p t o r mechanism. A s t i m u l u s change would cause a d i f f e r e n t p o p u l a t i o n o f r e c e p t o r s t o be a c t i v a t e d w i t h no i n c r e a s e i n t h e numbers o f r e c e p t o r s r e s p o n d i n g . T h i s p r o c e s s o f r e c e p t o r s u b s t i -t u t i o n has been shown by many a u t h o r s (3,,9, 14, 36, 54/ 58, 63, 79, 80, 97) t o be o p e r a t i n g i n the k i n e s t h e t i c r e -c e p t o r s o f t h e j o i n t c a p s u l e . These a u t h o r s have i n d i c a t e d t h a t d i f f e r e n t j o i n t a n g l e s cause d i f f e r e n t r e c e p t o r s t o f i r e . Some f i r e a t complete f l e x i o n , o t h e r s a t complete e x t e n s i o n , and o t h e r s between f l e x i o n and e x t e n s i o n . Thus j o i n t p o s i t i o n and degree of movement would be d e t e r m i n e d by the d i s c h a r g e r a t e o f a s p e c i f i c group o f r e c e p t o r s . T h e r e f o r e the r e s u l t s o f the p r e s e n t e x p e r i m e n t , i n c o n j u n c -t i o n w i t h p r e v i o u s p h y s i o l o g i c a l e v i d e n c e , would suggest t h a t the j o i n t r e c e p t o r s s i g n a l the j o i n t ' s p o s i t i o n and degree o f movement by the d i s c h a r g e o f a s p e c i f i c group o f r e c e p t o r s , o r i n o t h e r words, s i g n a l a m p l i t u d e o f move-ment m e t a t h e t i c a l l y . Whether c o r t i c a l c e l l s , w h i c h have been shown t o be conn e c t e d t o t h e j o i n t r e c e p t o r s r e s p o n s i b l e f o r k i n e s t h e s i s (60, 2 8 ) , a l s o f u n c t i o n m e t a t h e t i c a l l y , i s not c l e a r l y s u p p o r t e d by p a s t p h y s i o l o g i c a l e v i d e n c e . The r e s u l t s o f the p r e s e n t e x p e r i m e n t suggest t h a t the s u b j e c t i v e i m p r e s -s i o n o f the a m p l i t u d e o f movement i s formed m e t a t h e t i c a l l y . Y e t M o u n t c a s t l e , P oggio and Werner (62) have found t h a t the t h i r d o r d e r j o i n t r e c e p t o r a f f e r e n t s , w h i c h are l o c a t e d i n t h e v e n t r o b a s a l complex o f the thalamus, f i r e q u a n t i t a t i v e l y t o changes i n j o i n t a n g l e s . These a u t h o r s found t h a t a power N f u n c t i o n o f the t y p e : R =.KS , d e s c r i b e d the r e l a t i o n s h i p between j o i n t a n g l e and t h a l a m i c c e l l a c t i v i t y . The a u t h o r s p r o posed t h a t m e t a t h e t i c i n f o r m a t i o n d e r i v e d from j o i n t r e -c e p t o r s was- t r a n s f o r m e d i n t o p r o t h e t i c i n f o r m a t i o n a t t h e thalamus. As t h e r e s u l t s o f t h e p r e s e n t e xperiment suggest t h a t the f i n a l s u b j e c t i v e i m p r e s s i o n i s formed m e t a t h e t i c a l l y , a f u r t h e r t r a n s f o r m a t i o n may o c c u r a f t e r the t h i r d o r d e r a f f e r e n t s i n the thalamus. I n o t h e r words, p r o t h e t i c i n f o r m -a t i o n about j o i n t p o s i t i o n i n t h e thalamus may undergo y e t a n o t h e r o r a s e r i e s of o t h e r t r a n s f o r m a t i o n s b e f o r e the f i n a l 98. i m p r e s s i o n i s formed. As the t h i r d - o r d e r r e l a y o f a f f e r e n t s i n t h e thalamus i s c o n s i d e r e d e a r l y i n - t h e e n t i r e n e u r a l c h a i n between s t i m u l i and response (62) i t i s q u i t e p r o b a b l e t h a t a s e r i e s o f changes o c c u r i n the n e u r a l i m p u l s e b e f o r e the f i n a l i m p r e s s i o n i s formed. I t i s a l s o p o s s i b l e t h a t the m e t a t h e t i c k i n e s t h e t i c i n f o r m a t i o n passes t h r o u g h the thalamus w i t h o u t b e i n g a l t e r e d , so t h a t the i n f o r m a t i o n r e a c h -i n g the c o r t e x i s m e t a t h e t i c a l l y based. Support f o r t h i s l a t t e r p o s i t i o n was g i v e n by Mount-c a s t l e and P o w e l l (63) who found t h a t c e l l s i n t h e s e n s o r y a r e a s o f the c o r t e x , w h i c h a r e con n e c t e d t o t h e j o i n t r e c e p -t o r s , a r e a r r a n g e d i n a t o p o g r a p h i c a l p a t t e r n . These a u t h o r s have s t a t e d t h a t body a n g l e s , and changes i n them, a r e d e p i c t e d by t h e p a t t e r n o f a c t i v i t y o f the s e c o r t i c a l c e l l s . T h i s would s u g g e s t t h a t j o i n t p o s i t i o n and movement a r e s i g n a l l e d by a s p e c i f i c group o f a c t i v a t e d c o r t i c a l c e l l s , o r i n o t h e r words, m e t a t h e t i c a l l y . As t h e a c t i v i t y o f t h e s e s e n s o r y a r e a c o r t i c a l c e l l s would o c c u r l a t e i n the n e u r a l c h a i n , the s u g g e s t i o n i s s u p p o r t e d t h a t judgments o f a m p l i -tude o f movement a r e formed by a m e t a t h e t i c p r o c e s s . Wood (98), who used s i m i l a r methods as t h o s e used i n the p r e s e n t e x p e r i m e n t , showed t h a t the s u b j e c t i v e i m p r e s s i o n o f speed o f a s e l f - i n i t i a t e d arm movement was r e l a t e d t o a c t u a l speed by a p r o t h e t i c continuum. Wood's r e s u l t s and 99. c o n c l u s i o n s a r e s u p p o r t e d by Smith (80) and W i l l i a m s (9 7 ) , as they have s t a t e d t h a t speed o f movement was i n d i c a t e d by the r a t e o f t r a n s i e n t d i s c h a r g e s o f the• j o i n t r e c e p t o r s t o movement -- t h e f a s t e r the movement, the q u i c k e r the d i s c h a r g e r a t e o f the a c t i v a t e d group o f j o i n t r e c e p t o r s r e s p o n s i b l e f o r t h a t a n g l e . There-f o r e , speed o f movement was coded q u a n t i t a t i v e l y by fr e q u e n c y o f c h a n g i n g r e c e p t o r d i s c h a r g e . Two o t h e r s e n s o r y c o n t i n u a w h i c h c o n t a i n a k i n e s -t h e t i c component have a l s o been shown t o be s u b s e r v e d by a p r o t h e t i c p r o c e s s . These i n c l u d e f o r c e o f h a n d g r i p , u s i n g a hand dynamometer ( 8 1 ) , and judgments o f h e a v i n e s s , u s i n g l i f t e d w e i g h t s . (94).' That speed o f movement, judgments o f h e a v i n e s s , and f o r c e o f h a n d g r i p a r e p r o t h e t i c , does'not c o n t r a d i c t the r e s u l t s o f t h e p r e s e n t e x p e r i m e n t , w h i c h s u g g e s t s t h a t judgments o f a m p l i t u d e o f movement a r e formed m e t h a t h e t i c a l -l y , as t h e r e a r e many d i f f e r e n t a s p e c t s o f k i n e s t h e s i s and each may f u n c t i o n d i f f e r e n t l y . K i n e s t h e t i c Cues. T h i s s e c t i o n o f the d i s c u s s i o n - w i l l d e a l w i t h the s u b j e c t i v e r e p o r t s o f t h e e x p e r i m e n t e r as w e l l as r e -p o r t s from the s u b j e c t s . An attempt w i l l be made t o r e l a t e 100. t h e s e i m p r e s s i o n s t o s c i e n t i f i c f i n d i n g s , .in an attempt t o d e t e r m i n e what f a c t o r s a r e i n v o l v e d i n d i s c r i m i n a t i n g a m p l i t u d e o f movement. I n , t h e p r e s e n t e x p e r i m e n t , a t t e n t i o n t o in c o m i n g k i n e s t h e t i c i n f o r m a t i o n appeared t o be l o s t d u r i n g the m i d d l e range o f t h e movement. An e x p l a n a t i o n f o r t h i s phenomenon was found i n a s t u d y by K e e l e and Posner (30) who r e p o r t e d t h a t a t t e n t i o n t o k i n e s t h e t i c feedback was g r e a t e s t a t the b e g i n n i n g , d e c r e a s e d t o a low i n . t h e m i d d l e , and s l i g h t l y i n c r e a s e d a t the end o f the movement. Because o f t h i s l a c k o f a t t e n t i o n , t h e s u b j e c t may be. u s i n g f i n a l p o s i t i o n o f the j o i n t r a t h e r than a m p l i t u d e o f movement as a cue i n k i n e s t h e t i c judgments. T h i s i s s u p p o r t e d by P a i l l a r d and Brouchon (69) who have s u g g e s t e d t h a t k i n e s t h e t i c i n f o r m a t i o n about j o i n t movement comes from the f i n a l dynamic phase o f the movement, not from the f i n a l s t a t i c p o s i t i o n o r t o t a l movement. Many o f the s u b j e c t s o f the p r e s e n t e x p e r i m e n t r e p o r t e d t h a t much o f t h e a v a i l a b l e k i n e s t h e t i c i n f o r m a t i o n was,of l i m i t e d u se, f o r they were not a b l e t o use i t e f f e c t i v e l y i n f o r m i n g s u b j e c t i v e magnitude. They s t a t e d t h a t t h e r e was no comparison mechanism a v a i l a b l e t o which t h e i n c o m i n g k i n -e s t h e t i c i n f o r m a t i o n c o u l d be c o n t r a s t e d . Yet> i n s p i t e o f 101. t h i s , i t i s s u r p r i s i n g how a c c u r a t e the k i n e s t h e t i c r e -p r o d u c t i o n s o f the p r e s e n t e x p e r i m e n t and o t h e r s (45) were. P a i l l a r d and Brouchon (69) have su g g e s t e d t h a t t h e r e i s a comparator mechanism, c a l l e d the " s p a t i a l r e f e r e n c e system", t o w h i c h i n c o m i n g k i n e s t h e t i c i n f o r m a t i o n can be. c o n t r a s t e d . T h i s r e f e r e n c e system would be o f l i m i t e d use i n t h e p r e s e n t e x p e r i m e n t , however, f o r the movements used were u n f a m i l i a r t o the s u b j e c t . S i n c e t h e r e was no knowledge o f r e s u l t s t h e r e s h o u l d n o t be any i n f o r m a t i o n i n t h i s r e f e r e n c e system. I n t h a t c a s e , the i n c o m i n g k i n e s t h e t i c i n f o r m a t i o n can o n l y be compared t o the memory o f t h e sub-j e c t i v e i m p r e s s i o n o f the g i v e n s t a n d a r d movement. CHAPTER V SUMMARY AND CONCLUSIONS The purpose o f t h i s s t u d y was t o i n v e s t i g a t e the p s y c h o p h y s i c s o f a c t i v e k i n e s t h e s i s . I n essence the s t u d y i n v e s t i g a t e d whether t h e s u b j e c t i v e i m p r e s s i o n o f a m p l i t u d e o f movement o f s e l f - i n i t i a t e d , s h o u l d e r l a t e r a l f l e x i o n o f th e p r e f e r r e d arm was formed t h r o u g h a p r o t h e t i c , o r meta-t h e t i c continuum as o u t l i n e d by Stevens (82). F i f t y v o l u n t e e r s u b j e c t s , b o t h male and f e m a l e , r i g h t and l e f t handed, were randomly a s s i g n e d t o f i v e groups o f e q u a l N. Each group was randomly a s s i g n e d t o one o f f i v e e x p e r i m e n t a l c o n d i t i o n s l a b e l l e d : R a t i o P r o d u c t i o n , Magnitude P r o d u c t i o n , B i s e c t i o n of A s c e n d i n g S e r i e s , B i s e c t i o n o f Descending S e r i e s and C a t -egory P r o d u c t i o n . The R a t i o P r o d u c t i o n group was g i v e n a s t a n d a r d movement of one hundred degrees and asked t o produce movements t h a t were 1/4, 1/2,-1/3, 3/4 o f the s t a n d a r d movement. Each f r a c -t i o n a l movement was r e p e a t e d randomly f o u r t i m e s w i t h t h e g i v e n s t a n d a r d p r e c e d i n g each movement. The Magnitude Produc-t i o n group was given' a s t a n d a r d movement o f f i f t y degrees t h a t 103. was a r b i t r a r i l y c a l l e d 100. The s u b j e c t was then asked t o produce movements t h a t , when compared t o the s t a n d a r d movement r e p r e s e n t e d movements o f 50, 75, 125 o r 150. Each magnitude was produced f o u r times, a t random w i t h the s t a n d a r d g i v e n b e f o r e each movement. The B i s e c t i o n o f A s c e n d i n g S e r i e s group was g i v e n a s t a n d a r d o f 6.25 degrees and then was asked t o produce a movement t w i c e t h a t , then a movement t w i c e t h a t o f the second movement, then a movement t w i c e t h a t o f the t h i r d movement. The< t h r e e i n c r e a s i n g move-ments were produced i n s u c c e s s i o n f o l l o w i n g t h e s t a n d a r d . Each s e t o f t h r e e movements was r e p e a t e d s i x timesw The B i s e c t i o n o f Descending S e r i e s group was g i v e n a s t a n d a r d o f one hundred degrees and the n asked t o produce a movement o n e - h a l f t h a t movement, t h e n a movement o n e - h a l f t h a t o f the second movement, then a movement o n e - h a l f t h a t o f the t h i r d movement. The t h r e e d e c r e a s i n g movements were p r o -duced i n s u c c e s s i v e o r d e r f o l l o w i n g the s t a n d a r d and each s e t o f t h r e e movements was r e p e a t e d s i x t i m e s . The C a t e g o r y P r o d u c t i o n group was g i v e n two s t a n d a r d s . One was t h i r t e e n degrees and c a l l e d C a t e g o r y 1 and the o t h e r was n i n e t y degrees and c a l l e d C a t e g o r y 7. The s u b j e c t was- t o l d t h a t t h e r e were seven c a t e g o r i e s , a l l e q u i d i s t a n t from one a n o t h e r , and t h a t he was t o produce t h e c a t e g o r y asked f o r . Each o f the seven c a t e g o r i e s was g i v e n randomly f i v e t i m e s , w i t h b o t h s t a n d a r d s 104. g i v e n between each c a t e g o r y p r o d u c t i o n . The group a r i t h m e t i c means were c a l c u l a t e d f o r a l l judgments f o r a l l f i v e groups. The s u b j e c t i v e and phy-s i c a l v a r i a b l e s were compared g r a p h i c a l l y and s t a t i s t i c a l l y f o r R a t i o P r o d u c t i o n , Magnitude P r o d u c t i o n and C a t e g o r y P r o d u c t i o n . The s u b j e c t i v e and p h y s i c a l v a l u e s o f B i s e c t i o n o f A s c e n d i n g and B i s e c t i o n o f Descending were a l s o g r a p h i c a l -l y and s t a t i s t i c a l l y compared. The- r e s u l t s tended t o s u p p o r t t h e c o n c l u s i o n t h a t j u d g -ments ©f a m p l i t u d e o f movement o f s e l f - i n i t i a t e d , s h o u l d e r l a t e r a l f l e x i o n was s u b s e r v e d by a m e t a t h e t i c continuum. Recommendations 1. I f t h i s " s t u d y were r e p e a t e d , Magnitude E s t i m a t i o n and C a t e g o r y E s t i m a t i o n methods s h o u l d be used w i t h about twenty s t i m u l i p e r method. 2. T h i s s t u d y s h o u l d be v e r i f i e d by a r e t e s t and a l s o a c r o s s m o d a l i t y s t u d y u s i n g l e n g t h o f l i n e s and a m p l i t u d e of movement. Stevens (82) has recommended the use o f l e n g t h o f l i n e s as a r e f e r e n c e m o d a l i t y i n c r o s s m o d a l i t y s t u d i e s because o f i t s exponent b e i n g one. 3. 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Barker (Ed) Symposium i n Muscle Receptors, 'Hong Kong, Hong Kong Univ. P r e s s , 1962, 133-143. 71. P e n f i e l d , W., " A n t r e n a p h a l i c I n t e g r a t i n g System", B r a i n , 1958, 81, 231-234. 72. P e l l s b u r y , W.B., "Does the Sensation of Movement O r i g i n a t e i n the J o i n t s " , Amer. J . Psych., 1901, 12, 346-353. 73. Poggio, G.F., Mountcastle, V.B., "A Study of the Func-t i o n a l C o n t r i b u t i o n s of the Lemniscal and Spino-thalamic Systems to Somatic S e n s i b i l i t y " . C e n t r a l Nervous Mechanisms i n P a i n . Johns Hopkins H o s p i t a l  B u l l . , 1960, 106, 266-316. 74. P r o v i n s , K.A., "The E f f e c t of P e r i p h e r a l Nerve Block on the A p p r e c i a t i o n and E x e c u t i o n of F i n g e r Move-ments", J . P h y s i o l . , 1958, 143, 55-67. 75. Rose, G.E., Mountcastle, V.B., "Touch and K i n e s t h e s i s " i n Handbook of P h y s i o l o g y , Sec. 1, V o l . 1 Neuro-p h y s i o l o g y . (Wash. D.C.: Amer. P h y s i o l . Soc. 1959). 76. S e l l i n g , L.S., "An Experimental I n v e s t i g a t i o n of the Phenomenon of P o s t u r a l P e r s i s t e n c e " , A r c h . Psych., N.Y. 1930, ,118. 77. S h e r r i n g t o n , C.S. , "The Muscle Sense". In E.A. S c h a f f e r (Ed) Textbook of P h y s i o l o g y , Edinburgh, P o r t l a n d , 1900. 78. S i n g e r , Robert, N., Motor L e a r n i n g and Human Performance Mac M i l l a n , New York, 1968. 79. Skaglund, S., "Anatomical and P h y s i o l o g i c a l S t u d i e s of Knee J o i n t I n n e r v a t i o n i n the Cat". A c t a p h y s i o l . scand., 1956, 36, Supple. 124. 112. 80. Smith, J.L., " K i n e s t h e s i s : A Model f o r Movement Feedback", New P e r s p e c t i v e s of Man i n A c t i o n (Ed) by R.C. Brown, J . C r a t t y , P r e n t i c e - H a l l , New J e r s e y , 1968. 81. Stevens, J.C., Mack, J.D., "Scales of Apparent F o r c e " , J r Exp. Psych., 1959, 58, 405-413. 82. Stevens, S.S., "On the P s y c h o p h y s i c a l Law", The P s y c h o l . , Rev., 1957 , 64, 3. 83. . , "Problems and Methods of Psychophysics", P s y c h o l . B u l l . , 1958, 54, 177--196. 84. "Cross-Modality V a l i d a t i o n of S u b j e c t i v e S c a l e s f o r Loudness, V i b r a t i o n and E l e c t r i c Shock". J . of Exp. Psych., 1959, 57, 4. 85. . , "Measurement, Psychophysics and U t i l i t y " i n Measurement: D e f i n i t i o n and T h e o r i e s , C.W. Churchman and P. Ratoosh (Eds), Wiley, New York, 1959, 18-63. 86. . , "Mathematics, Measurement and Psycho-p h y s i c s " , i n Handbook of Experimental Psychology (ed) by S.S. Stevens, John Wiley and Sons, New York, 1959 . 87. , "The Q u a n t i f i c a t i o n of S e n s a t i o n " , Daedabes J . of Amer., Acad, of A r t s and S c i e n c e , 1959. 88. . , "Ratio S c a l e s , P a r t i t i o n S c a l e s , and Confusion S c a l e s " , P s y c h o l o g i c a l S c a l i n g - T h e o r y of  A p p l i c a t i o n s , H. G u l l i k s e n , S. Messick (Eds.) John Wiley and Sons,' New York, 1960. 89. . , "To Honour Fechner and Repeal His Law", S c i e n c e , 1961, 33, 80-86. 90. , "The Psychophysics of Sensory F u n c t i o n " i n W.A. Rosenbleth (Ed) Sensory Communication, New York, MIT P r e s s , and John Wiley, 1961, 1-33. 91. - . , "The S u r p r i s i n g S i m p l i c i t y of Sensory M e t r i c s " , Amer. P s y c h o l o g i s t s , 1962, 17, 29-39. 92. __. , "Concerning the P s y c h o p h y s i c a l Law", Q u a r t e r l y J . of Exp. Psych., 1964, 26, P a r t IV. 113. 93. Stevens, S.S., "Matching F u n c t i o n s between Loudness and o t h e r Continua", P e r c e p t i o n and Psychophysics, 1966, 1. 94. Stevens, S.S., G a l a n t e r , E.H., "Ratio S c a l e s and Cate-gory S c a l e s " f o r a Dozen P e r c e p t u a l Continua", J . -of Exp. Psych., 1957, 54, 6. 95. Weber, CO., Dallenbach, K. M., " P r o p e r t i e s of Space i n K i n e s t h e t i c F i e l d s of Force", Amer. J . P s y c h o l . , 1929, 41, 95-105. 96. Werner, G., and Mountcastle, V.D., "The V a r i a b i l i t y of C e n t r a l Neural A c t i v i t y i n a Sensory System and i t s I m p l i c a t i o n s f o r the C e n t r a l R e f l e c t i o n s of Sensory Events", J . N e u r o p h y s i o l . , 1963, 26, 958 - 977. 97. W i l l i a m s , H. G., " N e u r o l o g i c a l Concepts and P e r c e p t u a l Motor Behavior", New P e r s p e c t i v e s of Man i n A c t i o n , (Ed.) by R.C Brown, B.J. C r a t t y , P r e n t i c e - H a l l , New J e r s e y , 1968. 98. Wood, H., "Psychophysics of A c t i v e K i n e s t h e s i s " , J . of Exp. Psych., 1969, 79, 3, 480-485. 99. Woodworth, R.S., "Accuracy of V o l u n t a r y Movement". P s y c h o l . Rev. Monogr., Supple., 1899, 3,.13. 100. Woodworth, R.S.,•Schlosberg, H., Experimental Psychology, H o l t , R i n e h a r t and Winston, New York, 1958. 101. Yamane,.T., S t a t i s t i c s ; A n.Introductory A n a l y s i s , Harper and Row, New York, 1962. APPENDIX A 115. R e g r e s s i o n L i n e by Method o f L e a s t Squares Group I (R.P.) Y = a + bx Y = .6473 + .6854 (x) Graph 1 (A) L o g - l o g P l o t - Graph # 1 (Stevens) Y x = .6473 + .6854 (1.9) Y± = 1.94956 Y 2 = .6473 + .6854 (1.2) Y 2 = 1.46978 K = .6473 (log) o f R = K S N a n t i l o g . 6473 = 4.44 71.51% p r o p , o f t o t a l o b s e r v e d v a r i a n c e o f Y wh i c h i s acco u n t e d f o r by t h i s r e g r e s s i o n l i n e . (B) L i n e a r - Log P l o t - Graph # 2 (Fechner) Y = a + bx Y = -87.24 + 91.12 (x) Y1 = -87.24 + 91.12 (2.0) 'Y = 95.0 Y 2 = -87.24 + 91.12 (1.1) Y 2 = 12.991 116. - no "K" i n Fechner f r a c t i o n - 77.97% prop, of t o t a l observed v a r i a n c e of Y which i s accounted f o r by t h i s r e g r e s s i o n l i n e . R egression L i n e by Method of L e a s t Squares Group I I (M.P.) (a) Log.- Log P l o t - Graph # 3 (Stevens) Y = a + bx Y = .1984 + .9121 (x) Y±_= .1984 + .9121 (1.9) Y1 = 1.93139 Y 2 =•.1984 +,.9121 (1.2) Y 2 = 1.29292 N "K" = 1.984 (log) of R = KS a n t i l o g .1984 = 1.58 91.46% prop, of t o t a l observed v a r i a n c e of Y which i s accounted f o r by r e g r e s s i o n l i n e . (b) L i n e a r - L o g P l o t - Graph # 4 (Fechner) 117. y = a + bx y =-123.7 + 108.2 (x) y x = -123.7 + 108.2 (2.0) Y± = 92.7 y 2 =-123.7 +108.2 (1.3) y 2 = 16.96 no "K" i n Fechner f r a c t i o n 89.23% of t o t a l observed.variance of Y which i s accounted f o r by r e g r e s s i o n l i n e . P l o t P o i n t s f o r Category P r o d u c t i o n Power P o i n t s three R a t i o Scale of Subj. Mag. (Function) C Log of Am x R.P. (Graph 1) M.P. (Graph 3) 1 1.209 1.475 1.30 2 1.532 1.696 1.595 3 1.663 1.785 1.712 4 1.780 1.865 1.820 5 1.862 1.922 1.896 6 1.909 1.954 1.940 7 1.972 1.996 1.995 . 118. Group I (R.P.) i C o r r e l a t i o n Scores and '2' Best f o r S i g n i f i c a n c e Var •1 - 45.83 -- average of 4 Phy. degrees Var •2 = 1.619 -- l o g of mean of f o u r P h y s i c a l Degrees Var 3 = 1.757 -- l o g of Var 4 Var 4 .= 60.31 -- a r i t h . mean of fou r s u b j e c t i v e a r i t h . means r Z N Z 1 (1) Var- 2 vs Var 3 .845.7 1.238 40 (Log-log) (Stevens) (2) Var 2 vs Var 4 .883.0 1.398 40 (Log-Linear) (Fechner) >/Z' - Z • = / — + r=^--0 = .232379 1 2 lN^-3 N 2-3 / z ^ z 2 n u l l h y p o t h e s i s Z| = Z 2 Z = (1.238 - .1.398) - (0) = e Q 9  1 .232379 no s i g n i f i c a n t d i f f e r e n c e between " r ' s " g.". r e g r e s s i o n l i n e s f i t s both Stevens' and Fechner's Laws - " z " must be 1.95 to be s i g n i f i c a n t a t .05 l e v e l of c o n f i d e n c e f o r t w o - t a i l e d t e s t 119. Group I (R.P.) C o r r e l a t i o n Scores T e s t f o r S i g n i f i c a n c e r z (3) Var. 1 vs. Var 4 .8819 1.376 2 ( L i n e a r - l i n e a r ) N 40 (2) Var 2 vs . Var 4 (Log.-Linear) . 8830 1.398 40 (3) Var 1 vs. Var 4 ( L i n e a r - l i n e a r ) 8819 .376 40 (4) Var 2 vs. Var 3 (Log.-Log.) 8457 1.238 40 .232379 N x-3 N 2-3 Z2 = ( Z i Z « > - (Z- - Z'.) n u l l h y p o thesis Z|=Z^ 60398 - 1.376 - 0 . 232379 022 232379 = .094 Not s i g n a t .05 head 2 t a i l e d (zj_ - z - ) ( Z i - Z ' ) - Z2 1.376 - 1.238 - (0) .232379 138 .232379 = .593* Not s i g n a t .05 l e v e l 2 t a i l e d 120. Group II (M.P.) C o r r e l a t i o n Scores and "Z" t e s t f o r S i g n i f i c a n c e Var 1 = 50.00 average of 4 Phy. degrees Var 2 = 1.661 l o g of mean of fo u r P h y s i c a l degrees Var 3 = 1.713 l o g of Var 4 Var 4 = 56.01 a r i t h . mean of fo u r s u b j e c t i v e a r i t h . means (1) Var 2 vs Var 3 = ( l o g - l o g Stevens) .9564 Z 1.886 N 40 (2) Var 2 vs Var 4 = ( l i n e a r - l o g , Fechner) .9446 1.783 40 ^ 7 ^ 2 = / N ^ 3 + ^ 3 = - 2 3 2 3 7 9 Z = ( Z { - Z') - (Z- z 2 ) / Z i - Z2 n u l l h y p o t h e s i s : Z| = Z^ 7 = (1.886 - 1.783) - (0) .232379 - no s i g n i f i c a n t d i f f e r e n c e between " r " ' s , f i t s both Stevens' and Fechner's Laws r e g r e s s i o n l i n e - "Z" must be 1.95 to be s i g n i f i c a n t a t .05 l e v e l of c o n f i d e n c e f o r t w o - t a i l e d t e s t Group I I (M.P.)  C o r r e l a t i o n Scores and "Z" Test f o r Sign Var 1 vs Var 4 ( l i n e a r - l i n e a r ) Var 2 vs Var. 4 ( l i n e a r - l o g ) r 9528 9446 Z N 1.832 40 1.783 40 Var 1 vs Var•4 ( l i n e a r - l i n e a r ) Var 2 vs Var 3 (Log.-Log.) ,9528 ,9564 /Z' - Z i = / 1. 832 1.886 40 40 N l ~ 3 + N 2 - 3 1 2 (Zl - Z') - (Z' - Z') = .232379 Z„ = / z 1 - 7 1 1 Z2 (1. 832 - 1.783) - (0) • 232379 (1. 832 - 1.886) - (0) 232379 n u l l hypothesis Z _u±^ = 210' ,232379 • 0 5 4 = .232* .232379 not s i g n a t .05 l e v e l 2 t a i l e d 122. Curves of Best F i t by Polynomial Regression G£3 graph 5 Y=8.23667 + 2.45764 x - 0.02009 x e x p l a i n e d v a r i a n c e by t h i s l i n e i s .9998 of the t o t a l v a r i a n c e due to s u b j . means Gp4 graph 5 Y = 8.215 + 1.41674 x - 0.005 x e x p l a i n e d v a r i a n c e by t h i s l i n e i s .999 of the t o t a l v a r i a n c e due to s u b j . means Gp5 „ graph 1 Y = 1.32157 + 0.19590 x - 0.01460 x a g a i n s t power f u n c t i o n of Gp I (R.P.) Graph #1, e x p l a i n e d v a r i a n c e by t h i s l i n e i s .982 of the t o t a l v a r i a n c e due to s u b j . means Gp5 graph 3 Y = 1.09571 + .26082 x - 0.01939 x a g a i n s t power f u n c t i o n of Gp I I (M.R.) Graph #3, e x p l a i n e d v a r i a n c e by t h i s l i n e i s .982,8 of the t o t a l v a r i a n c e due to s u b j . means L i n e of Best F i t - Group V - L i n e a r - L i n e a r Graph # 8 r = .9723 v a r i a n c e accounted - 9 4.54% X = 7.230 + 12.64 x X = 7.230 + .12.64 (1) X = 19.87 Y = 7.230 + 12.64 (6) Y = 83.07 L i n e of Best F i t - Group II - L i n e a r - L i n e a r Graph # 6 r = .9528 v a r i a n c e accounted = 90.78% Y = 4.208 + 1.036 x Y = 4.208 +1.036 (10) = 14.568 Y = 4.208 + 1.036 (80) = 87.09 L i n e o f Best F i t - Group I - L i n e a r - L i n e a r Graph # 3 r = .8819 v a r i a n c e accounted 77.78% Y = 20.88 + 0.8602 (x) y = 20.88 + 0.8602 (10) = 29.48 y = 20.88 + 0.8602 (80) = 89.69 APPENDIX B 0*T*\ ffecoR O .^HC^ T 125. Ik S too \ s 3 as l o o 3 4 5 ais L 1 So s *7 S IS lo // h IZ Vac 13 So 75 / a S o /I ^ . 3 4 Orf* Record £V\ecV X26. s ('leo) IT* » 75 V ? . J T S ^ °«/ «ro a fs v>- s S So 3 tsv> 7s* s *t so AS" S so g& s s 5 S 9 so as 5 /o so a? s -S S S 15" las' S 127. Oa,T * CecorA SVN»«f 9 * scew<k iv , s S T f m ^ * b « * V « s No^ecTs s \ 3 s 5 1 3 5 \ 3 3 S \ 3 II If H it it t . 5 S So .©o 121 »6o S O ' 0 0 \ 5k. So So. oo $•©• o o as# oo So. oo <?5-0© f>0. 0<9 s \©o t. STo & as l oo 6" o l. a. Sib" ?». 1/ \ a.S s J op # So <1 •as 3. / / S l o o \. S o a. 5i S 3. /< 5 \ o o So a. £LS 3. // P nTf, K'cOovA S n e e l 128. j V e s > So 2. " as-3- '/ U- S S>*Tr\ v2e.cov4 s > W T 1 2 9 : \ iww\os> Q <,au < v e d R e a p 4 i SI 13 \ 1 So SI C2> 3 ^  2> C 5 toS 4 CI I 2> 5 CM- 5 £ 7 c 7 °! o * C I 1 3 to C 3 3c, l a c 7 <\ o r i c 7 ^ ° tH c t 7 >^ IS c 7 (jr <r o vi d 5 C A T ^ ^ o v - ^ 9 y c <d vj C V V o Wi C o w l 'ci . \ <\ C 5 k 5 ^ C H 3 C q <\ o A 7 C 4- S a s c a * b ^ C 5 4, S* C / \ 3 2 5 1 C ^ A f c 7 S ^ 3 C 3> 3 <\ C S L 5 c 1 ' °\ o " APPENDIX C TABLE I RESULTS Group D P I F degrees Log G. M. Log G.M. Md A. M. Log AM AMSD Log S.: i \ • Jr . S=100° 1/4 25.00 1.398 38. 55 1.586 1.552 40. 10 1. 592 9.730 .10 1/3 33.34 1.523 48. 42 1.685 1.583 50. 00 1.689 10.39 .09 1/2 50.00 1.698 67. 14 1.827 .587 67. 73 1.828 8.33 . 05 3/4 75.00 1.875 82. 99 1.919 . 415 83, 40 1.920 6.61 .03 md.: •. 1;043 Group I I 50 25.00 1.398 30. 41 1.483 .581 30. 99 1.486 5. 29 .07 M.P. 75 37.50 1.574 40. 46 1.607 .352 40. 81 1.609 3.88 .04 S=50° 125 62.50 1.796 71. 95 1.857 . 255 72. 20 1.857 6.27 .04 (100) 150 75.00 . 1.875 79. 43 1.900 .617 80 . 05 1.901 9.22 . 05 md: .451 Group I I I t w i c e 12.5 19. 5 3.68 S= as 25.00 40. 57 8 . 55 6.250 g r e a t 50.00 64. 43 15.19 B i A s c Group IV 1/2 50 .00 65. 163 1.814 . 707 65. 87 7.404 S=100° 1/2 25.00 40. 272 1.605 1.608 41. 88 11.26 BiDes 1/2 12.50 21. 979 1.342 2.381 24. 36 11.36 md: 1.565 Group V CI 13.0 1.114 15. 417 1.188 .763 16 . 18 1.209 . .4.124 0.615 S1=C1= C2 26.0 1.415 32. 885 1.517 1.205 34. 09 1.532 6.765 0.830 13° C3 39 .0 1.591 44. 771 1.541 2. 269 46. 04 1.663 8.960 0.952 S2=C7= C4 52.0 1.716 59. 566 1.775 .814 60. 38 1.780 7.867 0.896 90° C5 65.0 1.813 72. 444 1.860 .466 72. 91 1.862 4.836 0.684 C6 78.0 1.892 81. 096 1.909 .164 81. 26 1.909 2.919 0.465 C7 . 90.0 1.954 93. 756 1.972 .034 93. 79 1.972 3.086 0.489 md: .673 Gmd: .974 RAW DATA Subj e c t F 1 2 3 4 5 6 7_ 8 9 10 1/4 45. 5 55 30. 5 40. 5 40.5 35 63 41.5 47 39. 5 1/4 38. 5 44. 5 32. 5 33. 0 33.5 22 53. 5 36.5 52 26. 5 1/4 48 . 5 45 20 27 35.5 32. 5 60. 5 39 44. 5 35 1/4 35. 5 49 22 45 34 28. 5 64 34.5 34. 5 39 Group I 1/3 60 6- 33 40. 5 40 35 60 46 60 54 R a t i o 1/3 52 54. 5 42. 5 70 47 43 76. 5 54 63 53 P r o d - 1/3 53 55. 5 16. 5 60. 5 44 39. 5 61 51 47 44 u c t i o n 1/3 52 65 29 55 40.5 35 6 2 51 51. 5 43 1/2 77 72 62 80 60 53. 5 77. 5 64.5 72. 5 62 1/2 70 70. 5 59 79. 5 56.5 55. 5 80 64.5 74 67. 5 1/2 71 66 58. 5 82. 5 56 52 80 61.5 64. 5 66 1/2 68. 5 68 58 80 62 66 80 . 5 71.5 75 63 3/4 90 82 74 94 79 80. 5 86 79 77 77 3/4 90. 5 84 87 92. 5 75 75 95. 5 86.5 84, 76 3/4 86 82 70. 5 95 75 68. 5 95 82 87 76 . 5 3/4 90. 5 89. 5 77 95. 5 70.5 86. 5 90 84.5 86 . 5 83. 5 50 29 40 31 21 20.5 23 36 . 5 25.5 24. 5 35 50 39 38 34. 5 26 25 24. 5 33 31 28 28 50 35. 5 47 32 30 27 25. 5 34 27 32 30 Group I I 50 37 41 34 37 22.5 29. 5 36 26.5 30 33 Magni- 75 37 45 43. 5 33 30 45. 5 35. 5 33 41. 5 42. 5 tude 75 37. 5 • 47 42 40 35.5 46 32 34 40 37. 5 P r o d - 75 42. 5 52. 5 51 39. 5 43 40 41 41.5 37. 5 38 u c t i o n 75 43 48. 5 46 46. 5 37 - 43. 5 44. 5 38 42 39 125 70 70. 5 77. 5 78 71 80 63. 5 64.5 70. 5 76 125 70 60 76 72. 5 76 72 66 58 66 80. 5 125 70 68 82. 5 94 73.5 78 65. 5 65.5 67 76 125 72 75 75. 5 69 72.5 83 59 68 69 78 . 5 150 65. 5 67. 5 96. 5 74 84 87 71 73.5 77 87 150 78 50 93 81. 5 77.5 95. 5 75. 5 76 77 80 150 74 75 94 93 82 . 90 74 72 69. 5 87 150 80 72. 5 98 90 82.5 89 75. 5 67 80 82 RAW DATA S u b j e c t Group I I I 1 2 3 4 5 6 7 8 9' 10 twice as much 17 16 13.5 16 16.5 21.5 16 14.5 19 22 40 31 31.5 31 3 4.0 60 26 32.5 51 39.5 i i 75 50 48 48. 5 55.0 100.0 46.5 57.0 95 57 X 15 16.5 14.5 17 18.0 19 12.5 26 . 15 24 i i 31 50.5 35 34 42 41.5 25 52 50. 5 46.5 i i 70 66.0 51.5 47 58 60 44.5 92.5 96 . 5 58 15 16.0 20 14 24 21.5 13.5 21 14 24 .5 II 27 30.5 37 30. 5 44.5 41.5 26 46 . 47 35.5 II 38 56.5 53.5 52. 0 61 71 * 44 77.5 92 52.5 II 20 14.5 23 16. 5 24 20 15 .5 21.5 25 25.5 Twice much 35 33.5 45.5 29 47 44.5 27.5 48 73 45.5 II 49 52.5 61 46 61.5 74.5 51.5 78 94 74 i t 17 20 26.5 20 25 18.5 13.0 31- 14 37 II 25.5 39.5 54 33. 5 44 46 29.5 54.5 51 63.5 II 42.0 59 .5 69 43 65.5 77 43.0 82.5 • 9 2 89 II 20 20.5 28 13. 5 23 18 13 .5 24.5 22. 5 26 II 25 46 47 30. 5 34.5 46.5 30.5 51.5 46 47.5 i t 38 80 72 46 58 68 50.5 84.5 95. 5 95 . Group IV - B i s e c t i o n Descending 1/2 Less 76 56.5 85.5 69 58 63 61.5 71.5 65 67 II 60 26 57 48. 5 37.5 30.. 5 31 46 37 35 II 45.5 12 26 33 19 19.5 - 10.5 32 13 13.5 II 78.5 52 82.5 78 63 61 60 69.5 62 69.5 II 58 27 50 58 47 33; 5 31 48 37 36 II 40 16 32 36 . 5 23 20 11.5 30 15 23 .5 II 78 55.5 85 70 60.5 60 78 64 63. 5 77 •I 61 31 59 58 40 32 36.5 36 35 52.5 II 47 22 30 27 23 16 18.5 23 14. 5 19 1/2 Less 75.5 58 80 75. 5 63 54 52 66 55 66 II 65 34.5 45 49 36 30.5 19 44 27. 5 38 II 50 20 30.5 37 19 19 6.5 27 11. 5 17 II 73 64 36 74 64 55.5 55 6 8.5 52 16 . II 62- 36 50.5 51. 5 36 33 . 26 49 32 59.5 n 55.5 21.5 35 29. 5 19 18 11.5 32 . 16 20.5 t i 79 58 84 73 . 5 66.5 52.5 55 68.5' 61 60.5 H 68 36.5 50 49 42 27. 5 24 52 29 36 II 63 21.5 26 .5 31 4 24 18 8 26.5 15. 6 19 RAW DATA Subject Group V Cate-gory Prod-u c t i o n 1 2 3 4 5 6_ 7 9_ 10 CI 18 13 10.5 14.5 22 18.5 22. 16. 5 21 21 CI 10 13.5 12 14 9.5 16 .5 16.5 • 15 27 15 CI 16 16 14 7 17 15.5 10 21 28 14.5 CI 15 18 16 9 14 30 12.5 20 29.5 12. 5 CI 16 12 14 11 11 17.5 13 15 24.5 13 . 5 C2 49.5 32 30 29 41 31 34 36 44 25 C2 47 37 34.5 18.5 20.5 35 26 42 40 29 C2 37.5 39 .5 41 ' 24.5 35 44 26 37 42 27 C2 32 39 30 16.5 26 52.5 37 26 37 29 C2 30.5 . 31 32 14 36 54 35 38 45.5 29 C3 65 35 46 29.5 42 46 62 38. 5 63 46 C3 64.5 50 55 33.5 29 55 34 46 57.5 45 C3 45 47 54 32 33 52 36 49 50.5 44 C3 58 41 61.5 26 27 64 47 45 52.5 44 C3 53 44.5 54 31 35 52 56.5 40 42 43 C4 67 56 62 53 37.5 64.5 45 47 66.5 50 C4 66 60 61 47 54 63 45 64 71 64 C4 72.5 53 66 33 52 74 68 67. 5 70 69 C4 63 57 61.5 44 56.5 62 78 50 69 59 C4 67 60.5 67.5 36 56.5 75 65.5 57. 5 69 60 C5 76 73 76 72 67 82 . 5 84 72. 5 74 71 C5 75 82 76.5 56 63.5 72 56 75 92 71 C5 72 70 80 57 76 .5 73.5 85.5 84 87 73.5 C5 68,5 68 72 59 66 80 75 70 74 79 G5 73 72 80.5 67 70.5 66 69.5 61. 5 75 73 C6 70 84 77 82 76 80 71 82 89 8 2 C6 80 80 75.5 73 76 83 74 84 98 85 C6 80 82 81 85 94 81.5 84 81 87 83 C6 80 78 84 82 82 85 9 4 83 89. 5 80.5 C6 75 83 .5 88 81.5 . 76 72 86 64 78 . 81 C7 89 91 92 90 92 96 100 88 100 97 C7 91 100 100 85 98.5 97.5 . 94 91 99.5 93 C7 94 95.5 92 88 95 98 86 86 100 93 C7 90 96 94 89.5 92 98 9 4 96 100 92.5 C7 90 90 91 92.5 91 98.5 95* 95. 5 98 94 

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