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The application of electronic computers in forestry, and forestry research. Csizmazia, Joseph 1963

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THE APPLICATION OP ELECTRONIC COMPUTERS IN FORESTRY, AND FORESTRY RESEARCH by Joseph Csizmazia D i p l . Forestengineer, U n i v e r s i t y of Sopron, 1953  A Thesis Submitted i n P a r t i a l Fulfilment of the Requirements f o r the Degree of MASTER OF FORESTRY i n the Faculty of Graduate Studies  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1963  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that 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 study. mission for extensive  I f u r t h e r agree that per-  copying o f t h i s t h e s i s f o r . s c h o l a r l y  purposes may be granted by the Head o f my Department or by his representatives.  I t i s understood that copying, or 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 allowed without my w r i t t e n p e r m i s s i o n . .  Department of The U n i v e r s i t y of B r i t i s h Columbia,. Vancouver 8, Canada. Date  (/(/^Oslsl  ~7j  /#63  ABSTRACT  ii  A short h i s t o r y of the electronic data processing i n North America i s given. processing  development  The basic p r i n c i p l e s of computers and data  systems are analysed and a b r i e f description of ALWAC III-E  and IBM 1620 computers i s provided.  S u f f i c i e n t information  i s given to  acquaint professional foresters or research workers i n f o r e s t r y with the basic knowledge required to understand where and how computing can be applied i n t h e i r work. The major factors that govern how and when to use a computer are: required speed and accuracy, s i z e , repetitiveness, and complexity of the calculation. I t i s pointed out that the advantages of an electronic computer are:  speed, accuracy, v e r s a t i l i t y , r e l i a b i l i t y and memory. The disadvantages are:  high r e n t a l cost, extra cost f o r trans-  posing data on cards or tape, and complicated program writing. In f o r e s t r y the main f i e l d s of electronic computer applications are: Management Mensuration Utilization Logging engineering Research Examples are presented f o r each f i e l d i n the text, t y p i c a l programs are appended, and sources of further information  are noted.  I t i s concluded that i n the future the importance of electronic computers w i l l increase i n f o r e s t r y practices; however, i t w i l l remain only a t o o l and cannot replace the f o r e s t e r .  iii  ACKNOWLEDGMENT The author wishes t o express his gratitude to Dr. J.E.G. Smith f o r h i s encouragement i n learning and applying the computer i n f o r e s t r y research and f o r the opportunity to p a r t i c i p a t e as a junior author i n the research work basic t o the study of economics of r e f o r e s t a t i o n of Douglas f i r , western hemlock and western red cedar i n the Vancouver Forest D i s t r i c t (Smith, Ker, Csizmazia, 1961).  As a research assistant and graduate student  at the Faculty of Forestry and as a member of the s t a f f of the Vancouver Forest Products Laboratory,  the author has had ample opportunity to use  electronic computers i n analysing many f o r e s t r y research projects. out t h i s experience  With-  t h i s thesis could not have been written.  The author also wishes to acknowledge the help and advice of members of the University of B r i t i s h Columbia Computing Center and of Mr, Hugh Dempster i n p a r t i c u l a r . Review of the thesis by members of the committee, including Professor F.M. Knapp, Assistant Professor L. Adamovich and Instructor D.D. Munro i s g r a t e f u l l y acknowledged. The assistance of Mr. A. Kozak i n providing examples was very helpful.  iv TABLE OF CONTENTS Page T i t l e Page Abstract Acknowledgement Contents  i i i i i i iv  Introduction  1  Early E l e c t r o n i c Data Processing Development  2  What i s a Computer?  k  D i g i t a l Computer i n General  7  Binary Number System  8  Machine Language  9  Input, Calculation, Control and Output  10  ALWAC III-E  13  IBM 1 6 2 0  14  When and How to Decide on Using Electronic Computers  1^  Economy  18  Research  20  Mensuration  26  Wood Technology  27  Silviculture  29  Page Research (cont'd) Utilization  30  Entomology  30  Statistics  31  Examples  kO  Summary and Conclusions  ^5  Glossary of Terms  4?  Bibliography  50 '  Appendix I Appendix I I Appendix I I I Appendix IV  Calculation of B.C.fbm/cu.ft. Calculation of spring and summerwood area Regression analysis Example of a "Program Write Up"  THE APPLICATION OF ELECTRONIC COMPUTERS IN FORESTRY, AND  FORESTRY RESEARCH  Introduction  This thesis was  written to substantiate the author's b e l i e f that  electronic computers have almost unlimited  application p o s s i b i l i t i e s i n  forestry practice. The  electronic computer i s a sophisticated t o o l ; however—despite  the f a l s e concepts held by the p u b l i c — t h e puters i n t h e i r work are not superhuman. electronic computers was  numerous people who  use com-  I t i s true that the f i r s t use  f o r the solution of complicated and  of  specialized  mathematical problems; but the present users of computers are from a wide range of p r a c t i c a l f i e l d s — s u c h as business, engineering, government, and forestry. The a p p l i c a t i o n of data processing systems i n f o r e s t r y started soon as punched card systems were introduced.  For example, the B.C.  Service's inventory data were punched on cards before World War  II.  orious f o r e s t r y c a l c u l a t i o n s , c l a s s i f i c a t i o n s , lengthy regression investigations  of complicated b i o l o g i c a l interactions, y i e l d and  Forest Lab-  analyses, inventory  c a l c u l a t i o n s , and m i l l studies are i d e a l classes of problems f o r solution with data processing equipment.  as  - 2 E a r l y E l e c t r o n i c Data Processing Developments The following i s a short review of material presented by the Department of Labour of Canada (l960^and c o l l e c t e d by computer manufacturers :  and d i s t r i b u t o r s , and by a number of i n d i v i d u a l businessmen and u n i v e r s i t y professors who were associated with Electronic Data Processing i n i t s early stages. During the l a s t years of World War I I and the years immediately following i t , developmental work i n computer technology began to mushroom i n the United States. research.  This early work was c l o s e l y r e l a t e d to m i l i t a r y  In the private f i e l d , the International Business Machines Corp-  oration (IBM) and Harvard University designed and b u i l t t h e i r f i r s t mechanical computer—the Harvard Mark I — i n 19^;  electro-  Mark I I was b u i l t i n 19^7 •  B e l l Telephone Research Laboratories b u i l t a series of prototype electronic computers, beginning i n  19^0.  The f i r s t general purpose electronic computers i n North America were constructed simultaneously i n 1952 and Princeton University.  Since 1952  by the University of Pennsylvania the number of computer manufacturers  and the v a r i e t y of electronic computers have increased r a p i d l y . One of the main features of data processing that prompted greater i n t e r e s t and a c t i v i t y i n computer development was the computer's a b i l i t y to s w i f t l y use, manipulate, and store large volumes of data.  The f i r s t i n -  d u s t r i a l users of electronic computers were the Metropolitan L i f e Insurance Company and the General E l e c t r i c Company.  The International Business  Machines Corporation invested large sums i n developing a commercially oriented computer and associated equipment such as tape u n i t s to handle and store the masses of data.  -  3  -  In Canada one of the f i r s t d i g i t a l computers—the CRC102A—was i n s t a l l e d by the AVRO A i r c r a f t Company i n Malton, Ontario, i n 1 9 5 3 . to t h i s date, i n 1 9 ^ 8 , the U n i v e r s i t y of Toronto was  Prior  engaged i n b u i l d i n g  an e l e c t r o n i c computer s i m i l a r to the Mark I at Harvard.  The Toronto  project was not completed, and i n 1950 a British-designed F e r r a n t i computer c a l l e d Perut was  installed.  By 1950 the U n i v e r s i t y of Toronto was g i v i n g  courses i n computer technology and applications to students i n engineering, physics and mathematics.  In 1957 an ALWAC III-E computer was  the U n i v e r s i t y of B r i t i s h Columbia.  i n s t a l l e d at  In 1961 an IBM 1620 was added to the  Computing Center. It i s appropriate here to acknowledge the c h i e f representatives of the coastal B.C. Forest Industry, i n p a r t i c u l a r : B.C. Forest Products Limited Canadian Forest Products  Limited  Crown Zellerbach Canada Limited MacMillan, Bloedel and Powell River Limited Western Plywood Company Limited and congratulate them f o r t h e i r foresightedness i n helping to develop the computing center at the U n i v e r s i t y of B r i t i s h Columbia with t h e i r generous 1  support and encouragement. By January, i 9 6 0 , there were 89 electronic d i g i t a l computers i n operation i n Canada.  This number i s probably not impressive i f we compare  i t to the 1000 large computers i n s t a l l e d i n the U.S.A. by 1 9 5 8 . t h i s r e l a t i v e l y small number of computers i n Canada should not be  However, allowed  to obscure the f a c t that computer u t i l i z a t i o n grew from l e s s than h a l f a dozen early i n s t a l l a t i o n s to an impressive number of 89 i n a short four-  year period, and that the number of computers i n operation more than quadrupled i n the two-year period between January 1, 1958,  and January 1, I960;  or that i f the present rate of expansion were to continue over the next decade, E l e c t r o n i c Data Processing could be expected to become a major feature of the o f f i c e operation i n Canadian business, industry and government. What i s a Computer?  A computer i s a device used to perform c a l c u l a t i o n s . During the h i s t o r y of mankind various simple and  ingenious  instruments have been developed and used to speed up routine c a l c u l a t i o n s , such as adding, subtracting and multiplying.  The ancient abacus i s one of  the best known, and i s s t i l l i n use i n many parts of the world. In modern terminology, the word "computer" r e f e r s to devices which can c a l c u l a t e c e r t a i n arithmetical operations  automatically.  Computers can be divided into two basic categories (a) Calculators (b) E l e c t r o n i c computers (a) The c a l c u l a t o r s are the f a m i l i a r adding, or multi-function machines which are able to add, subtract, multiply, divide. The modern calculators are a c t u a l l y semi-automatic computers, or i n other words, once the machine has received the data and the corresponding operation button i s pushed, the c a l c u l a t o r w i l l automatically carry out the operation.  The older calculators require more attention, and need manual  power to turn the mechanism.  The modern calculators use e l e c t r i c power,  and are c a l l e d e l e c t r i c desk c a l c u l a t o r s .  Desk c a l c u l a t o r s , however, are  not able to perform series of c a l c u l a t i o n s without the operator's manual intervention.  Most of these c a l c u l a t o r s cannot store information i n t e r n a l l y .  The operating speed of e l e c t r i c c a l c u l a t o r s i s l i m i t e d by the operator's speed and a b i l i t y to enter and r e g i s t e r information.  I t would  not be very p r a c t i c a l to design f a s t e r desk c a l c u l a t o r s f o r t h i s reason. The desk calculators are useful and t h e i r importance w i l l not be diminished g r e a t l y by the rapid development of e l e c t r o n i c computers. Because of the r e l a t i v e importance and low investment cost of desk c a l culators, i t i s possible that i n the future the designers w i l l b u i l d an electronic desk computer.  The Priden Company, f o r example, already has  developed a prototype, which can read punched information, store data i n t e r n a l l y and perform complex operations. (b) The main difference between desk c a l c u l a t o r s and computers i s that the computers are able to perform complex operations.  In other words,  the computers can "recognize", "remember", "decide" and "execute" i n s t r u c tions.  Consequently, i f a computer received a complex, f a u l t l e s s operation  i n s t r u c t i o n and data, i t could perform the c a l c u l a t i o n s at high speed without  error or human intervention. In summary, the basic differences separating calculators and  computers are as follows: The term c a l c u l a t o r r e f e r s to a machine which: ( i ) can perform a simple arithmetic operation a t one time, ( i i ) i s mechanical, ( i i i ) has keyboard input, ( i v ) has manually operated controls.  - 6 The term computer refers to devices which: ( i ) can solve complex problems i n arithmetic or decision making, ( i i ) are e l e c t r o n i c , ( i i i ) can store instructions and data i n t e r n a l l y , (iv) have rapid and f l e x i b l e input and output devices controlled automatically by the computer according to the command of stored instructions  (Program).  The term Data Processing r e f e r s to a series of planned actions and operations upon information to achieve a desired r e s u l t . The data manipulating procedure and the processing equipment used constitute the Data Processing System.  The procedure w i l l vary with the  i n d i v i d u a l , the equipment can vary from pencil and paper to desk calculators, card tabulating and sorting equipment or electronic computers.  However, a l l  systems are common i n t h e i r objective—namely, to convert data into a new form. The Punched Card System, of course, i s a t y p i c a l Data Processing System, and i s widely used i n f o r e s t r y p r a c t i c e s . are best recorded by the punched card system. sorted, manipulated or stored.  Most f o r e s t r y data  The cards can be e a s i l y  Using sorting, reading, bookkeeping, and  p r i n t i n g machines—which may work e l e c t r o n i c a l l y but are not electronic computers—the punched data are e a s i l y obtainable f o r s p e c i f i c tabulations, summarizations,  or reports.  I f desired, the data punched on cards can be  further processed by electronic computer. A l l data must be represented by numerical codes to f a c i l i t a t e processing operations, such as summarization,  sorting, etc.  The tabulating equipment can be rented on a monthly or y e a r l y  basis and of course i s s i g n i f i c a n t l y cheaper than- electronic computing.  D i g i t a l Computer i n General A d i g i t a l computer i s a c a l c u l a t i n g device which processes numbers represented as d i s c r e t e quantities.  I t d i f f e r s from analogue computer which  deals with continuous quantities such as graphs, lengths, etc. In p r i n c i p l e , the computer i s a simple machine, incapable of performing anything much more sophisticated than elementary arithmetic. However, because of the speed with which i t can perform a series of given operations, i t has become one by  of the most promising devices yet developed  man. Most e l e c t r o n i c computers have four major u n i t s ; ( i ) Input-Output ( i i ) Control ( i i i ) Storage ( i v ) Arithmetic These four sections are basic i n any data processing system. A forester c a l c u l a t i n g basal area with a desk c a l c u l a t o r f i r s t  enters the diameter into the keyboard (input), sets the decimal places ( c o n t r o l ) , pushes the m u l t i p l i c a t i o n button ( c o n t r o l ) ; the machine s t a r t s the c a l c u l a t i o n (arithmetic), the operator r e g i s t e r s the p a r t i a l r e s u l t on paper (storage), and continues the c a l c u l a t i o n ( c o n t r o l ) .  Upon completion  of the c a l c u l a t i o n he reads and records the r e s u l t (output). It i s the superior a b i l i t y of the computer: ( i ) to read (input) and remember (storage) thousands of numbers i n minutes ( i i ) to modify part or a l l of the stored information by a series of  - 8i n t e r n a l l y - s t o r e d instructions  (arithmetic),  ( i i i ) t o control arithmetical and organizational  operations by i t s  decision-making a b i l i t y ; —that  makes i t comparable to the human brain.  This i s the reason why some  authors c a l l the electronic computer an " e l e c t r i c The  brain".  four major units of a computer form a complex system and work  together much the same as the human brain and the human body. The  control u n i t , according to the s p e c i f i c a t i o n s of a stored i n -  s t r u c t i o n , i n s t r u c t s the input device to "read".  The input device transmits  the information to the control u n i t , which converts the data into binary form and stores i t i n memory as s p e c i f i e d by the i n s t r u c t i o n .  This informa-  t i o n may consist of a new series of i n s t r u c t i o n s , or of a series of numbers to be processed.  A new series of i n s t r u c t i o n i s executed i f and when a  previously-stored  i n s t r u c t i o n d i r e c t s the control unit to enter t h i s new  series.  Data are processed according to previously-stored  instructions.  The r e s u l t s are e i t h e r stored f o r future reference, or are transmitted to an output device, depending on the program.  The output device then records  the data according to i t s mechanical design. Binary Number System  In pure binary notation each binary d i g i t — o t h e r w i s e c a l l e d a b i t — i n d i c a t e s whether the corresponding power of 2 i s absent or present. Using t h i s system, the number 5 w i l l be represented by the notation "101", 1 X 2  2  + 0 X 2  1  + 1 X 2 ° = 4 + 0 + 1 = 5 .  By using t h i s system, the number of possible  states f o r each  p o s i t i o n i s reduced to two, whereas i n the decimal system, the number of  - 9 possible  states i s  ten.  Any d e c i m a l number, a l p h a b e t i c  c a n be r e p r e s e n t e d b y d e s i g n a t i n g a s p e c i a l The b i n a r y s y s t e m i s bit  can e x i s t  by e l e c t r o n i c either in  i n o n l y one o f t w o s t a t e s ,  information is A tube  conducting or not conducting; a f e r r i t e  netized or not magnetized. modified,  and t e s t e d  the  F o r the  on a m a g n e t i c  same r e a s o n ,  s i x - b i t numeric code.  count,  The I B M 1620  the  seven-bit  by four b i n a r y  A computer i s designed  one d e c i m a l d i g i t ,  to recognize  other languages  codes  use  the computer's  of  the  System in  to translate  IBM computers  A special  t h i s language  the  executing  I n the case of  (Fortran = Formula t r a n s l a t o r ,  language.  formula into  actual  SPS = S y m b o l i c  SPS a n d F o r t r a n make p r o g r a m m i n g e a s i e r  they resemble  and  and i s  Because  a s w e l l — s u c h a s t h e SPS a n d F o r t r a n  t r a n s l a t i o n program i s necessary  for  and execute c e r t a i n i n -  F o r t r a n i s not r e a d i l y understood by the machine.  versatile,  mag-  alphameric code,  t o u n d e r s t a n d t h e s e codes and c a p a b l e  Programming System).  is either  d a t a can e a s i l y be h a n d l e d ,  which i n t u r n are combinations of numbers.  machine language  magnetized  Language  them, t h e y a r e c a l l e d the machine language. there are  tape  is  bits.  Machine  computer i s a b l e  or t r a n s i s t o r  is either  each  represented  u s e s t h e B i n a r y Coded D e c i m a l  E a c h " p o s i t i o n " i n memory r e p r e s e n t s  structions,  Since  on the b i n a r y system have been d e v i s e d ;  two-out-of-five  turn represented  core  easily  character.  by the c e n t r a l c o n t r o l u n i t .  Many c o d e s b a s e d example,  a spot  character  of b i t s t o each  of a l l computer d e s i g n .  c i r c u i t r y or magnetic m a t e r i a l .  one d i r e c t i o n o r t h e o t h e r ;  (BCD).  the b a s i s  series  or s p e c i a l  a n d more  o r d i n a r y E n g l i s h and m a t h e m a t i c a l n o t a t i o n s ,  a b i l i t y to translate  these symbolic languages  into  and  - 10 o r i g i n a l machine language.  A series of machine language, Fortran or SPS  i n s t r u c t i o n s , i s c a l l e d a program.  Input, Calculation, Control and Output A l l program information or data entering the computer must f i r s t be read by a reading or input device and stored i n main storage or memory. Each d i g i t of information i s given a storage l o c a t i o n number.  The input and  storage locations must be c a r e f u l l y assigned to avoid clashes of the data or i n s t r u c t i o n l o c a t i o n s .  Once the data are entered, the control i n s t r u c t s  the computer to s t a r t the c a l c u l a t i o n s .  Upon completion of the computations,  the computer outputs the calculated r e s u l t s .  Before output, the r e s u l t s are  changed again from binary mode to decimal or alphanumerical form. Data input and output are the slowest phases of the computing process.  The input and output devices are mechanical machines.  I t takes  time to move the tape or card to the next reading p o s i t i o n , and release i t again.  I t i s even slower i f the information i s typed manually on the control  typewriter. To prevent errors due to e r r a t i c data, i t i s essential to prepare proper data or information media. over-emphasized.  The checking of cards or tapes cannot be  The most commonly used media for:input-output are:  ( i ) Card ( i i ) Tape ( i i i ) Magnetic  tape  IBM Punch card (see Appendix). The IBM punch card i s the most common medium f o r communicating with machines.  - 11 The card contains 80 v e r t i c a l columns with 12 punching positions i n each column; 10 of them are numbered from 0 to 9> the next row above 0 i s c a l l e d the 11 punch and the next above the 11 i s c a l l e d the 12 punch. The information i s presented by small rectangular holes, punched by a punching machine generally known as a keypunch.  A keypunch i s a  typewriter, which, instead of typing characters on paper, punches holes on cards.  The numerical characters 0 to 9 are represented by a single rec-  tangular hole i n a v e r t i c a l column.  The alphabetical characters and signs  are represented by two punches i n a single v e r t i c a l column; one i s i n the 0 to 9 section and the other i s in' the 11 or 12 zone. Each card can contain a v a r i a b l e amount of information. The advantages of cards are as follows (1) Information of a p a r t i c u l a r set can be recorded separately:  f o r example,  the D.b.h., Ht., and age of a tree can be punched on one card; thus the card becomes a record of the tree. (2) In case of sequence changes i n the input, the cards can be e a s i l y re-arranged. ( 3 ) E r r a t i c cards can e a s i l y be detected and corrected. (k)  Easy and rapid access to the punched information i s possible with card processing machines (sorter, p r i n t e r , e t c . ) .  ( 5 ) Storage i s easy. (6) I t can be used e i t h e r f o r e l e c t r o n i c computer or mechanical data processing equipment. Disadvantages (1) The cards can be e a s i l y damaged, mixed, or l o s t . (2) There are d i f f i c u l t i e s i n handling great quantities of cards because  - 12 of t h e i r large volume and weight. Punched paper tape serves much the same purpose as punched cards. Punched paper tapes with s i x , seven, or eight channels are used with computers.  The ALWAC III-E uses seven punching positions on a 7/8 or 1 inch  wide paper tape.  The symbols, numbers and l e t t e r s are represented by com-  binations of numbers of holes and hole positions.  •  • • • ••  e • ••eeee • 1 2 3  • •  ee  h 5" 6  See Figurel below:  ••• • • • ••• • ••••  • •  ••  • •  ••••••  •  eeeeeeeeeee • 7 8  9 0  Figure 1 .  4h  c , '.$ ;  •  • •••  » • ••  +=% ?  ...  •  ALWAC I I I - E tape.  Advantages of tape; (1) R e l a t i v e l y easy to handle; l i g h t e r ; p a r t i a l information cannot be mixed or l o s t . (2) Faster loading. Disadvantages: (1) D i f f i c u l t to correct errors. (2) D i f f i c u l t to gain access t o information. (3) Tape cannot be used f o r record keeping as comfortably as cards. (4) I f a tape breaks the whole tape section should be repunched. Magnetic tape i s the most recently developed medium f o r recording data f o r machine processing. corders.  I t i s similar to the tape used i n tape r e -  I t i s p l a s t i c and coated on one side with a m e t a l l i c oxide.  are recorded as magnetized spots.  Data  Information recorded on tape i s permanent.  - 13 Previous recordings are destroyed as new information i s written on i t .  The  size of data record i s l i m i t e d only by the length of a tape or the capacity of the computer s storage u n i t . 1  I t i s the fastest input-output medium. ALWAC III-E  The f i r s t computer i n s t a l l e d by the Computing Center at the U n i v e r s i t y of B r i t i s h Columbia was an ALWAC III-E computer. The ALWAC III-E i s a general purpose numerical binary computer. A magnetic drum i s used as the memory unit; both data and instructions are stored i n s e r i a l manner by means of magnetized spots on the surface of the drum.  The memory capacity i s 8192 words or c e l l s ; each c e l l can hold 32  binary d i g i t s and a sign. input-output u n i t .  I t has a console typewriter and a high speed  The high-speed unit i s a paper tape reader and punch.  The typewriter i s also able to sense (read) or punch information from or on to tape.  Typewriter input-output i s slow—10 characters per second.  The high-speed  input-output unit reads the tape with aphoto-cell device,  thus permitting the tape to move continuously at a reading rate of 1 5 0 characters per second; i t punches out information at the r a t e of 50 characters per second.  The ALWAC III-E*s great f l e x i b i l i t y and r e l a t i v e l y large  memory make i t possible to meet the needs of the business, s c i e n t i f i c and practical fields.  However, with the r a p i d evolution i n computer design, the  ALWAC I I I - E with i t s vacuum tube c i r c u i t r y w i l l soon become obsolete. The ALWAC III-E has a large l i b r a r y of excellent programs.  Many  of these programs were written or adjusted f o r f o r e s t r y a p p l i c a t i o n s . Between 1958 and 1961 most of the research work of the Forestry Faculty i n v o l v i n g computer computations was done on t h i s computer.  - Ik IBM  1620  In 1 9 6 1 an IBM 1 6 2 0 computer was i n s t a l l e d at the U.B.C. Computing Center.  The IBM 1 6 2 0 computer—or more s p e c i f i c a l l y , the IBM  1 6 2 0 Data Processing System—is  a new t r a n s i s t o r i z e d computer, designed  f o r business and technological applications. I t has 4 0 , 0 0 0 decimal d i g i t s of core storage and completely transi s t o r i z e d c i r c u i t r y , thus providing adequate storage capacity and speed to solve problems that i n the past have required the use of more expensive and l a r g e r systems. The IBM 1 6 2 0 Data Processing System i s arranged i n two main u n i t s . One i s the actual computer, consisting of the core memory, control panel arid typewriter.  The second section i s the input-output system.  Data or programs entered into the system are placed i n memory as decimal d i g i t s .  The IBM 1 6 2 0 i s a variable f i e l d length computer, or i n  other words, each of the 4 0 , 0 0 0 positions of core memory can be addressed individually. In 1 9 6 2 the Computing Center i n s t a l l e d a disk f i l e with a capacity of 1 0 m i l l i o n characters t o increase the storage f a c i l i t i e s of the computer. The card input unit reads 2 5 0 cards per minute, the output u n i t punches 1 2 5 cards per minute.  The p r i n t e r p r i n t s approximately one l i n e  per second. When and How to Decide on Using Electronic Computers The speed with which problems can be solved with computers i s not comparable to any conventional method.  In advertising the advantages  -  15  -  of electronic computers, many popular pamphlets t r y to astound the reader by s t a t i n g that a c e r t a i n machine can multiply  two numbers together i n two  or three millionths of a second. However, multiplying  two numbers with a computer—despite the  f a n t a s t i c c a l c u l a t i n g speed of the machine—would be very slow and f a r too expensive an operation. To explain the problem, l e t us consider the same example and investigate with a computer.  the time required to complete the m u l t i p l i c a t i o n  The time estimates based on experience are as follows: Time Required  Steps  (min. and sec. ") 1  5"  (1)  Write two numbers on paper  (2)  Go to punching machine  10"  (3)  Punch numbers on card  10"  (4)  Write program to i n s t r u c t the computer to accept the two numbers and execute the m u l t i p l i c a t i o n , adjust the s c a l i n g of the product, and p r i n t the result  5'00"  (5)  Punch the program on cards and v e r i f y i t  5'00"  (6)  Arrange computer time  2'00"  (7)  Enter program and data into computer  5"  (8)  Calculate  1"  (9)  Take paper containing r e s u l t out of p r i n t e r  (10)  and p r i n t r e s u l t  Walk back to working desk  2" 10" 12"4-3"  In t h i s example the a v a i l a b i l i t y of computer time was assumed, which i s seldom the case.  - 16 So i t takes anywhere from 10 to 15 minutes to multiply two numbers together with a computer. In a small problem—as i n our example—the computing time represents only a small f r a c t i o n of the t o t a l time involved.  On the other  hand, i f the c a l c u l a t i o n i s highly r e p e t i t i v e — a s i s the case i n many s t a t i s t i c a l analyses, where multiplying, d i v i d i n g , summing and taking  the  square roots of hundreds of numbers are necessary—the time spent on programming i s i n s i g n i f i c a n t , e s p e c i a l l y i f compared to the time required to calculate the same analysis on a desk c a l c u l a t o r . For example, c e r t a i n computers have the capacity to do i n ten hours what i t would take 300 man-years to do; others are slower, but can perform 3-6000 operations per second.  still  At t h i s rate, the computer can  c a l c u l a t e and output i n one-half hour the equivalent  of what one man  could  do working eight hours per day, f i v e days per week, f o r eight years. The decision to use an e l e c t r o n i c computer i s not an easy one make.  to  In most f o r e s t r y problems, the usual hand methods or desk calculators  are more appropriate.  A computer i s useful only when r e p e t i t i v e calculations  must be made, either i n repeating a simple process many times, as i n c a l c u l a t i n g volume tables, or i n solving complex problems, as i n Linear Programming.  I t can be said as a 'rule of thumb"that i f a problem i s highly  r e p e t i t i v e i n nature and the c a l c u l a t i n g process follows d e f i n i t e r u l e s j i f frequent decisions and modifications  of the c a l c u l a t i n g procedure are  not  necessary; i f the formula being solved i s large and complicated,; or i f large amounts of data are to be processed, the use of electronic computers should be considered. When an electronic computer i s r e a d i l y available f o r an organ-  - 17 i z a t i o n , revolutionary changes can be achieved i n management and production. The computer can handle the bureaucratic functions of an organization such as bookkeeping, p a y r o l l , employee records, and supply inventory.  I t can  help management c o n t r o l and improve the a c t i v i t i e s of the organization, develop new and better methods of production, and explore the p o t e n t i a l of new markets.  I t can be used to f a c i l i t a t e or accelerate s c i e n t i f i c ,  engineering, s t a t i s t i c a l and other a n a l y t i c a l or p r a c t i c a l c a l c u l a t i o n s . Furthermore, by applying a computer on a f u l l - t i m e basis, a completely automatic  operating system i s possible i n almost any f i e l d of industry,  commerce, banking, defence or space exploration, just to mention a few. The l i m i t s of and j u s t i f i c a t i o n s f o r the a p p l i c a t i o n of electronic computers to c e r t a i n problems are widely separated and dependent on whether the equipment i s being used on a f u l l - t i m e or r e s t r i c t e d b a s i s .  Organiza-  tions renting computer time must c a r e f u l l y consider what problems can be solved economically by t h i s method. Most f o r e s t r y organizations, with the exception of Forest Services and a few large companies, are i n the renting category.  The  following l i s t can serve as a guide to f i e l d s and problems u s u a l l y large and laborious enough to j u s t i f y the renting of electronic computers: P a y r o l l s , accounting, cheque w r i t i n g Timber c r u i s i n g Timber sale appraisals Continuous f o r e s t inventory Log r a f t inventory Equipment and supply inventory Inventory re-order c a l c u l a t i o n s Operational research  Technical f o r e s t management Project costs Road l o c a t i o n , traverses and earth volume c a l c u l a t i o n s Statistical  analyses  Forestry research A e r i a l photo i n t e r p r e t a t i o n and evaluation Weather report and f i r e control Recovery and q u a l i t y study i n lumber industry Rate of earning computation Scheduling f i e l d operations (Monte Carlo Technique) Pulp and paper ..process control Economy To evaluate the economics of computer use i s a d i f f i c u l t  task.  It i s not p r a c t i c a l to compare computer c a l c u l a t i o n methods with old manual methods, because computers not only speeded up routine procedures, but a l s o created and opened new  f i e l d s of endeavour.  Problems which previously were  impossible or impractical to solve now became quite f e a s i b l e . However, i n c e r t a i n cases an attempt can be made to compare computer costs with the costs of hand c a l c u l a t i o n s . In general, the following points can be considered i f an economic evaluation must be made. The cost of computer use i s high.  The present rate f o r private  organizations f o r computing time on the ALWAC III-E i s $40 per hour and IBM 1620  i s $50 per hour.  on  The i n i t i a l high investment, expensive mainten-  ance, high s a l a r i e s f o r programmers and service personnel, c o s t l y r e t r a i n i n g and method changes, are the main cost f a c t o r s .  - 19  -  On the other hand, the speed and accuracy with which i n t r i c a t e calculations are performed can e a s i l y compensate f o r the high costs.  An  up-to-the-minute progress report or day-to-day inventory assessment i n the hands of an executive manager cannot he appreciated enough. H a l l (1962) stated that writing, checking and 'debugging ' a program 1  usually takes more time than can be saved by the speed of the computer i n one production run.  But, when the c a l c u l a t i o n i s repeated several times  with d i f f e r e n t data, the r e l a t i v e program cost r a p i d l y decreases and i s soon i n s i g n i f i c a n t when compared to the work done. It must be emphasized that the i n d i r e c t value of computer data processing i s sometimes more important culations.  than the speeding up of routine c a l -  For example, one company u t i l i z e d t h i s p o s s i b i l i t y during a  comprehensive inventory of a l l i t s lands.  As each d i s t r i c t f o r e s t e r com-  pleted h i s f i e l d work, summary 3heets f o r h i s d i s t r i c t s were back i n h i s hands long before the inventory of the entire property was enabling him to use the r e s u l t s i n h i s every-day work.  completed—  Another company  gained an appreciable c a p i t a l benefit from income tax deductions by quickly examining a l l i t s continuous forest inventory p l o t s a f t e r extensive frosts damage, and analyzing the loss on a computer.  In these cases the economic  evaluation of using computers cannot be discussed, since the projects could not be done by any conventional method. In s t a t i s t i c a l analyses, where the computer as a tool i s now  taken  f o r granted, a multivariate l i n e a r regression analysis with 8 to 10 variables and several hundred observations was previously considered impossible or nearly impossible to solve.  Using a computer to solve a 40-variable regres-  sion equation with thousands of observations and a l l the possible s t a t i s t i c a l  requirements requires at present  20  -  only a few hours of routine computer c a l -  culation. For future economical evaluation i t must be considered present computers are expensive and r e l a t i v e l y clumsy devices.  that the The  trend  f o r the future i s to construct f a s t e r , smaller, mere v e r s a t i l e and inexpensive computers.  To reduce programming costs, computer research  organizations  are working on program translators which can accept instructions i n everyday English.  They are also developing machines which w i l l read  printed information and understand spoken words and may  ordinary  even be able to  answer by voice. Already there are s i g n i f i c a n t advances i n the case of machines that read printed data.  Magnetic character sensing devices now  can  recog-  nize numbers and l e t t e r s printed i n a r i g i d format. The applications of such machines are unlimited, and w i l l  un-  doubtedly increase the economical f e a s i b i l i t y of computers. Research The computer promises to become the research f o r e s t e r ' s major t o o l i n performing the innumerable calculations necessary to investigate and analyse h i s problems.  In the past, f o r e s t r y r e s e a r c h — e s p e c i a l l y i n  s i l v i c u l t u r e , management and u t i l i z a t i o n — w a s mostly observational. and d e s c r i p t i v e i n nature.  Many problems i n f o r e s t r y are so complex and com-  p l i c a t e d that even highly s p e c i a l i z e d research workers eould not always recognize  or explain a l l the variables a f f e c t i n g a problem.  The  inter-  relationships between these variables have been so d i f f i c u l t to measure that the investigator had to r e l y on h i s experience and i n t u i t i o n alone i n  - 21 i n v e s t i g a t i n g data and i n t e r p r e t i n g r e s u l t s . Mr. Dyer said i n h i s introduction to the meeting of Southwestern Technical Committee i n Shreveport, Louisiana, i n 1962, p r a c t i c i n g "Forestry as an A r t " .  "...we have been  This i s a phrase I f i r s t heard i n Forestry  School and I have long rebelled against i t .  We practice Forestry as an a r t  only to the extent that we lack the knowledge to practice Forestry scientifically." The computer w i l l free the research s c i e n t i s t from laborious c a l c u l a t i o n s , enabling him to devote his f u l l attention to the research problem. Though the f i e l d s of computer a p p l i c a t i o n i n f o r e s t r y research are unlimited and cannot be dealt with thoroughly where computers can be used w i l l be  i n t h i s t h e s i s , a few problems  discussed.  In b i o l o g i c a l sciences, such as Forestry, the forming and t e s t i n g of mathematical models to simulate and examine conditions could be a basic research approach.  These models are complicated  solve by ordinary c a l c u l a t i n g methods.  and f a r too complex to  Using e l e c t r o n i c computers, however,  they are not only e a s i l y calculated, but using automatic programming languages such as Altran, the model can be readjusted or modified to f i t the actual pattern. In lumber-industry  research, the main concern should be to f i n d  and suggest the most e f f i c i e n t method of u t i l i z i n g the timber.  Physical  f a c t o r s , such as species, l o g diameter, length, s p e c i f i c g r a v i t y , damage, and the number of k n o t s — a s well as economic considerations, such as f i n a n c i a l capacity, market conditions, plant capacity and u t i l i z a t i o n and scheduling—could  efficiency,  a l l be analysed simultaneously by a  -  22  -  computer to optimize the p r o f i t . In research i n the Faculty of Forestry at the U n i v e r s i t y of B r i t i s h Columbia, the a p p l i c a t i o n of computers soon became normal p r a c t i c e . Without a computer the professors and students i n v e s t i g a t i n g the wide v a r i e t y of f o r e s t r y problems could not p o s s i b l y have accomplished as much research as they have since the ALWAC III-E was  i n s t a l l e d i n 1957.  Research workers spend a large amount of time surveying ature.  liter-  The volume of present day research and s c i e n t i f i c l i t e r a t u r e i s  enormous.  Rapid access to a special problem t o p i c i s e s s e n t i a l .  These  problems could be overcome—and to a c e r t a i n extent are already being overcome—by equipping one large, c e n t r a l computer with a complete f i l e on a l l publications.  Then, on command, t h i s computer could supply any  interconnected computer across the nation or across the continent with a complete f i l e on any t o p i c .  Thereby, considerable money and e f f o r t could  be saved by not repeating experiments which have already been done. i s an example by Savory ( 1 9 6 2 ) .  Here  A cloud seeding experiment was c a r r i e d out  i n the U.S.A. at a cost of $265,000; the report was published.  Later,  another s i m i l a r experiment was conducted; and when more than 3 m i l l i o n d o l l a r s was  spent the f i r s t p u b l i c a t i o n was discovered.  Had  proper  r e t r i e v a l methods been developed, the 3 m i l l i o n d o l l a r s could have been saved. The a p p l i c a t i o n of data processing methods i n f o r e s t r y p r a c t i c e began as soon as the systems were a v a i l a b l e to the industry.  However, i t  would be d i f f i c u l t to determine when and where e l e c t r o n i c computers were f i r s t applied to f o r e s t r y work. The Forestry Faculty of the U n i v e r s i t y of B r i t i s h Columbia  - 23 c e r t a i n l y belongs to the pioneer group of computer users i n f o r e s t r y . Br. Ker was the f i r s t to employ the a i d of the IBM Computing Center i n Vancouver i n a m i l l study i n 1 9 5 6 . When the ALWAC III-E was i n s t a l l e d on the., campus, Dr. Smith became a member of the University Computer Committee. Ever since, h i s enthusiasm f o r s c i e n t i f i c f o r e s t r y practices has encouraged many undergraduate  and graduate students to study computer programming and  computer operation.  Several of these students have become confident com-  puter users and programmers. Some research r e s u l t s without s t a t i s t i c a l tests have l i t t l e conv i n c i n g value i n f o r e s t r y .  These s t a t i s t i c a l tests are u s u a l l y very  laborious, and, before the a p p l i c a t i o n of electronic computers, were slow or impossible to compute. In f o r e s t r y research and practice, one of the most important a n a l y t i c a l methods i s Multivariate Regression and Correlation  Analysis.  The techniques of multiple regression and c o r r e l a t i o n analysis are described  i n many s t a t i s t i c a l text books; f o r example, Fisher, 1 9 5 2 ,  and Snedecor, 1 9 5 6 . The value of these techniques has been proved i n a l l f i e l d s of f o r e s t r y research and p r a c t i c e . The f a c t o r which discouraged t h e i r wider a p p l i c a t i o n to f o r e s t r y problems was the large amount of computation  involved.  The computer a l l e v i a t e d t h i s s i t u a t i o n .  Regression analysis, of  course, i s also one of the more widely used s t a t i s t i c a l tests i n other scientific fields.  Due to i t s i m p o r t a n c e p r o f e s s i o n a l computer programmers  developed several e f f i c i e n t (1958)  regression programs.  Dr. H u l l and Dr. Froese  wrote a Regression program f o r the ALWAC III-E,' l i s t e d under  the ALWAC III-E Library.  S7  I t i s a very f a s t and e f f i c i e n t program. The  in  - 24 slowest operations are input and output. of observation,  With 10 variables and 100 sets  the data are read i n l e s s than 10 minutes, the c a l c u l a t i o n  i s completed i n approximately the same amount of time, and the r e s u l t s are output i n 4 to 5 minutes.  During t h i s time the computer calculates and  p r i n t s out the.following: Means Variances and covariances Standard deviations Simple c o r r e l a t i o n c o e f f i c i e n t s Regression c o e f f i c i e n t s Y intercept Multiple c o r r e l a t i o n c o e f f i c i e n t Residual  variance  This program can accommodate a maximum of 32 variables. The p r a c t i c a l implications of so f a s t and so f l e x i b l e a program are s i g n i f i c a n t . In p a r t i c u l a r , the a b i l i t y to compute a number of regressions i n series from the basic v a r i a b l e s , f a c i l i t a t e s the determination of the e f f e c t s of secondary variables on the predicted v a r i a b l e .  By various  transformations of the variables, better l i n e f i t t i n g can be achieved, reducing the residual variance;  thus, the unexplained, v a r i a t i o n of the  dependent variable can be reduced and the e f f e c t s of the dependent variables on the independent variable can he ."easily studied. In f o r e s t r y p r a c t i c e , problems usually involve many observations of various factors from which c e r t a i n conclusions  or decisions can be derived.  The quantity of data used and the repetitiveness of the calculations make these problems i d e a l f o r computer use.  - 25 To date the computer has been applied i n f o r e s t r y i n two ways: (1)  To speed up computation of problems.  (2)  To analyse data s t a t i s t i c a l l y . In March, I960, the International Union of Forest Research  Organizations conducted a survey of the use being made of electronic d i g i t a l computers by forest research organizations.  J e f f e r s (1961A) sum-  marized the f a c t s and stated: "...The f i r s t applications of these machines were very n a t u r a l l y concerned with the speeding up of computations which were already being undertaken by other means.  Later, however, i t became apparent that the  most important use of computers was i n t h e i r extension to types of computation that had never before been attempted, not merely because they would take too long, but also because they were too complex to be handled by the conventional machines.  Examples of these calculations are multi-  variate analysis of complex problems,  b u i l d i n g of mathematical models  to simulate p r a c t i c a l problems, as i n the various techniques known as operation research, e.g. Monte Carlo methods, l i n e a r programming, ..." The Forestry Faculty of the University of B r i t i s h Columbia took advantage of the campus computer at every opportunity. of 1962, 1620  In the f i s c a l year  the t o t a l computing time used by the Forestry Faculty on the IBM  alone was 130 hours.  This time would cost about seven thousand d o l l a r s  i f i t had to be purchased at commercial rates. It i s a compliment to the Forestry Faculty that the majority of the computer time used was spent not f o r routine c a l c u l a t i o n s , but f o r complex research problems, as referred to by J e f f e r s . The main f o r e s t r y research f i e l d s i n which the ALWAC III-E and  - 26 the IBM 1620  were used hy the Forestry Faculty are: (1) Mensuration (2) Wood technology (3)  S i l v i c u l t u r e and management  (4)  Utilization  (5)  Entomology  (6) S t a t i s t i c s The computer also could have been useful i n the research of f o r e s t engineering,  fields  f o r e s t economics, forest protection and f i r e control.  I t would be desirable i f the Forestry Faculty and students would take advantage of the campus computers and the already a v a i l a b l e  engineering,  economics and finance programs. To f u l l y discuss each problem solved with the a i d of our computers i s not possible i n t h i s t h e s i s .  However, to demonstrate the applica-  b i l i t y of the e l e c t r o n i c computer i n f o r e s t r y research and p r a c t i c e , a  few  t y p i c a l examples are presented f o r each f i e l d l i s t e d above.  1.  Mensuration  Volume equation improvement and  modifications.  Description: The project i s presently i n progress.  A series of modified  equations were tested and calculated on the IBM 1620.  Results ware compared  with actual volumes and the comparisons were s t a t i s t i c a l l y analysed.  Routine c a l c u l a t i o n of (R) r a t i o of B.C.  F.b.m. over c u . f t .  volume f o r various taper classes. Description: In the chapter l a b e l l e d "Examples", a d e t a i l e d problem write-up,  - 27 program references, and r e s u l t s are presented. Y i e l d and mortality study i n Haney U n i v e r s i t y Research Forest. Description: The data f o r p e r i o d i c a l remeasurements of permanent sample p l o t s were punched on tape. A program- was developed to determine the following information: (a) T o t a l numbers of trees per sample p l o t s , per acre, per period. (b) D.b.h. d i s t r i b u t i o n by species per sample p l o t s , per acre, per period. (c) Total area and t o t a l area y i e l d per species, per sample p l o t s , per acre, per period. (d) Volume and volume y i e l d by species per sample p l o t s , per acre, per period. (e) M o r t a l i t y (No. of dead trees) by species per sample p l o t s , per acre, per period. 2.  Wood Technology  S p e c i f i c g r a v i t y and tracheid length v a r i a t i o n i n second-growth western hemlock (Wellwood, l ° 6 o ) « Description: A multiple regression analysis program was used to study the 2  e f f e c t s and interactions of the r a d i a l distance from the p i t h , the height of the sample i n the tree, the i n i t i a l f i b e r length and the rate of change i n radius on the f i b e r length.  1. Program and Program Write-up are a v a i l a b l e at the Forestry Faculty, University of B r i t i s h Columbia. 2. Program S?, U n i v e r s i t y of B r i t i s h Columbia Computing Center.  - 28 Application of multiple l i n e a r regression to t r e a t i n g experiments of round western hemlock (jurazs, 1962). Descriptions The influence of weight, length, average radius, number of annual r i n g s , s p e c i f i c g r a v i t y , vacuum, bath duration, bath temperature, pressure and pressure duration on the average retention was  analysed.  In t h i s study, a program^ was written to calculate Formula X.  v ;  ;  The Formula X i s indicative, of the retention R.  k l / 6 •_/_  1/2  R-.G73(1.2A - p'7$Lr  «-  1/2 6r> 2 '. t_ +l»7t_5(»OOl4P+100)s_n  ,1/2 ^ l.W(1.-3..B)* T  (D—237  +  ^ " 7  D  The program outputs the experimental values of R, the calculated values of R and the (R exp. - R calc.) deviations; i t also calculates the sums and sum  of squares of the R's and deviations.  The l a t t e r computation f a c i l i t a t e d  a s t a t i s t i c a l analysis to test the difference between actual and calculated R values. Calculation of spring-and summer-wood area. Description: A detailed example of the program and printed r e s u l t s are exhibi t e d i n the Appendix.  Figure 2.  Spring- and summerwood diagram.  - 29 A program was written to calculate the area of r-^ (springwood area of an annual r i n g at a c e r t a i n distance (R) from the p i t h ) , the t o t a l area of the annual r i n g ( r ) , and the percentage of summerwood area.  The  c a l c u l a t i o n may be repeated N times, f o r various sections of a tree. F i n a l l y the program calculates the averages of summerwood width, springwood width, annual r i n g width, springwood area, summerwood area and annual r i n g area f o r each section (Figure 2). 3.  Silviculture  Climatic and s o i l factors c o n t r o l l i n g basal area growth ( G r i f f i t h , I960). Description The effects of average a v a i l a b l e s o i l moisture, p r e c i p i t a t i o n , maximum temperatures, minimum temperatures, average temperatures, and hours of bright sunshine, on monthly growth on Douglas f i r basal area were analysed on the ALWAC III-E. Variation i n natural pruning and other tree c h a r a c t e r i s t i c s of Douglas f i r , hemlock and cedar on Campus and Haney Forests of the University of B r i t i s h Columbia (Smith, et. a l . , 1 9 6 l ) . Description The minimum and maximum values, means, and standard deviation of 18 c h a r a c t e r i s t i c s of 428 Douglas f i r , hemlock and cedar were computed on the ALWAC III-E to permit comparisons of the species and to serve as a reference f o r l a t e r discussions on s i l v i c u l t u r a l controls of the most important tree and wood q u a l i t y f a c t o r s .  -  4.  30  -  Utilization  Log and tree q u a l i t y evaluation, Forest Products Laboratory, Vancouver. Description The f i r s t part of the program computes a l l information pertinent to m i l l studies concerning grade d i s t r i b u t i o n , recovered volumes and  values.  Part two computes c e r t a i n volume, shape, and lumber recovery c h a r a c t e r i s t i c s f o r each l o g and punches these r e s u l t s i n a set of Log D e t a i l Cards.  In addition, t o t a l s f o r each tree are also calculated.  The Program Write-up i s attached i n Appendix 4.  Programmer -  H. Dempster. Determination of Economically  Marginal  Tree Size Through  Conventional and Linear Programming Techniques (Valg, 1962). In t h i s Master's thesis Mr. Valg demonstrated the a p p l i c a t i o n p o s s i b i l i t i e s of Linear Programming i n Forest U t i l i z a t i o n .  Three theoret-  i c a l examples of u t i l i z a t i o n problems were set up and two of them were analysed  on the ALWAC III-E. A standard program of Linear Programming i s available from the  University of B r i t i s h Columbia Computing Center program l i b r a r y . 5.  Entomology-  Analysis of factors associated with d i s t r i b u t i o n and i n t e n s i t y of attack by cone and seed insects i n Douglas f i r , by A. Kozak f o r h i s Ph.D.  thesis. The main purpose of t h i s study i s to determine the character-  -  31  -  i s t i c s that make trees r e s i s t a n t to cone and seed insects.  By an exten-  sive sampling method more than 3500 cones from 9 3 trees were sampled i n 1961,  and close to 4000 cones from 9 7 trees i n 1 9 6 2 .  The number of damaged  seeds was observed with respect to four d i f f e r e n t species of cone and seed insect, (Barbara oolfaxiana. D i o r y c t r i a a b i e t e l l a . Megastigmus spermotrophus. and Contarinia oregonensis).  An e l e c t r o n i c computer (IBM 1 6 2 0 ) was used i n  every aspect of evaluating the data c o l l e c t e d .  Fortran programs were  developed f o r tabulations, percentage calculations of infested seeds, s t a t i s t i c a l t e s t s such as analysis of variance, multiple regression and c o r r e l a t i o n , curve f i t t i n g , and analysis of frequency d i s t r i b u t i o n s . The analysis of t h i s study i s s t i l l i n progress.  6.  Statistics  The Computing Center of the U n i v e r s i t y of B r i t i s h Columbia provides a large number of excellent s t a t i s t i c a l programs.  Most of these  programs were written by professional mathematicians or programmers, but t h e i r improvement i n v e r s a t i l i t y was often i n i t i a t e d by Forestry Faculty research personnel to make them more applicable to f o r e s t r y and other b i o l o g i c a l research  analyses.  The programs l i s t e d below are r e a d i l y a v a i l a b l e at the Computer Center and can be applied to f o r e s t r y problems. For IBM 1 6 2 0 : L i b r a r y No.  Name of Program and Remarks  52- 1  M u l t i v a r i a t e Contingency Tabulation.  53- 3A  Standard Correlation and Regression. Transformation features.  Maximum variables 2 0 .  -  S3-^A  32 -  Correlation and Regression with s e l e c t i o n and automatic reduction.  Maximum variables 20. Transformation features.  Automatic reduction.  Interchange of v a r i a b l e s .  S3-6  Estimation of Parameters f o r a straight l i n e approximation.  Sk-1  Three-factor analysis of variance (P by Q by R, with P and R l e s s than 5). For ALWAC III-E  L i b r a r y No.  Name of Program and Remarks Means Variances and Covariances of Grouped Data f o r 2  S-l  variables. S-3F  Correlation and Regression, etc. f o r up t o 32 variables.  S-^F  Quadratic Regression.  S-6  Means, standard deviations, c o r r e l a t i o n and covariance matrices, and regression c o e f f i c i e n t s f o r up to 8 variables.  S-7  S t a t i s t i c s Package (up to 32 v a r i a b l e s ) .  S-7.1  S t a t i s t i c s Data Input  S-7.2  Means.  S-7.3  Covariances.  S-7.A-  Standard deviations.  S-7.5  Correlations.  S-7.6  Regression C o e f f i c i e n t s .  S-7.7  S t a t i s t i c s Data Input (polynomial).  S-7.8  Residual variance.  S-7.9  •  (linear).  Data Input f o r Grouped Data.  S-7.10  Trigonometric Input.  S-8  D i s t r i b u t i o n of Subjects i n a Group of Subjects of Their Common C h a r a c t e r i s t i c s .  -  S-10  33  -  Selection of subjects i n a Group of Subjects According Specified  S-ll  to  Conditions.  Frequency of Occurrence of Specified Clusters of Subcategories i n a Group of Subjects.  S-12  Analysis of Variance, Randomized Block.  8-13  Analysis of Variance, up to 4^ F a c t o r i a l Design. A t y p i c a l a p p l i c a t i o n of s t a t i s t i c a l methods using the  S t a t i s t i c s Package was demonstrated i n E i s ' (1962) Ph.D.  S-7  thesis " S t a t i s t i c a l  Analysis of Several Methods f o r Estimation of Forest Habitats and Tree Growth Near Vancouver, B.C.", i n which forest productivity and the environment of forest plant communities were evaluated using regression and c o r r e l a t i o n analyses.  This work was  summarized i n University of B r i t i s h Columbia,  Faculty of Forestry, B u l l e t i n No.  4.  To demonstrate the computer procedures i n the case of a regression analysis, a set of four variables and f i f t e e n observations the Forestry Handbook for B r i t i s h Columbia, page 3^7,  were obtained from  to i l l u s t r a t e the  problem of Determination of Photo-volume Relationship—Mathematical  Deter-  mination. The steps and r e s u l t s are presented i n the chapter headed "Examples". In this regression analysis the r e l a t i o n s h i p of crown closure, stand height and crown width on t o t a l cubic foot volume was determined.  The  square of the crown width and the logarithmic function of the t o t a l cubic foot volume were computed to demonstrate the method of variable transformation.  Then three sets of regression analyses with automatic reduction were  computed. In the f i r s t set the order of variables was: height, crown width on t o t a l cubic foot volume.  Crown closure, stand  - 3* In the second:  Crown closure, stand height, crown width, crown  width squared on t o t a l cubic foot volume. In the t h i r d :  Crown closure, stand height, crown width, crown  width squared on logarithmic function of t o t a l cubic foot volume. It i s i n t e r e s t i n g to note that there i s a s l i g h t difference between the Handbook and computed Set I r e s u l t s .  In i n v e s t i g a t i n g the discrepancy  the error appeared quite mysterious; a f t e r the input data were checked several times and no v i s i b l e error was or machine error was  suggested.  However, i n l o c a t i n g error an important  f a c t should always be kept i n mind: people" (Guttenberg, 1962).  located, the p o s s i b i l i t y of program  " V i r t u a l l y a l l errors are made by  By i n v e s t i g a t i n g the o r i g i n a l data again, i t  was discovered that the difference was due to a p r i n t i n g error i n the table, "Basic Data", on page 3^7;  the t o t a l cubic foot volume No.  I * should have 1  been printed as 65 instead of 82. Industry, unlike many research organizations, i s p r i m a r i l y i n t e r ested i n speeding up routine c a l c u l a t i o n s .  However, the larger f o r e s t r y  companies are adapting computers to such problems as q u a l i t y control, market research, and operational research.  The following examples were chosen from  these f i e l d s . A Solution to the Papertrim Problem (Berry,  196l)  There are two main considerations i n paper trimming: (a)  The d i r e c t i o n of a homogeneous bulk of raw or semi-finished product i n t o various sizes and shapes, according to some scheme.  (b)  The packing problem of placing objects of known dimensions into an empty space of u s u a l l y known dimension. An IBM program was developed by the Portland IBM  office.  This  - 35 program was designed to search and suggest the most economical cuttings of parent r o l l s . The program i s available i n the l o c a l IBM o f f i c e . Process Control on the Paper Machine (Linkhart, 1962) Potlatch Forests, Inc., Lewiston, Idaho, and IBM began a study to determine the problems of process control i n paper-making. It i s an accepted and useful method i n the case of computer applicat i o n to b u i l d a completely mathematical model of the entire paper-making process.  Information on the paper-making process was s t a t i s t i c a l l y analysed  on a computer; from the r e s u l t s a preliminary "mathematical model" of the paper machine was b u i l t .  The objective was simply to provide the operators  with a guide to good test r e s u l t s .  With t h i s model, a computer program was  written f o r the common product with respect to grade requirements.  A paper  tape reader connected to the computer was used to simulate instrument readings.  When the grade requirements were typed on the console typewriter, the  computer calculated and typed out the operating procedure necessary to maint a i n optimum q u a l i t y and output.  At the same time, allowable deviations were  computed f o r each s p e c i f i c variable and were stored i n memory.  When ( i n -  strument) readings v i o l a t e d any of the allowable deviations, the typewriter printed the v i o l a t i o n i n red.  The project i s s t i l l i n progress.  In f o r e s t r y i t seems that data processing was most welcomed i n the f i e l d of Continuous Forest Inventory ( C F l ) .  The a p p l i c a t i o n of computers i n  t h i s f i e l d i s very prominent because CFI i s more than an inventory method. It i s a system of checks and balances f o r the management of the f o r e s t . I t includes a modernized continuous forest inventory, with systematic individual  - 36 tree a  grading  system  of  and  forest  CPI are  from  increase  in  1950.  systems. in  CFI  has  the  an  impressive  the  speed  At  the  In  1952,  electronic  computing,  management  planning  and  balances.  from  1925  to  measurement,  Minnesota of  same  history  the  National  routine  time,  i n  North  America.  Forest,  U.S.A.  calculations  experiments  application  of  were  by  using  The  f i r s t  by  systems  records  f i r s t  IBM c a r d s  conducted  IBM c a r d  _The  was  IBM m a r k  became  attempt made  .  sensing  widely  used  practices. The  u t i l i z a t i o n  (1)  The  technique  of  the  IBM c a r d  system  is  summarized  below.  machines;  i f  a  transformed  entire  mark  to  range  tabulators  and  (i)  sorter  A  card  information. ( i i )  A  card  groups, ( i i i ) top  An  at  take  margin  computers,  a  the  speed  routine  of  machine time. of  card,  perform  forestry  a  can  such  600  is  also  these  f i e l d  punching  sensing machine.  on punched  cards,  card  to  sorters,  cards  the  were  use  of  calculators,  to  the  value  of  200G  cards  per  typewriter  accumulate  that  totals  of  the  punched  minute.  can  print  an  pre-selected  etc.  which  prints  reading  of  machines,  can  be  the  punched card  although  sophisticated  calculations  manual  punching  as  automatic  easy  the  by  available.  totals,  f a i r l y  used,  according  machine  cards  automatic  sorter an  on  transposed  cards  is  for of  an  became  these  is  was  machines  a  It  combination can  by were  separates  totals  of  data  business  interpreter  A  Most  The  punched  system  interpreters,  tabulating  entire  were  cards  the  of  data  sensing  punched Once  (2) an  f i e l d  hole  on  the  content. they  calculations  computed  data  with  are at this  not a  electronic  rapid  rate.  equipment;  and,  - 37 because t h e i r r e n t a l p r i c e i s not p r o h i b i t i v e , t h e i r a p p l i c a t i o n i n large f o r e s t r y organizations should be encouraged. The CPI r e s u l t s are not an end i n themselves; they are the basis of another complex f i e l d , the f i e l d of modern Forest Management. The manager of a large f a c t o r y or b i g transport f i r m can e a s i l y check a l l parts of h i s organization through personal v i s i t s , telephone or reports submitted by supervisory personnel.  calls,  Forest property, however, i s  never seen i n i t s e n t i r e t y . Maps, a e r i a l photographs, and reports may  help  the manager i n h i s decisions, but a f u l l and comprehensive view of h i s operation i s d i f f i c u l t to achieve.  The complicated nature of the f o r e s t ,  wood operations, and the a l t e r n a t i n g market conditions make h i s managing decisions hazardous, e s p e c i a l l y i f h i s decisions are based on so-called "old experience".  The r a p i d l y changing i n d u s t r i a l and marketing require-  ments demand more from a manager than experience; they need s c i e n t i f i c a l l y analysed f a c t s and suggestions.  The s c i e n t i f i c analysis can only be achieved  by c o l l e c t i n g a large number of observations and transposing t h i s data i n t o charts, graphs, tables, figures of p r o f i t , and rates of return.  Therefore,  a f t e r d e r i v i n g the IBM card r e s u l t s , further data processing may be necessary; because of the complex nature of these c a l c u l a t i o n s , the d i g i t a l computer becomes indispensible i n f o r e s t r y management.  Although the use of  operations research and decision theory i n "optimizing"returns from an entire wood-supply system requires an e l e c t r o n i c computer, i t must again be emphasized that i n many problems the old hand c a l c u l a t i o n methods and desk c a l c u l a t o r s are quite appropriate. The computer should be used only i n complex and highly r e p e t i t i v e c a l c u l a t i o n s , or i n programmed decision-making factor.  where time i s an  important  - 38 A few examples are discussed i n the following paragraphs. I t i s now  evident that the computer has made the standard volume  tables obsolete i n inventory work.  New  techniques have been developed^using  computers f o r volume c a l c u l a t i o n s (Palley, 1963). A computer program r e c e n t l y developed at Purdue calculates the i n t e r e s t rate earned i n any complex long-range investment i n which a l l costs and incomes are known or can be estimated  ( H a l l , 1962).  This computer  program enables the i n d u s t r i a l f o r e s t manager to use the rate of returns as a basic guide i n choosing a c t i v i t i e s i n which to invest; since t h i s i s the c r i t e r i o n on which many corporate a l t e r n a t i v e s are judged, he i s i n a p o s i t i o n to compete f o r c a p i t a l on the same basis as other portions of h i s company.  This approach i s , of course, not new;  however, because of the  lengthy c a l c u l a t i o n s required, i t was previously impractical and  neglected.  Of the various aspects of wood management, the maintenance of the timber supply i s the most important one.  An excellent example of the  a p p l i c a t i o n of computers i n t h i s f i e l d was demonstrated by the Hiwassee Land Company ( H a l l , 1962).  In the f a l l and winter of I960, a complete CPI system  was designed f o r the company's 500,000 acres, d i s t r i b u t e d over f i v e states. This estate was  divided into 27 administrative compartments, which i n turn  were sub-divided i n t o management u n i t s .  The blocks varied from ^0 to 1000  acres.  on punched card equipment except  A l l data from CPI were processed  f o r tree and plot volumes, which were computed on an IBM 650 computer. the spring of 1961, application.  a l l information was processed  By  and ready f o r further  The next question was which p l o t should be cut and replanted  f i r s t to maintain maximum returns, i n other words, what maximum wood flow from company lands could be expected f o r the following 25 years.  Two  sets  - 39 of p r o j e c t i o n equations were developed f o r pine and hardwood.  The pine  equations were based on those of Schumacher and Coile (i960).  The hardwood  equations were developed from increment core data. i n t e r v a l were calculated.  Volumes f o r each 5-year  Then, using a regression program on the IBM  a set of growth regression equations was developed.  1620,  These equations could  predict hardwood volume i n any stand at any future date f o r which cutting was planned.  The Schumacher pine equations and the hardwood equations were  amalgamated i n a computer program, f i r s t f o r the IBM 7090, then f o r the IBM 1620.  The projection program was applied to a Monte Carlo schedule  technique f o r CPI p l o t s to give an estimate of wood flow.  The r e s u l t s gave  the executive management a dependable picture of wood supply from company land f o r the next 25 years.  The wood flow was a l s o converted into d o l l a r s  to show the expected cash flow of the company's investment. The scheduling of f i e l d operations was also programmed f o r a 1620 computer.  The program computes the operation schedule i n about 2 hours.  I t i s i n t e r e s t i n g to mention that the operation schedule c a l c u l a t i o n was attempted by four company foresters and that a f t e r a week of 12-hour days of desk c a l c u l a t o r computation i t was discontinued. By re-measuring the CPI p l o t s , the company can make further improvements i n management control.  The developed equations w i l l not only be  strengthened by each re-measurement, but w i l l be continuously adjusted to give a more r e l i a b l e set of production guides. This may sound f u t u r i s t i c , but the time i s r a p i d l y approaching when B r i t i s h Columbia f o r e s t r y companies—if they wish to maintain t h e i r competitive p o s i t i o n — w i l l have to apply s i m i l a r techniques.  - ko  -  Examples  In the following pages the use of the e l e c t r o n i c computer w i l l he i l l u s t r a t e d by examples i n : Mensuration Wood Technology Statistics These have been chosen because of the association of the author with either the development or a p p l i c a t i o n of the programs. The interested reader can see how both extensive and intensive uses of the e l e c t r o n i c computer has been reported i n Forestry B u l l e t i n No. 3 by Smith, Ker, and Csizmazia ( l 9 6 l ) .  Other examples are available i n recent  publications of the Faculty of Forestry (e.g. E i s , 1962) and of the agencies mentioned i n the bibliography. The author has been most intimately associated with the development of regression programs f o r studies of growth and y i e l d and f o r evaluat i o n of factors that should determine l o g and tree grades. example of y i e l d study was  A detailed  reported by the author i n Forestry U66 and i n  1962-63 the author completed a report on development of an IBM  Fortran  program i n p a r t i a l f u l f i l m e n t of the requirements f o r Forestry 566. The examples that follow should convey a general impression the present p o t e n t i a l f o r use of e l e c t r o n i c computers i n f o r e s t r y and f o r e s t r y research.  of  Description of Conversion Factor^ (R) Program  E  17^54545(Dr +  (L  +  1.5)  D )  2  2  r  X The program was written i n ALTRAN ' language f o r the ALWAC III-E i|  computer.  The ALTRAK i n s t r u c t i o n s and the compiled machine language program  are exhibited i n the Appendix I. The program calculates R values f o r 1-40  f t . l o g lengths, and any-  desired top diameter and taper classes. The program requires three input s p e c i f i c a t i o n s T space Dp. space DE where T  = Taper, 1" i n X length i n f t .  Dr = Minimum diameter top Dg = Maximum diameter top In the presented  example, R values were calculated f o r 1-40  6'*-20 top diameter and a taper r a t i o of 1" i n n  f t . logs with  6. 1  The required time f o r computation and output on punched tape i n t h i s case was approximately 5 minutes.  The r e s u l t s can be reprinted at  any time i f desired, using the punched output tape and the Flexowriter (free of charge).  Description of the Springwood  and Summerwood^ Program  The program was written i n Fortran 2 f o r the IBM 1620. l i s t i n g and r e s u l t s are i n Appendix I I . The program expects the input of  3. Forestry Handbook f o r B r i t i s h Columbia, pages 114-115 4. ALTRAN i s s i m i l a r language to FORTRAN.  Fortran  - k2 N  = Number of sections  RO  = R distance from p i t h  R ( l ) = r i r a d i a l distance of springwood IR  = Tree No.  Control Cards: ( 1 ) Blank card stops the c a l c u l a t i o n . ( 2 ) - 1 i n card column 5 n d 6 causes the machine to separate trees and a  calculate sums and averages f o r a tree. Output: ASP AS  springwood area = summerwood area  AT  r i n g (springwood and summerwood) area  RATIO = springwood percentage i n radius RSP  = average springwood radius  RSU  = average summerwood radius  average r i n g radius  RTO ASP  = average springwood area  AS  = average summerwood area  ATO  = average r i n g area  Time required to calculate the r e s u l t s of the presented example was 5 minutes. Procedure f o r a Regression Analysis IBM working cards and sheets are i n the Appendix. used: Step 1 :  IBM 1 6 2 0 .  Program used:  Punch data on cards.  S 3 - 4 A (See Appendix I I I ) . See Card No. 1 .  Computer  Step 2:  P r e p a r e t r a n s f o r m a t i o n c a r d s (Card No. 2) and i n s e r t them i n t o Program  S3-4A (Page  k).  Step 3*  Prepare "Introductory"  c a r d ( C a r d No. 3).  Step ki  P r e p a r e " C o n t r o l " c a r d o r ( C a r d No. k) c a r d s .  Step 5s  E n t e r Program S3-^A i n t o computer f o l l o w e d b y t h e I n t r o d u c t o r y C a r d , D a t a , and " C o n t r o l " c a r d o r c a r d s . Computer completes  the c a l c u l a t i o n s and p r i n t s t h e r e s u l t s ( s e e  Results). I n t h i s example f i f t e e n and one dependent—were  sets of four v a r i a b l e s — t h r e e  punched on c a r d s a s d a t a .  Then a s h o r t  t i o n F o r t r a n program was w r i t t e n t o p l a c e the ^ t h v a r i a b l e position, calculate  independent transforma-  (Y) i n t o t h e 5th  t h e square o f v a r i a b l e No. 3 and p l a c e i t i n p o s i t i o n  No. *f and f i n a l l y t o compute t h e l o g a r i t h m o f Y and p l a c e i t i n p o s i t i o n No. 6.  T h i s program was punched onto c a r d s as F o r t r a n i n s t r u c t i o n s and was  i n s e r t e d i n t o t h e a p p r o p r i a t e s e c t i o n o f Program 33-^A. To a n a l y s e t h e r e s u l t s , ' output f o r m a t .  one must f i r s t become accustomed t o t h e  The output format used h e r e i s t h e s o - c a l l e d E - t y p e  float-  i n g p o i n t c o n v e r s i o n code, which means t h a t t h e r e s u l t s a r e p r i n t e d a s a d e c i m a l f r a c t i o n t o a power o f 10. mean v a l u e o f crown c l o s u r e — s e e  F o r example,  "Results",  t h e f i r s t number i s t h e  page 1—and appears as  6.633333 E + 01 which means 6.6333333 x 10 - 66.33333 1  or t h e mean o f L o g ( T o t .  cu.ft.  V) i s  ^.527205E-00 = ^.527205 The p r i n t e d t a b u l a t i o n o f R e s u l t s i s c l e a r and needs no e x p l a n a tion.  However, t h e i n t e r p r e t a t i o n o f t h e meaning o f r e s u l t s  requires  - 44 knowledge of the theory and the data upon which the r e l a t i o n s h i p i s based. When analysing the r e s u l t s , i t i s apparent that Set I I I , i n which the logarithm  of the dependent variable was calculated and the transformed  crown width was a l s o included, gives the best solution, since the Regression equation explains 87.08 per cent (R t o t a l cubic foot volume.  = .8708) of the t o t a l v a r i a t i o n of the  Between Set I and Set I I , with a l l variables i n -  cluded, the difference of R  2  i s only .0114 and .0242 respectively, and does  not j u s t i f y the extra e f f o r t spent i n c a l c u l a t i n g the square of the crown width and the logarithmic value of the t o t a l cubic foot volume. Observing the equations of Set I, i t can be seen that crown c l o s ure i s the most important variable i n determining the t o t a l cubic foot volume of stands from a e r i a l photographs.  The difference between  R — 2  including crown closure, stand height, and crown width—and r — i n c l u d i n g 2  crown c l o s u r e — i s only .0313.  In other words, stand height and crown width  contribute only 3.13 per cent i n removing the v a r i a t i o n of the t o t a l cubic foot volume. The recommended equation i s Y = 2.974 + 1.893X SE  E  = 1.139  r = .902 where Y = Total cubic foot volume of a l l species i n cunits. X = Crown closure. SEg = Standard error of estimate i n cunits, which i s the probable error l i m i t (+) and (-) from the value of Y. r = the single c o r r e l a t i o n c o e f f i c i e n t showing highly s i g n i f i c a n t correlations at the 1 per cent l e v e l .  This exercise was completed f o r demonstration  purposes.  The  volume equation presented above was based on the observation of only one photo interpreter f o r a r e l a t i v e l y even;::-aged stand; therefore, the r e s u l t s and conclusions are not necessarily generally v a l i d .  Summary and  Conclusions  E l e c t r o n i c Data Processing has made i t s i n i t i a l impact on forestry.  Publications concerning various applications of Punch Card  Systems and computers increased g r e a t l y i n the l a s t f i v e years. Foresters are quite aware of the importance of e l e c t r o n i c c a l culations and despite i n i t i a l d i f f i c u l t i e s i n applying these devices, more and more f o r e s t r y organizations are applying them.  The i n i t i a l  difficulties  were due to the f a c t that electronic computing demands a new way of thinking, data c o l l e c t i n g and r e s u l t i n t e r p r e t a t i o n . With a better knowledge of the c a p a b i l i t i e s , l i m i t a t i o n s and f i e l d s of a p p l i c a t i o n of electronic data processing devices, f o r e s t e r s w i l l be able to explore more and more of the secrets of the forest enabling them to p r a c t i c e more s c i e n t i f i c f o r e s t r y .  To keep up with technological advance-  ments f o r e s t e r s have to be able to judge when and how computers.  to use electronic  I t would be advantageous, but not necessary, that f o r e s t e r s  write or wire t h e i r own programs; however, to be able at l e a s t to discuss t h e i r project with professional programmers i s absolutely essential to understand what, why,  and how a computer or data processing system works  in principle. The electronic data processing i s expensive.  I t i s important to  develop proper data c o l l e c t i o n , transposition technique and a well-written  - k6 program to avoid countless corrections, expensive re-runs and worthless results. " I t i s possible f o r computers to make up to m i l l i o n s of errors i n seconds—an e f f i c i e n c y that we can hardly a f f o r d and no human being can match" (Guttenberg, 1962). Computers, no doubt, w i l l become an important t o o l i n analysing and c o n t r o l l i n g our forest p r a c t i c e s .  However, i t must be emphasised that  computers always w i l l be an a i d only and although the understanding and mastering of t h i s device i s demanding, one must remember not to think l i k e a computer, but to t r y t o make the computer think l i k e a man!  - k% Glossary of Terms  Electronic data processing i s a r e l a t i v e l y new f i e l d and, of course, has a vocabulary of terms a l l i t s own.  These terms have not been c l e a r l y  defined and, though they are well understood by computer users, may sound strange to the p u b l i c . This Glossary i s designed as an a i d i n c l a r i f y i n g the meaning of the  computer terms used i n t h i s thesis; i t does not attempt to be a computer  term lexicon. Accumulator:  A part of the l o g i c a l - a r i t h m e t i c u n i t of a computer, i n which sums, products, etc., are b u i l t up.  Address:  The sequential number of a l o c a t i o n i n memory where information i s stored.  Alphameric character:  A term f o r numeric, alphabetic and/or special characters.  Analog computer:  A device which performs computations i n terms of measured continuous quantities, such as elevation, t emperature, etc.  Automatic programming: A procedure i n which the machine i s used to translate the  English or algebraic-type symbols i n t o machine  language. Binary d i g i t :  E i t h e r a 0 or 1 which may be used to represent the binary conditions On or Off.  Bit:  One binary d i g i t .  Blank:  The absence of any character or information.  Card f i e l d :  A f i x e d number of consecutive card columns assigned  - k& to a u n i t of information; e.g., card column 10-1$ can be assigned to the i d e n t i f i c a t i o n number. The basic symbol i n terms of which a program must be  Codes  expressed  i n order to be accepted by the machine.  Commands  Same as " i n s t r u c t i o n " .  Consoles  The panel containing control switches and keys, and operational d i s p l a y l i g h t s .  Control units  The part of the machine which d i r e c t s the i n t e r n a l a c t i v i t i e s of the computer.  Data processings  Any system f o r r e c e i v i n g information and producing a specific result.  D i g i t a l computers  A computer which represents i n t e r n a l information i n d i g i t a l form.  Drums  A type of storage device.  Executions  The operation of the computer under d i r e c t i o n of the program.  Fixed points  An integer without a decimal point or decimal portion.  F l o a t i n g points  Any number written with a decimal point.  Flow charts  A schematic outline of the computer program.  Format s  The arrangement of the input and output  Input,  outputs  data.  The process of entering data i n t o the machine, or externally recording information stored i n the machine.  Instructions  A set of codes that w i l l cause the machine to carry out a single operation.  Librarys  An inventory of proven programs.  Locations  A u n i t of storage i d e n t i f i e d by an address.  Loading:  The process of feeding information i n t o the memory v i a the input u n i t .  Machine language:  The basic code system t o which the computer responds.  Memory:  Same as "Storage".  Printer:  A device that records output data on paper.  Programming system:  Any method of programming problems, other than machine language, c o n s i s t i n g of a language (e.g. Fortran) and i t s associated processors.  Punched tape:  A paper tape on which information i s represented by punched holes.  Read:  To transmit information from an input device t o the computer.  Storage:  A section of the computer i n which data and i n s t r u c tions are stored.  Store:  To place information i n a l o c a t i o n i n storage so that i t may be r e t r i e v e d f o r l a t e r use.  Word:  A group of d i g i t s normally treated as a u n i t by machine.  - 50 -  Bibliography ALWAC. 1957. Alwac Manual of Operation. Hawthorne, C a l i f . 67 pp.  ALWAC.  130^0 South Cerise Ave.,  Berry, A.B. 1956. A Test of Punch Card and Sense Marking Techniques f o r Permanent Sample P l o t Measurement and Analysis. Dept. of Northern A f f . and Nat. Resources. Forestry Branch, Forest Research Div. S. & M. 56-8. 6 pp. Berry, C S . 1961. A Solution to the Paper Trim Problem. Portland, Oregon. 26 pp. Davis, H.O. 1962. Computers and You. n i c a l Paper 62-TP-98. 6 pp.  IBM Corporation,  American Pulpwood Association Tech-  Department of Labour, Canada, i960. No. 9-A The Current Status of E l e c t r o n i c Data Processing i n Canada. 30 pp. Dyer, D.M. 1962. P r i n c i p l e s of Data Processing Machines. wood Assoc. Shreveport, Louisiana. 2 pp. Edenfield, T.C. 1962. Computers i n Wood Procurement. Assoc. Technical Paper 62-TP-100. 12 pp.  American Pulp-  American Pulpwood  E i s , S. 1962. S t a t i s t i c a l Analysis of Several Methods f o r Estimation of Forest Habitatsand Tree Growth Near Vancouver, B.C. Forestry B u l l e t i n No. k, Faculty of Forestry, U n i v e r s i t y of B r i t i s h Columbia. 16 pp. Forest Club, U n i v e r s i t y of B r i t i s h Columbia. 1959. Forestry Handbook f o r B r i t i s h Columbia. Vancouver 8, B.C. 800 pp. F r a z i e r , G.D. and R.B. Carney. 1961. Computing Average Log Values f o r Timber Appraisals Using IBM 650 or Univac S o l i d State 80 Computers. Technical Paper No. 5^. P a c i f i c Southwest Forest and Range Experiment Station, Berkeley, C a l i f . 16 pp. Froese, C. and T.E. H u l l . 1962. Computing Center, University of B r i t i s h Columbia Report on A c t i v i t i e s Prepared October, 1962. Computing Center, U n i v e r s i t y of B r i t i s h Columbia. 17 pp. Froese, C. 1958. A l l You Need t o Enow to Use the Library of S t a t i s t i c s Programs f o r ALWAC III-E. Computing Center, University of B r i t i s h Columbia. 32 pp. Gedney, D.R. and D.E. Martin. 1959. S p e c i f i c a t i o n s f o r C a l c u l a t i n g Several Equations of Relationship between Two Variables on a Type 650 E l e c t r o n i c Computer. P a c i f i c Northwest Forest and Range Exp. Station. 15 pp.  -  51  -  George, C.S. 1959• Management i n Industry. Englewood C l i f f s , N.J. 585 pp.  Prentice-Hall, Inc.  G r i f f i t h , B.G. I960. Growth of Douglas F i r at the University of B r i t i s h Columbia Research Forest as Related to Climate and S o i l . U.B.C, For. Bui. No. 2. 6k pp. Guttenberg, S. Industry. 6 pp.  1962. Computer Programs of Interest f o r the Pulp American Pulpwood Assoc. Technical Paper 62-TP-102.  Hensel, J.S. 1959. IBM Port-A-Punch Board and Port-A-Punch Card. American Pulpwood Assoc., 220 E. kZ St., New York 17, N.Y. Technical Release No. 59-R 18. 3 pp.  H a l l , O.F.  1962. Computers i n Forest Management. Technical Paper 62-TP-101. 10 pp.  American Pulpwood Assoc.  IBM Application Report 79* Continuous Forest Inventory with IBM Mark Sensing. International Business Machines Corp., 590 Madison Ave., New York 22, N.Y. 8 pp. IBM.  1959* Management Decision-Making Laboratory. International Business Machines Corp., 590 Madison Ave., New York 22, N.Y. 12 pp.  IBM.  1959* Reference Manual IBM 1620 Data Processing System. International Business Machines Corp., 590 Madison Ave., New York 22, N.Y. 38 pp.  IBM.  i960. General Information Manual Introduction to IBM Data Processing System. International Business Machines Corp. 95 pp.  IBM.  1961. General Fortran Manual. International Business Machines Corp., 590 Madison Ave., New York 22, N.Y. 103 pp.  J e f f e r s , J.N.R. 1961A. The Electronic D i g i t a l Computer i n Forestry. I.U.F.R.G. 13. Congress. Band 2. 25 17. J e f f e r s , J'.N.R. 196l£>. New Developments i n Forest Management. Paper given to Section K* (Forestry) of the B r i t i s h Assoc. f o r the Advancement of Science, Nordvich, 1961. 7 pp. Jurazs, P.E. 1962. Application of Multiple Linear Regression to Treating Experiments of Round Western Hemlock. Faculty of Forestry, University of B r i t i s h Columbia. 23 pp. Typed Report. Linkhart, R.C. I 9 6 I . Process Control on the Paper Machine. Forests, Inc., Lewiston, Idaho. 5 PP«  Potlatch  Martin, D.E. 1961. Electronic Computer Program 650-16 Lumber T a l l y V o l ume by Lumber Items by Logs f o r Lumber Recovery Studies. S t a t i s t i c a l Techniques Report No. k-6l. P a c i f i c Northwest Forest and Range Experimental Station. 10 pp.  - 52 McCormick, E.M. 1959. D i g i t a l Computer Primer. Inc., New York, N.Y. 214 pp.  McGraw-Hill Book Co.,  McCracken, D.D. 1961. A Guide to Fortran Programming. Inc., New York, N.Y. 88 pp.  John Wiley & Sons,  M i l l e r , R.M. 1955. Flow Charts—The Beginning and the Guide. Forest & Range Experiment Station. 40 pp.  California  Myers, D.M. i960. Computing Center, University of B r i t i s h Columbia Report on A c t i v i t i e s . 16 pp. Newport, C A . and T. Leach. 1959* A Method f o r the Application of Change i n Grade Factors to Individual Logs—An IBM 650 Program. Technical Paper No. 41. P a c i f i c Southwest Forest and Range Experiment Station. Berkeley, C a l i f . 9 pp.. Palley, M.N. 1963. P l o t or Point Sample Volumes i n Even-aged Stands Using a Computer. Journal of Forestry. V o l . 6 l , No. 1:28-31. Savory, L.E. 1962. Research and Computers. Technical Paper 62-TP-99. 5 pp.  American Pulpwood Assoc.  Smith, J.H.G., J.W. Ker and J . Csizmazia. I96I. Economics of Reforestat i o n of Douglas F i r , Western Hemlock and Western Red Cedar i n the Vancouver Forest D i s t r i c t . Forestry B u l l e t i n No. 3> Faculty of Forestry, University of B r i t i s h Columbia. 144 pp. Smith, K.T. Essay.  195^. The Application of IBM Machines to Forest Inventory. Faculty of Forestry, University of B r i t i s h Columbia, 13 pp.  Schumacher, F.X. and T.S. C o i l e . i960. Growth and Y i e l d of Natural Stands of Southern Pines. T.S. Coile, Inc., Durham, N.C 115 pp. Snedecor, G.W. 534 pp.  1956.  S t a t i s t i c a l Methods.  Iowa State College Press.  The Timberman. 1957. Business Machines. The Timberman. December 13, 1957. P P . 33, 36-40, 43-44, 48, 52, 57-58, 60, 70, 7^, 76, 84-85. Valg, L. 1962. Determination of Economically Marginal Tree Size Through the Application of Conventional and Linear Programming Techniques. M.F. Thesis. University of B r i t i s h Columbia. Wellwood, R.W. i960. S p e c i f i c Gravity and Tracheid Length Variations i n Second-growth Western Hemlock. Jour. For. 58 (5):36l-68. Wright, J.P. 195^. Continuous Forest Inventory Using Business Machine Methods. 1954 Proceedings, Society of American Foresters Meeting. 4 pp.  - 53 Wrubel, M.H. 1959. A Primer of Programming f o r D i g i t a l Computers. McGraw-Hill Book Co., Inc., New York, N.Y. 230 pp. U.B.C. Computing Center. 1959. A Progress Report on Computer Applicat i o n s . Computing Center, University of B r i t i s h Columbia. 6 pp.  Appendix I Calculation of B.C.fbm/cu.ft.  ALTRAN program,computing the r a t i * o f B.C.fbm / cu.  read c  programmer: Csizmazia, I 9 6 I . read, x  5  read, db,de el= 1  k 1  d= db r=(l7.U5U545*(d-l.5)**2)/(d**2+(el/x+d)**2) punch,r-l.2 d=d+l test=de-d i f (fest  2  )Z,l,l  el=el+l punch,lcr test= +0-el 1  i f (test) 3,U,U 3  punch,le,50f go to 5 end  AIHAC  III-E  M a c h i n e l a n g u a g e PROfRAM.Coded b y J . C S I Z M A Z I A , i n ALTRAN, Program c a l c u l a t e s the B . C . B o a r d S c a l e and c u . f t .  230f kO 5520292e 8l7dUl3f 5bU09d89 C5U579U5 U860172U C5U3U1UI 5bUU9d01 87130OOO 552c8cOO c 5 W l ^ Ob089d8 83UHI20 0001l a8 5b3b9dlc c52fUlUU 00000000 872d8l2c Ob089d87 Ob089d87 8ba2e885 9d6bU9U0 C537U133 5b2f9d01 00000000 9d.60U.9Ul 5b379d87 c52fUl37 c000008l 9d6oU9U2 c537^1^3 5b2f9d89 80000081 UO 527c05eU 230f Ul 5b3f8lU>l 5b2e9d01 83U2II20 31287db0 9d038l7d c5^3df5a 83U211a0 671bld8b UlUU5b3e 36085529 a0000086 f5aUUdl3 9d01c5UU 00000000 80000081 Ud932800 UlU25bUU 36'08Ul2a 0000872d a300al00 9dlcc^hG 5bU39dlc 83Uoila9 11600000 79^6ld3a C5U679U6 OOOOllbc 00000080 H32UIU3 ld260000 80000081 00010002 kl c335Uc0c 230f U2 113bdf78-00000000-00000000-00000000 3632552U-00000000-00000000-00000000 df28l728-00000000-00000000-00000000 36321133-00000000-00000000-00000000 11300000-00000000-00000000 8l2c8 2d -00000000-00000000-00000000 83U01138 -00000000-00000000-00000000 0000872d -00000000-00000000-00000000 83U01la5 U2 f5a58e30. 230f 7d Oa0065c3 28007ddU U l U a l O l 290elll0 00000080 5da6 fb8 2922118a lllc2800 Ud8ca505 119b2800 3 9 2 e 6 l c d 7ddc5dae 1903alOO 7dde5daO ldla3000 7fb06lc2 Dddll982 7fb26l0U 7fb33000 670U5da6 33abl90a 26006708 19l6339f e5783000 9f000000 5daa3200 290e9f00 lllU51ce 3b2e3aOO al01e96l 00000000.If803c00 7d fcd9db20 7  7  s  7  7  I96I.  ratio (R).  Dt. Lth 2 3 1+ 5 6 7 8 9 10 11 12 13 1U 15 16 17 18  19 20 21 22 23 2h 25 26 27 28 29 30 31  32 33 3h 35 36 37 38 39 1+0  6  8  10  11  12  13  lh  15  16  17  18  19  20  "+.77 5.26 5.61+ 5.95 6.20 6.1+1 6.59 6.7U 6.87 6.99 7.09 7.18 7.27 7.3^ 7.U0 1+.61+ 5.1"+ 5.53 5.8U 6.10 6.31 6.50 6.66 6.79 6.91 7.02 7.11 7.20 7.27 7-3^ 52 5.02 5.1+1 5.73 6.00 6.226.1+1 6.57 6.71 6.81+6.95 7.0I+ 7.13 7.21 7.28 k.39 I+.90 5.30 5.63 5-90 6.13 6.32 6.1+9 6.63 6.76 6.87 6.98 7.07 7.15 7.22 U.27 I+.78 5.19 5.52 5.80 6.03 6.23 6.1+1 6.56 6.69 6.80 6.91 7.00 7.09 7.16 1+.16 I+.67 5.09 5.U2 5-71 5.9"+6.15 6.32 6.1+8 6.61 6.73 6.81+ 6.9U 7.02 7.10 1+.05 I+.56 1+.98 5-33 5.61 5.866.06 6.21+ 6.1+0 6.5I+ 6.66 6.77 6.87 6.96 7.01+ 3.9U 1+.1+6 1+.88 5.23 5.52 5.775-98 6.16 6.33 6.1+7 6.59 6.71 6.81 6.90 6.99 3.83 h.35 1+.78 5.13 5.h3 5.68 5.90 6.09 6.25 6.1+0 6.53 6.61+ 6.75 6.8U 6.93 3.73 1+.25 1+.6B 5.0I+ 5.3I+ 5.60 5.82 6.01 6.18 6.33 6.h6 6.58 6.69 6.78 6.87 3.63 1+.16 "+•59 I+.95 5-25 5-51 5.7"+ 5.93 6.11 6.266.39 6.51 6.62 6.72 6.81 3-53 1+.06 I+.50 1+.86 5.17 5."+3 5.66 5.86 6.03 6.19 6.33 6.1+5 6.56 6.66 6.76 3.hh 3.97 l+.l+l 1+.77 5.08 5.35 5.58 5.78 5.96 6.126.26 6.39 6.50 6.61 6.70 3.35 3.88 1+.32 I+.69 5.00 5.27 5-51 5.71 5.89 6.05 6.20 6.33 6.UU 6.55 6.65 3.26 3-79 1+.23 1+.60 U.92 5.19 5.^3 5.61+ 5.82 5-99 6.13 6.27 6.38 6.1+9 6.59 3.18 3.71 1+.15 1+.52 1+.81+ 5.12 5.36 5.57 5.76 5-92 6.07 6.21 6.33 6.1+U 6.5U 3.10 3.62 I+.07 1+.1+1+ I+.76 5.0I+ 5.29 5.50 5.69 5.86 6.01 6.15 6.27 6.38 6.1+8 3.02 3-5*+ 3.99 I+.36 l+.6"9 I+.975.2.1 5. "+3 5.62 5-79 5.95 6.09 6.21 6.33 6.1+3 2.9h 3. "+73.91 1+.29 it.61 I+.90 5-lh 5.36 5.56 5.73 5-89 6.03 6.15 6.27 6.38 2.87 3.39 3.83 1+.21 h.$h I+.83 5.08 5.30 5.^9 5.67 5.83 5.97 6.10 6.22 6.32 2.80 3.32 3.76 1+.11+ 1+.1+7 I+.765.01 5.23 5."+3 5.61 5.77 5.91 6.01+ 6.16 6.27 6.22 2.73 3.21+ 3.68 1+.07 l+.l+o 1+.69 1+.9U 5.17 5-37 5.55 5-71 5.86 5.99 6.11 2.66 3-17 3-61 1+.00 1+.33 ^.62 1+.88 5.10 5-31 5.^95.65 5.80 5.93 6.06 6.17 2.60 3.11 3-55 3.93 1+.26 U.551+.81 5.0U 5.21+ 5.U35-59 5.7"+ 5.88 6.01 6.12 6.07 2.5U 3.01+ 3.U8 3.86 It-.19 1+.1+9 "+.75 1+.98 5.18 5.37 5.5^ 5.69 5.83 5.95 6.02 2.1+8 2.98 3M 3.79 1+.13 1+.1+2U.68 1+.92 5.13 5.31 5.U8 5.61+ 5.78 5.90 5.97 2.1+2 2.91 3.35 3-73 I+.06 I+.36I+.62 1+.86 5.07 5.26 5-^3 5.58 5.72 5.85 5.92 2.36 2.85 3-29 3.67 1+.00 I+.30 1+.56 1+.80 5.01 5.205.37 5.53 5.67 5.80 5.88 2.30 2.79 3.22 3.60 3.9h 1+.2I+ 1+.50 1+.7I+ 1+.95 5.1*+ 5.32 5.1+8 5.62 5.75 5.83 2.25 2.lh 3.16 3.5"+ 3.88 U.181+.1+1+ 1+.68 1+.90 5.09 5.26 5.1+2 5.57 5.70 5.78 2.20 2.68 3-11 3-"+9 3.82 1+.12 h.39 1+.63 1+.8U 5-Ol+ 5.21 5.37 5.52 5.66 5.73 2.15 2.63 3.05 3-"+3 3.76 1+.06 h.33 "+•57 1+.79 h.98 5.16 5.32 5.U7 5.61 5.69 2.10 2.57 2.99 3.37 3.71 h.Ol 1+.27 1+.51 1+.73 "+.93 5.11 5.27 5.1+2 5.56 3 . 6 ' 5 3.95 1+.1+6 U.68 U.885.06 5.22 5.37 5.51 5.61+ 2.05 2.52 2. h 3.32 1+.22 3.60 3.90 l+.l+l 1+.63 1+.83 5.01 5.17 5.33 5. **75.60 2.01 2.1+7 2.89 3.26 1+.16 3 . 5 * + 3 . 8 1 + U.36 1+.58 I+.78 1+.96 5.13 5.28 5.1+2 5-55 1.96 2.1+2 2.81+ 3.21 l+.ll 5.51 3M 3.79 I+.30 1.92 2.37 2.79 3.16 i+.o6 1+.25 U.52 1+.73 1+.91 5.08 5.23 5.38 5.1+6 3 . 1 + 1 + 3 . 7 " + 1.88 2.33 2.7"+ 3.11 1+.1+7 1+.681+.86 5.03 5.19 5.33 1+.01 1.81+ 2.28 2.69 3.06 3-39 3.69 3.96 1+.20 1+.1+3 I+.631+.81 I+.98 5.1U 5.29 5.U2 1.80 2.21+ 2.61+ 3.01 3-3^ 3-61+ 3.91 1+.15 I+.38 I+.58 "+.77 I+.9U 5.10 5.2I+ 5.38 9  Appendix I I  Calculation of spring and summerwood area  P RIN T F 0  FOR  J .  CSIZMAZIA  ON  MAR.  19  F. O K I - B A N . L. C O M P I L F . . . . .. C  CALCULATION  OF  C  COOED  KOZAK  A .  SPRING-  AND  SUMMER-WOOD  AREA  U I f'FNS I ON  S u M S P ( 2C ) , S O M S ( 2C ) , S U M I' ( 20  DIMENSION  k ( 2C ) , R M 2.Z ) , A R E ( 2C ) , R A " l I 0 (  [) I M E N S I O N  A V S P ( 2.Z ) , AV T R ( 2Z ) • A V S P ( 2 C ) , A V S ( 2 Z ) , A V T ( 22  KFAD  2\  BY  4 i  i  u  =  ) , A R F T ( /.Z ) , A V P R ( 2.Z )  (16) i  F O R M A T ( / / V X , .'^HASR, DO  11  s(  M  i C X , 3HA  S,l2X,iHA  T , 12 X , b H R A T I  0 / / )  I=2,N,2  S U M S R ( I.)  = C. G  I ) =C.  C  SUM'T ( [ ) = C. C SSP(I)=C.C S S R ( I )= l l _  ST R ( I ) =  _  kF. AD  1  FORMAT IF G  1t  Ib ,  WILL  4  FN=FM+1 .Z  2  FORMAT .  "  1) = RA( 1 DO  ka  I b  i2  r  (  MRET(  b  7  4  o ,  STUP.-1  CARD  wILL  CALCULATE  SUMS  N  1G X , H H T R F F  o'  I  -1  1 ) =3.  C(  I ) =  )+R(  N0.  , I5,F6 . G / / )  I )  14 1 b 9 *  iv,  2  1  CC  I ) = ARE(  (RA(  . OR(  I)  **2.-RA(  ) /( k(  I  I - 1 )+ARE(  I )+R  (I  I +  I ) **2  )  1 ))  I )  =1/2  PRINT _  R  )=R0  1=2,  KAl" I  J  ) ,I  C. C  )=RA(  9 _  5  ( / /  A R E ( I-  ,0 '  = 2, M  I=iJ,M  DO  3 "  2 , I R , F  b  il  7  1  (KO) CARD  k (  tI  R(>» ( R ( I )  ( E6 . 0 , I 4 t - U . 2 , 4X , I 2 )  F K IM T  f~  C.0  c.:  FN=C . C  1C'  C  ) •  I-i + 1  PRINT i  2C  »N  FORMAT M  ) , S S P ( ? C ) , S S k ( 22 ) , S T R ( 2',  FORMAT " SSP  4  SSR(  •:  SIR  ("i j  7 , J , A R E (  I-1  ) , A R E ( I ) , A R F T ( I ) , R A T IO(  ( 2X , I 3 , I X , E l i = SSP ( I  I ) = SSR(  )+R (  I ) +R(  I )  I+1  ( I ) = S T R ( I ) +R ( I )  . 6 , 2X  )  +R  ( I +1 )  , E M  . o , 2X  I )  , E l o .ft , 2X  , El 3 . 6 )  , i i U M S P ( I ) = SUM SH ( I ) + A R F S U MS U 6  S U M T ( I ) = S U M T < I ) +ARF.T ( I )  lib To 'Vc" lb 132_  PRINT  "  "  32  FORMAT  ( / / S X  , 8HAVFRA0F  FORMAT(SX,_>HPSP, UQ  S / /)  of  PR I K I 31  ( I - l )  ) = S U M S ( I ) + Ak F ( I )  1 C X , 3 H R S U , 1GX »3H R T C , 1GX , 3 H A S P  , 1GX,2HAS,  I _____ N » 2 _  A V K R ( I ) = S S P ( I ) 7P N A VSR ( I )= SSR ( I ) / F N A V T R J I ) = ST R ( I ) / F M A V SP ( I ) = SU M S P AVS( _<  A V_J _ I ) =SUf-lT ( I J~  d  V , J , A V P R ( I ) , A V S R ( I ) , AVTR ( I ) , A V S P ( I ) , AVS ( I ) , AVT ( I )  FORMAT  (  I 2 , 6 b l 3 . 6 )  CONTINUE 00  TO  1_6 _ C O _ N T STOP" bND  ) / F M  -175*  PRINT 9  ( I ) / F N.  I ) = SUM S.(. I ) / F N  21 1NUE_ "  "  1GX  T  3 H A T 0/)  '-Oi  o CL  3 C  o  c "J  c) ; 4 4 .JJ UJ '.u •-G j " , c •o n c •c n -c x .n c  cD c3 c3 c : 4 4 + 4 'ju :xi a.) LL; o ' N - h- < : AI J~I i D o r— •— c 3 -c rv! -o CD  D  4  O  LP, - O  o  X CV CV  x  -n x  x  r-  X  rvi O J  cv cv rv cv C.J  O o 4 4 4  CD  4  LO  cv cv cv cv cv cv  C  r-  j~,  •—  —  C 3 ;v X •0 CV j p, 0  CD  c  Jl  cv  r-j  cv cv  CV P J  cv C3  0  C 3 (.3  rvj CD ,C3 CD CD  4  •o r>  X  c; 4 4  t3  4  4  UJ O  JJ  •—  cv > C D ' X cv r— J-; O 0 -0 r> O >- O -c > cv - 1 -o J I ro ro LP, c v i r - X  •r> X  4  4  O  Jl-.-l  X  O  cv cv  CV  C3  C3  4  4  O  JJ O  LU LU  C3 O  -0 vi  •C V) 0 - i-o CV C V < >  PI LO  C3  -0 Jl  ;.0  X  4  4  > >  '—  r—  Jl  4  UJ U J rO  4 LU -PI  rvi  4  4  > -PI  -O  -O  1—  «—  •  CM  0 ro ro ro  —  •O  -O  rv  >  Jl Jl  1  X  00  •0  ro r— CD  cv r--  >  •0  cv  •rv •cv rv rv CV cv c 3 C 3 CD CD CD CD C D 4 4 4 4 4 4 4  —  <;  CD CD CD 4 4 4 LU LU LU VI O O  r - cv ro .pi V ) X X 1— •r— J l , — X 0 C D N- X cv x O L P O •-p.  c—  r-_  CM >—  —• —•  >— <— ;  '—  CD CD CD CD JCD CD CD ; 4 4 4 4 414 4 L U L U ' J J L U !JJ L U L U : r— — r- , x > Ol •— — C 3 X | r - CM J~I cv 1— ;—• <D x | > -O -O —• , x -o - 1 r— * x !LO LO • • p i ;  cv r-_ PI  j -  cv cv cv cv  _  LU  O  '— JI J* 0 0 X LP, J l  -  4  ro O  r— ro r> cv " O x  Jl Jl JI r-_ LP, C 3 N - CD - 0 J l CD r X O J l cv cv O  (  4  4  !  JJ  cv  4  •x  4  UJ X  4  1—  CV  0  J J .JJ J J U J CD -*j CD 0 CD X CD —  LU  X  r-  0  4  4  0  r-  LL) LU  4  .U X  LP,  ;M cv rvj CD C J O 0  x  UJ  cv cv cv cv  •—  o  n x  oO  -o  •JJ  CD  O  m  N-  rvi  X  :JJ U J  rvj  x  C -c o  -e  r, Jl  1  CV  ro O  4  4 JU  4 4 U J :JJ ro CM  '—LP,  O CD CD 0 4 4 4 4 L U U J LU LU  LP.  C3  o rv <; — — r> rvj ro j - r, <— o <2 cv ro x o '— > r \ ! ro i— co x cv ro ro X •— ro O CV CO N- CD  4 UJ  cv  •— J l r—  C3  o  4 LU  CO  ' 0 rvi CD r-_ rv; c 3 O X rCD X •0 JI ''3 > , — JI  rv  CD  4 4 UJ U J  cv cv cv  >-  ,  CO CD CD CD CD CD  x o CD C 3 CV ( 3 CM ' o c 3 X - C CV  X  o-  o 4  uj 'UJ  0  o  C )  LU 'JU  0  UJ  >—  •-o I / I J I CV J rO  j~t :r,  UJ "O  ^ r—  _u  CD 0  4  UJ  o o o o ci 4 4 4 4 +  r - j - , O r> r-- c) CD rv X c 0 CD  O LP,  JJ LO  X  4  LU UJ  ~n  -c u*  Jl-  (3  r~  •—  -Pi  •—  - X ,CD  r-  ; x  LO  ro  X,  x  1  v  rv  4  -O  <:  —  —  cv  cv  -n  c\  1 CV'CV C3|C3 0  C3  LU ' LL' LU Pi  LU CV  4 • 4 4 O X  •cv!rv — -CK3 0 CV) LP,  <; 0  ! JJ-;  O  •0  4  .>  > 0 C3  -  !>  •JJ" LU LU UJ CTi  rO -O "O r> 0 —  —  LU CD  UJ'JJ  LU  X > CD C 3 ro on > •> O LO rv — O rv r— r_ - O X " O ••c ro r— CV ro CD r-~  X X  O  .•v  CV  CM  -O  Jl  —  n  C  :  LD  CV CD 4  CM CV CV 'CM <— CM CD CD CD | C D CD CD 4 4 4 - 4 4 4  LU  LU LU LU  x rv o xi r~ cv > o • o > LO  O X •O  LU L U L U LD -O r~ .PI x <—  o ro JI '' N O PC) <— X X r> ''CD r-- cv C D X C> •— ro •— ro LO o  ,—  CV  ro  --  . cv ~o 3 'Jl  0  5»v  rj  —I  o  CTi co  r--. u>  u*>  O  N  *r ro  CNJ  O  A) AJ A I Al AJ rsj O O O O C 3 o  + -JJ + UJ + J+J + LU + LU +  LL'  C N ; 1—  I S  n >- x. •— •— o  > > xi  o  c  — I  St  I-  •—  •—  <  i—  O  •— s  ,—  j^- "O X A '— AJ c ; 'X .—  < 3  J * x. I- c  s  r>- i — c X X, c  •—  —  A )  ,—  —  ,—  ,—  O  o  O  o  O  C 3  O  •—  c .> -<•> X) X : t 3 r-O O x> X 'XI Al • C X ' X "O X, x ,*•«- X A' > X ro O cv c o x  + + + J+J + L+U L+L I LU LU •JJ  -c •A  •—  <t  J-  ."fl •c (. 3  ix  '—  •T)  -6  •o  cv A ! A) c -. o O  •Al O t 3  A '  + + + + + + u LL! LU  .-— A !  cA!c X •C  'JJ  UJ  S\  I -  y-  X  i—  rO  S  A  :  o  X A X X C J X .— •— JJ IX. St <-  (  o O  o  I  iJJ  o  n  I UJ  c  St  C 3  I  I  ; O o <") ( ) n  'JJ  L U  L U 1 U  C J  (.3  C i  '.3  AJ  s  <  'JJ X f. J  II  I  L U  O O D O O O D O t) () O Q O c < 3 O 3 ( 3 O C ) '  3 )  X: 'X XI X .n - X I <• 3 X X X O X A) O r 3 I - X X X , X, s  •—  A  1  —  •—  •—  •—  ' —  I  O  I  o  C3 I  O I  C3 C.3 O  I  St  O I I I  LLI J J • U J LU LU LU LU O l H ) 0 ( ) O O (5 O O O O O  <)  (Jo o o t)o a o o o o o o o (.'• X j o O A.' rx !ro o  >—  j o ^  •n/i .}  1  O O I  a. I  LL' > <  M  I  | I  I  I  I  I  J J I U J LU J J ' J J LU O jO O O . O < 3 o o >o O O C3 o o o jo O c J ' O o •X C3 | X X XI O X AJ XI jX) > O X C3 XI st ; J X i CAIIO •— J J  rjc.  .2  O 0 O O ' — C3 C3 j O O C3 C3 CD :  O  a  o•>  C3 c > X X •—  a. A  ILL  iO A J  ro st  X I I  O  I S  Q  N  to i,n »-.r •^r  tn  to  Appendix I I I Regression a n a l y s i s  Data card  ?5  ii£  27  113  / a o o o o o o o y ij o a o o o o n o o a o o s c o o o o o 3 o o o o o o o o o o o o n n o o o o o o o o o o o n o o o o o o o o o o o o o o o o o o o o o o o o 1  2 3 4 5  6  I  8 9 IC II 12 13 14 lb 16 I ' .8 13 20 21 22  21 It  25 26 2) 28 29 30 31 32 J3 34 35 36 3 ' J8 39 40 41 12 43 44 45 <E 47 46 19 50 51 52 53 54 55 56 51 58 54 60 61 62 63 64 65 66 61 68 S3 10 11 12 73 74 15 76 77  It 79 8 f  i.i 1111 M i Qgi 1111 11111 [][] 11 M 11111 i i 11 11 111 J i« 1111111111 111111) n 111111 i i 111111 n i 12 222222222n222  2 n 2 2 2 Z 2 2 2 2 Z Z 2 2 2 2 2 2 2 ? 2 2 ? 2 2 2 2 2 2  .13 3 .1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3  ? 2 2 Z 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  2 2222222222?7  033333333333333333333333333333333333333333333333333333333  4:4 444444444444444444444444444444444444444444444444444444444444444444444444444444 5;5  5 5 5 [ ] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 b 5 5 5 5 5 5 5 b 5 5 5 5 5 5 5 5 b 5 b 5 5 d S 5 5 5 5 5 5 5 5 5 5 5 b 5 5 5 S 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5  6.6  6 6 6 8 6 6 6 6 6 8 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 0 6 6 6 6 8 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6  7 7 7 7 [] 7 7 7 7 7 7 7 7 7 7 7 7 [] 7 7 7 7 7 7 7 7 7 7 7 7 7  7  7 7 77  7 7  7  7  7  7 7  7  '7  7  7 7  7 7 77 7 7  8 8 8 8 8 8 8 88 8 8 8 8 8 88 8 8 88 88 88 88 8 8 8 8 8 S8 8 8 8 8 8 8 88 88 8 8 8 8 88 8 8 8 8 8 8 8 8 8 8 8 8 8 8 « 8 8 8 8 8 8 8 8 8 8 8 8 8 8 88 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 8 3 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 3 5 9 9 9 0 I ) 3 l 5 6 1 8 9 10 11 12 13 14 15 16 11 18 19 20 21 22 23 24 25 26 fi 26 29 30 3> 37 33 34 3b 36 33 3 35 4C "1 <2 43 44 «s 4(, l[ 43 49 50 51 52 53 54 5b 56 57 58 59 FO 81 6? 63 64 65 66 67 St 69 70 11 7 ; 73 74 75 76 77 78 79 IHMf.081  Card No. I  SO  7  7 7 7 7 7 7  7  7 7 7 7 7  Transformation card! (FORTRAN arithmetic statement o f  = x| )  >:<4> = X<3>*X<3>  STATEMENT NUMBER  n  n  ron V J » COMMENT-  n IJ  1  \  FORTRAN  IDENTIFICATION  STATEMENT  UU oo o o oIJLJ 0 0 0 [ J U 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0o o o o o o o  010  0 0 0 0  1|2  3 4 5 6 73 74 75 76 77 78 79 60 7 1 9 10 11 12 13 H 15 16 17 18 19 20 21 22 23 24 25 26 2? 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 4 3 44 45 46 47 48 49 50 51 52 53 54 55 5S 57 58 19 (0 61 62 63 64 6S 68 67 68 69 ID 71 72 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1-1; 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  mill 1 l  212  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  24  j 313 1 1  3 3 3 3 3 3 3 3 3 D 3 3 3 Q 3 3 3 3 . ; S 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3. :  414 4 4 4 4 4 Q Q Q 4 4 4  1  515 | 1  4 Q4 Q 0 4 tl4"D4  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4  4 4 4 4 4  4'  4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 - 4  5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5-5 5 5 5 5 5 5 5 5 5 5 5 5 5 5-5  616 6 6 6 6 6 6 1  )  717 7 7 7 1 818 8 8 8  66  6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 8 6 6 6 6 6 6 6 6 6 6 6  (J 7  7•  7 7 7 7 7 7  D7  8S  0 8 Q 8 Q B  8D80Ll8|]8D888888888888888B888888888888 8  7 7 7  7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7  77  7 7 7 7 7 7 7 7 7 7 7 7 7 7 7.7  8 8 8 8  6 88 8 8 8 8  6 6 6 6 6 6-6  7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7  8 8 8 8 8 8 8 8 8  9!9 9 9 9 S 9 S 9 9 9 9 9 S 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 i | 2 3 4 5 6 7 8 3 10 11 12 13 14 15 16 17 13 19 211 21 22 23 24 25 2S 27 28 20 30 31 32 33 34 25 3 5 37 38 39 4 0 41 43 4 3 44 4 3 4 5 07 45 49 50 51 52 53 S 55 55 5? 53 59 B0 51 F2 ?3 C4 C5 06 F7 C3 60 70 71 IEM94GQI  Card no. 2  68 83 9  8 8 8 8 8 8 8  3 9 9 9 9 9 9 9 73 71 75 76 77 73 79 80  Introductory card k i n column 6 i n d i c a t e s the ntimber of v a r i a b l e s at input. 6 "in column 12 indicates the number of variables a f t e r transformation* %  a  0 0 0 0 0 0  1  2 3 4  5 6  I. I J 1 I I t  fl 0  ;  8  9  i n columns 17, 18 indicates; the number of rows of data  0 0 0 0 0  \C  3 3  0 0 0 0 D C 0 0 0 0 0 3 0 0 0 0 0 0 U 0 0 0 U 0 0 0 0 0 0 0 0 U 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 0 0 0 U 0 0 0 0 0 0 0  .8 19 20 21 !? 23 24 35 26 2? 28 29 30 3 1 32 J3 34 3 5 36 3 ' 38 39 40 41 42 43 44 45 46 41 45 13 50 51 52 53 54 55 56 57 58 55 60 61 62 63 B4 65 65 8 1 68 69 70 71 72 7 3 74 15 76 77 78 7 9 U f  1 1 J I 1 1 1 1 I [j I 1 1 1 I I I 1 I 1 11 I 1 1 1 1 1 1 11 1 1 11 1 J i I I 1 11 1 11 1 I 1 1 1 1 1 11 1 t 1 1 11 1 1 11 11 1 1 11 1 I  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  i  oo m  11 12 13 14 l b IB P  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  2 2 2 2 2 2 2 2 2 2 2 2  ?  3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3  4 4 4 4 4 [ ] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ' I 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ' { 4 4 4 4 4 4 4 4 4 4  5 5:5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 [| 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 b 5 5 5 5 5 5 5i 5 5 b 5 b 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6[] 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6  fi6  6 6 6 6 6 6 6 6 6 6  GS  6 6 6  G  6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 8 6 6 6 6 6 6 6  G  6 6 6 6  6  7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 77 7 7 7 77 77 77 77 7 7 ' 7 7 77 7 7 7 7 777 7 7 7 77 7 8 8 8 8 8 8  B  8 8 8 8 8 8 8 8 8 8 8 8 6 8  e  3 8 8 3 8 8 8 8 8 8 8 8 8 8  B  8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 8 8 8 8 8 8 « 8 8 8 8 8 8 3 3 8  S  8 8 6 8 8 8  9 9 9 9 9 9 S 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 S 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 3 9 9 9 9 9 9 9 9 9 9 9 9 9 9 I  > 3  4 5  6  7 6  9 10 11 17 13 14 15 16 11 18 19 20 21 22 23 24 25 26 11 28 29 30 31 37 3 3 34 35 3S j i ,18 *  <1 >l 43 44 45 48 «  !BM.508i  Card No. 3  48 49 50 51 52 53 54 55 56 57 5B 59 60 61 6? 63 64 65 66 67 68 69 70 71 77 73 »  75 7 5 n ; j  )  9 go  Control card 1 i n column J, indicates; that C o r r e l a t i o n and' Regression on a subset of o r i g i n a l variables w i l l be calculated. k i n column 6 indicates the number of variables; included i n Set I .  / SO 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 9 G 0 0 0 0 0 8 0 0 0 0 0 0 1  2 3  1.1  4  5  gm  6  7  8  9 10 If 12 13 14 lb 16 17  18 IS  U  0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  20 21 22 23 24 25 26 21 28 29 30 31 32 J3 34 35 36 3 ' 38 39 40 41 42 43 44 45 46 47 48 19 50 51 52 53 54 55 56 57 58 55 60 61 £2 63 64 65 66 £7 68 69 70 71 72 73 74 75 75 77 ; 8 79 Of  1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 11 1 1 11 1 1 1 1 1 1 11 1 ! M i l  1 1 11 11 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  112 2 2  2 2 2 2 2 2 2 2 2 2 2.22 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 22 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ?  1,13 3 3  33 3 3 3 3 3 3 3 3 3 3 3 3 3 3  3  3 3 3 3 3 3 3 3 33 3 3 3 3 3 3 3 3 33 3 33 3 3 3 3 3 33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3  44 4 44 4 44 4 44 44 444 4444444 4 4 4 4 4 4 444444444444 4 4 4 4 4 4Q444444444 4 4 4441444444444 4 4 4 4 4 44 4 5 5 5 5 5 55 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 55 5 55 5 55 5 5 55 5 5 5 5 5 5 5 5 5 5b 55 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 8 6 6 6 66 6 6 6 6 6 6 6 6 6 6 6 8 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 66 6 6 6 6 6 6 6 6 66 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 77 7 7 77 7 7 7 7 7 7 7 7 7 7 77 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 77 7 7 '.! 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 77 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 88 8 8 8 8 8 8 8 8 8 8 8 8 8 88 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 88 8 8 8 8 8 8 8 8 8 8 0 8 8 8 8 88 8 8 0 8 8 8 8 8 8 8 99 9 9 9 39 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 8 9 3 9 9 9 9 9 9 9 3 - 1 5 6  7  B  9 10 11 IV 13  U  15  16 17  18 19 20 21 22 23 24 25 25  21  28 29 30 31 3? 33 .34 35 3* J ' l  Card  a  .15 «• •> 417 43  No.UA  « <b 4S 47 49 49 50 51 52 53 54 5b SB 57 58 59 60 61 62 63 64 65 66 67 tt 63 70 71 7? 71 14 75 7ft 77 7a 79 SO  Control card 1, 2, 3, and 5 i n columns 3, 6, 9 and 12 s p e c i f y the v a r i a b l e s w i l l be included i n Set I .  /  3 5  1 2  s 0 0 0 0flfl0 0 I  2  !l 0 fl 0 0 0 0 fl G  00000  C  000003000B 00  t)  00000000D 0000000  on  0000000000000  D  0000000000 0  3 4 5 6 7 8 9 10 11 12 13 14 lb IB 17 . 8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3' 38 39 40 41 42 4 3 44 45 4t 47 48 tS 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 10 71 72 73 74 75 76 77 78 79 8f  . 11 g 1111 ii 11 i i 111 n i 11 n 11111111111111111 n 111 II 11111111 ii u i ii I 11 I 1111111 u 11111 2 2 2 2 2 [] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 2. 2 2 2 2 2 2 2 2 2 2 2 ? 33333333  0 3 3 3 3 3 3 3 3 3 3 33 3 3 3 3 3 3 3 3 3 3 3 33 3 3 3 3 3 33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3  33 3  4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5.5 5 5 5 5 5 5 5  51]  55 5 5 5 5 5 5 5 5 5 5 5 5 5  55 5 5 5  5 55 5  6 6 6 6 6 6 6 6 6 S 6 6 6 6 6 8 6 8 6 6 66 86 6 6 6 6 6 6 6 6 6  55 55  86 86 6 6 6  55  5  55 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5  66 6 6 6 6 66 6 66 6 6 6 6 6 66 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6  4 * 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 77 7 7 7 7 7 7 7 7 7 77 7 1 7 7 7 77 7 77 7 77 7 77 7 7 7 8  8 8  77  77 7  7  7 77 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7  8 8 8 8 8 8 8 8 8888 8 8 8 8 8 88 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 88 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8  88 8 8 8 8 8 8 8 8 8 8 8 8 8 8  88 8  9 9 9 9 9 9 9 9 9 3 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 Q 9 9 9 9 9 9 99 9 9 9 99 9 9 9 9 9 99 S 9 9 9 9 9 9 3 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 1  1 3  i  5 6 7 8 9 10 1! 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33,14 35 36 j f 3 8 * .  42 43 44 45 4* 47 43 49 5(1 51 52 S3 54 55 56 57 5B 59 63 61 62 63 64 65 66 67 68 69 70 71 77 73 74 75 76 17 78 70 8(1  1673*308 i  Card No. I4./B  Control card 0 i n column J indicates; that C o r r e l a t i o n and *~ Regression with Automatic Reduction w i l l be calculated.  /  0  u oQO ao o o o 3o  1  2 3  4  5  6  Do  o o o nn o o o o a c o o o o o 3 o ao o o o uo o o u o o o o o o o o u o oo o o n o o oo o o o oo ooo o oo oo o oo o ooo  J 8 9 IL' II 12 13 14 IS 16 I I iS 19 20 21 22 23 24 25 26 2) 28 !9 30 31 32 33 34 3 5 36 3> 38 3 9 40 « 1 42 1 3 44 45 4f 4) 48 (9 50 5 1 S2 53 5< V i 56 5) 58 55 ED 6 1 62 63 64 63 66 6 ' 6 8 69 70 71 72 73 74 75 76 77 79 79 OC  .1.1,1 i 11 111 11 1 1 I 1 i t i l 1 l 1 I 1 1 M l i i i I i n i i i i i i i i ' i i i 1 i I I i i I I i l i i 111 r 11111111111 11111 i 2 2-2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 2 2 2 7 2 2 i 2 2 2 ? 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ? 7 U  333333333333333333333333333333333333333333  3 33333333333333333333333333333333333  4.4:4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ^ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5:5:5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 b b 5 D 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 -6 6:6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 B 6 6 6 6 6 6 6 6 (i 6 6 6 6 6 8 6 6 6 6 6 G 6 6 6 6 6 6 6 6 6 S 6 6 6 6 6 6 6 6 6 6 6 6 8 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 / 7 7 7 7 7 7 7 7 7 7 7 '7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7-7 7 7 7 7 7 8888888888888888883888838888888888888888888888888888888888388888  8888888888388888  9999999999999999999999S9399999999999399399399SS999999999999999999399999999S9999 B 1  7 3  .1 5  6  7 9  9 10 11 12 13 14 15 16 17 19 19 20 21 22 23 24 25 26 2 7 28 79 30 31 32 33 34 35 35 J ( JS J l B! ' Ittil «  «  It.  Card No. U/C  47  Is  n SI 5 ! 52 53 54 55 56 57 5B 59 EO 81  62 63 64 65 66 67 68 69 70 71 77 73 74 75 76 71 78 79 81)  R e suits PRINTED FOR  J . CSIZMA7.IA  ON  MAR.  IV  AJt.J_A ».MEAN VALUES OF VARIARLFS  AT 19J  HR. 14-  F Q K T R  c\x/. c l o s u r e  (3. 633 33 3E+C 1 4 .5272C5E-0C  stand Ht  log(tot.cuft.V)  cw width 2 .240G0GF+GI 3  Z  cw. width b.28f999E+32  h .  .  tot cu.fi.V. 9.S79999E+01  5  6  COVAR IANCES ROW 1 1 .48G9b2E +02 ^ C b 3 34 2E-GC_  2.42 1428E+C1  ROW 2 k!. 42 1 42bE+G I 9 ..-54 0 57 IE-G 1  2.G92bS7E+01  - 1.C7bC71H + C3  2.H374 2bb+ 32  2.9bMb7lt+Cl  1.2699b7E+C3  _R0W __3_ ' 2. CV2Hb7E+C l" • 1 .4C7 9b2E-G 1  2. 95bb71t+Cl  2 .897I42E+CI  1 . 338085E+03  - 1 .6 77 1 4 2E+0 1  ROW 4 •1 .G7SG71E+G3 • ( .689 1vGE -GG  1 . 26W57E + G;-)  1.336G8bE+03  . 6 . 27 6445E + C4  -9 . 1 1 11 42E+C2  ROW b 2 . HG2rib7E +02 7 .04737 IE-0 0  b . 3742t>SE + C 1  1.6/ri42E+0 1  -9 . 11 M 4 2h+ 32  . b . S 0.S.999E +0 2  KOW _ 6...... 3.On 3 34 2E-0 0 7,8 0b37 IE-0 2  V. 3udb71£-01  1.4G795 2E-0 1  -7.68919GE-00  2. C2Hb7E+C2 p  t'W  Uil  8 .374285E+!  ;  :  Y  '2 . 11. 10  7 .04 7 37  IE-C!  ,1  9 8 7 6 .  STANDARD DEVIATIONS I  5  4 3  1 .2lb943E+C I 2.794382E-G 1 6  -  1 . 6 8 4 4 6 6 E + C1  3 5.382b1lE-GG  4 5 2.b0b283E+G2  2.SbC6dbE+Cl  C O R R E L A T fON "c0EFF f C Y E W T S ROW_ _ 1 ~1 . CC'CCCC .8978820 V .  ROW 2 .11812414 .19c6G8J2 ROW  ".11812414  -.31930973  3S262241  .9029702 1  l.CCCCCCCC  .32631320  30093293  . 194V0736  9922979'4  -. 1-22 1 3973  3  -.31950973 -.09.560892 ROW _ 4 -.3526224 1 -. 1C985429A  .32631320  •"  b .9C297C2 1 • 9 88 74 b 1 4 A  ) U  . 30093293  U 1/ U -_• U  U  < >  -. 1425801 1  .99229794  ROW  ROW 6 .8978fcs2Cl  S e t I-  . 1.949 .:73o  -.122 13973  14258C11  . 198608  -.09.560892  1098 34 2V  Y - tot. cu.fiV. t  REGRESSION COEFFICIENTS  cyvdosdre 2 .G0b7"92E-GC  l  10  3  3  7  CONST AN TaTERlM "RESIDUAL R SQUARED  s t a n d HI  " 3 . 7564 7CE -02  =  =  8 .302So4E-0 1  -b . 9803CbE +C1 =  VARIAM'C'E'  cw width  1.269473E + 02 . 8466o860  1 .fCGCCCCC  . 9887431<+  COEFFICIENTS  REGRESSION 2.CC3792E-CC  CONSTANT  3.75647CE-C2  TFRM  .RESIDUAL  =  THE  -5.98C3OSE+C1  VARIANCE  R SOU A RED  =  REGRESSION  To  BE  cw closure  CONSTANT  I  -  --  OMITTED  IS  stand Ht 1.35bl46E-(  TERM  RESIDUAL *  .84o6888C  C O E F F I C l E M TS  1.P7C447E-GC  -  I.269473E+C2  =  VARIABLE  8.3C2364E-C1  =  - U . 30 1 6 9 9 E + 01  VARIANCE  =  1.341573E+02  - - - - -  R SOUARED  -  .82323240  12 'I 10  9  THE  VARIABLE  TO  BE  OMITTED  5 4 3  REGRESSION COEFFICIENTS cw. c l o s u r e 1 .8926C4E-0C  IS  2  CON ST.ANT TERM  2.974 27'7E~ + 0 i  RESIDUAL  1 . 29 37C7E + C2  R  VARIANCE  .81b3bblC  SQUARED'  3eHT  Y ?t-oTcuTO  REGRE_SS_ION  COFFFJCIENTS  enclosure 2.C75498E-C0  s t a n d Hi. c'w. w i d t h 6 „ 2 0 b 3 0 7 E - 0 2 • -3.678948E-00  CONSTANT TERM  .=  RESIDUAL R  VARIANCE  SQUARED  =  VATn"KKTCE  VAR I A B L E  9 .82  1  067E-02'  ~7 728"C31 C'E + 02"" . 8b943630  SQUARED  THE  '  -1 .81bl48E + 01  10  R  8b'94 3> 3 G *.* "  " " 6 T 2 C 5 T 0 T t ' - 0 T " - 3 Y 6 7 8 9 4 H E -00'  CONSTANT TERM RESIDUAL  1.28031CE+02  COEFFICIENTS  2.C?5UVbE-Cir~  y  -1„81bl4 8E+Cl  ~ ~ "  REGRESSION  c w width 9.821067E-C2  TO  BE  OMTTTEO"  t ' S 4  Because the  the first  rest of the  variable  results  is to be omitted  are same  as Set T-  is  2  C O N S T A N T  T E R M  R E S I D U A L  V A R I A N C E  =  -2  = ='*"  S Q U A R E D  Jk.C]JL-  .  . 974  277  E+0  1  1.2937078+32 " "Vbl  53  5510  Y.= log(. ot..cu.ft."/) 2  T  R E G R E S S I O N A C O E E E I C I E N T S  iwdosurg  sj&QfLM  2.315 lo3E-C2  CONSTANT  6 ,;395594E-G4  TERM  -5 . ^ 2ori23E-0 2  cw. width * "1 .4393748-03 1  F.4I I 8 9 8 E - G 2 . «7 0847 20  REGRESSION  COEFFICfENIS  2.315 133E--_G2  0 . 3955 94 E- 04  TE"RM  =*"  VARIANCE  R SQUARED  THE  width  :  K SQUARED  RESIDUAL  w  3.3'9 87 8 3 L - G G  TtTs i D U ^ ~ V A R T A N C E ~ "=  •CONSTANT  c  V A R I A B L E  = =  TO  BE  ""3 7398T83E-G'G I.411898E-C2 .870847 20 **  O M I T T E D  REGRESSION COEFFICIENTS  cw closure  2.21GC4CE-C2  -5 .526823E-G2.  stand Hi  2.80o374E-G4  I S  4  cw. width 1.081863E-G2  1 . 43 93 74 E - 0 3  'CONSTANT TERM RESIDUAL  =  2.788338E-0C  VARIANCE  •K SQUARED  = =  THE VARIABLE  1.51C27 2E-C2 .84805340  TO BE OMITTED  IS  5  REGRESSION COEFF I CI FN'I S ' ' cu/ c l o s u r e stand 2.C56 2«rjL--C2 I .bboVvlb-03  CONSTANT  TERM  RESIDUAL  VARIAMCF  R SOUAR ED .  THE VARIABLE  '=  ' 3 . C0706bt-00 = =  1 . 68o4o1b- 02 . 8-14 8 78 00 **  TO BE OMITTED  IS  2  KITG R t SS'l ON" CO E F F I CI FN TS  cw. c l o s u r e 2.06 174 28-02  3. lbV582fc-CC .1 . 62V776E-C2  R = .d3062  Appendix 17 Example of a "Program Write Up"  Log and Tree Quality Evaluation Program write-up, Forest Products Laboratory, Vancouver . May,  1962  Programmer - H. Dempster  Program I This program reads a set of BOARD CARDS (punched by hand) giving the grade and size of each piece of lumber obtained and punches LOG SlIMMARY CARDS. These contain the t o t a l volume (ft.b.m.) of lumber recovered from each l o g , i t s value (according to a given p r i c e table) and the average p r i c e of each l o g . Grade. Size, and P r i c e Seven grades and nine sizes of lumber are recognized by the program. The grades are designated by the codes: 08, 07, 10, 20, 30, 40, 50. The sizes ( i n inches) are: 1x4, 1x6, 1x8, 2x3, 2x4, 2x6, 2x8, 2x10, 2x12. (On board cards thickness i s given i n quarter inches, width i n inches). The p r i c e table must be supplied as a set of nine cards, one f o r each lumber s i z e ( i n the order just s p e c i f i e d ) , each card giving prices f o r that s i z e f o r the seven grades (again i n the order specified above). The p r i c e s occupy s i x card columns each (format 7P6.2), and one input i n $/l000 ft.b.m. but stored i n 0/1000 ft.b.m. Card Formats and Variable Names The formats f o r the board cards and l o g summary cards with the program name f o r each quantity are as follows: Format 11: Columns  Board Card (input) Width  Code Name  Name  1- 3 4- 6  3 . 3  JCODE) KCODE)  A r b i t r a r y 6-digit code, copied d i r e c t l y to l o g summary cards.  7-10  4  LTNO  Tree l o g number.  11-12  2  LGRA  Lumber grade.  13-14  2  ITS"  Thickness (quarter inches)  15-16  2  IW  Width (inches)  17-18  2  LENG  Length (feet)  41-44  4  MLNO  M i l l l o g number  - 2 Format 31:  Log Summary Card  (output)  Code Name  Name  Columns  Width  1- 3 4- 6  3 3  JCODE) KCODE)  A r b i t r a r y code copied from board cards.  7-10  4  LOGT  Tree l o g number.  41-44  4  LOGNO  M i l l l o g number.  45-49  5  LV  Total l o g volume (ft.b.m.)  50-55  6  LC  Total l o g value  56-60  5  LPR  Average l o g p r i c e (0/1000 ft.b.m.)  (cents)  Running Time Board cards are processed at a speed of about 80 cards per minute. Operating Procedure Card input sequence i s as follows: ( l ) Program deck. 2) P r i c e table as described above. 3) Board cards. These are assumed to be sorted by m i l l l o g numbers; each change of t h i s number causes punching of a new l o g summary card. (4) Terminating card. This card should have a negative or zero number i n columns 41-44, the m i l l l o g number f i e l d . (Thus a blank card w i l l do). Note: I f the terminating card i s not read the l a s t l o g summary card w i l l not be punched. (5) The deck may be followed by two blank cards. The card punch should be on, with blank cards i n the hopper. I f a board card i s read f o r which the grade or thickness and width do not correspond to the allowed values, the computer w i l l h a l t a f t e r typing the message: CARD IN ERROR. (At t h i s time the error card i s the second l a s t card i n the read stacker). I f START i s pressed the program w i l l carry on, ignoring error card. Error card then can be corrected and replaced. Program I I This program reads a combined set of LOG DIMENSION CARDS (punched by hand) and the LOG SUMMARY CARDS punched by Program 1. I t computes c e r t a i n volume, shape, and lumber recovery c h a r a c t e r i s t i c s of each l o g and punches these i n a set of LOG DETAIL CARDS. In addition, t o t a l s f o r each tree are calculated and punched i n TREE TOTAL CARDS.  - 3Card Formats and Variable Names The formats f o r the four card types involved, with the names used by the program f o r each quantity, are as follows: Format 1: Log Dimension Card (input) Columns  Width  Code Name  Name  1- 2  2  JI  Card type code, should be 20.  3- 6  4  Et  A r b i t r a r y code, duplicated on output.  7-10  4  LO  Log tree number.  12-13  2  MT  Top diameter (inches).  14-15  2  MB  Butt diameter (inches).  16-17  2  LL  Scale length of l o g ( f e e t ) .  26-27  2  LDD  Length deduction ( f e e t ) .  28-29  2  MTDD  Top diameter deduction (inches).  30-31  2  MBDD  Butt diameter deduction (inches).  32-34  3  LA  Actual length of l o g (feet, x 10).  Format 2: Columns  Log Summary Card (input) Width  Code Name  Name  1- 2  2  JZ  Card type code, should be 10.  3- 6  4  K  A r b i t r a r y code, duplicated on output.  7-10  4  L02  Tree l o g number.  41-44  4  MO  M i l l l o g number.  45-49  5  LV  Total lumber volume from l o g (ft.b.m.).  50-55  6  LC  Total l o g value (cents).  56-60  5  LP  Average l o g p r i c e (cents per 1000 ft.b.m.)  Format 3:  Log D e t a i l Card (output) Code Name  Name  Columns  Width  1-2  2  JI  Card type code = 21.  3-6  4  Kl  A r b i t r a r y code, copied from output.  7-10  4  LO  Tree l o g number.  12-13  2  MT  Top diameter (inches).  14-15  2  MB  Butt diameter (inches).  16-1?  2  LL  Scale length of l o g ( f e e t ) .  18-21  4  LYG  Gross l o g volume ( f t . 3 , x 10).  22-25  4  LVN  Net l o g volume ( f t . 3 , x 10).  26-28  3  JD  Per cent damaged (volume l o s s ) .  29-31  3  JR  Lumber recovery factor (ft.b.m. per f t . 3 , x 10).  32-34  3  LA  Actual length of l o g ( f t . , x 10).  35-37  3  JT  Taper (inches per f t . , x 100).  38-40  3  LB  Distance from tree butt ( f t . ) .  41-44  4  MO  M i l l l o g number.  45-49  5  LV  Total lumber volume from l o g (ft.b.m.).  50-55  6  LC  Total l o g value (cents).  56-60  5  LP  Average l o g price (cents per 1000 ft.b.m.).  61-63  3  LPG  Log value (cents per f t . 3 gross volume).  64-66  3  LPN  Log value (cents per f t . 3 net volume).  - 5 Format 4:  Tree Total Card (output) Code Name  Name  Columns  Width  1-2  2  J  Card type code - 31•  3-6  4  K  A r b i t r a r y code, copied from input.  7-9  3  NT  Tree number.  10-11  2  LG  1st d i g i t - 0, 2nd d i g i t = highest log position.  12-13  2  IT  Tree top diameter (inches).  14-15  2  IB  Tree butt diameter (inches).  16-17  2  LT  Total scale length of tree  18-21  4  KVG  Total gross volume of tree ( f t . ^ x 10).  22-25  4  KVN  Total net volume of tree (ft.3 x 10).  26-28  3  KD  Per cent damaged (volume l o s s ) .  29-31  3  KR  Lumber recovery f a c t o r (ft.b.m. per ft.3 x 10).  32-34  3  LTB  Total actual length of tree  35-37  3  KT  Taper (inches/ft., x 100).  38-40  3  KL  Length r a t i o , scale/actual  41-44  4  KG  Number of logs i n tree.  45-49  5  KV  Total lumber volume from tree (ft.b.m.).  50-53 54-55  4 2  KS) KC)  Total value of tree  56-60  5  KP  Average tree p r i c e (cents per 1000 ft.b.m.).  61-63  3  KPG  Tree price (cents per ft.3 gross volume).  64-66  3  KPN  Tree p r i c e (cents per ft.3 net volume).  (ft.).  (ft.).  ($).  (cents).  - 6 Data Handling The input data f o r t h i s program i s obtained by merging the l o g dimension cards and the l o g summary cards (the l a t t e r being the output of Program I ) , and s o r t i n g the combined deck by TREE LOG MMBER. The essential sequence conditions f o r the r e s u l t i n g deck are: 1.  Logs f o r each tree should be together.  2.  For each tree, butt l o g should be f i r s t and top l o g l a s t .  3.  For each l o g , l o g dimension card should ajnmediately precede l o g summary card.  Any v i o l a t i o n of the t h i r d condition w i l l cause an error h a l t during processing; v i o l a t i o n s of the f i r s t two conditions can be detected l a t e r by examining the tree t o t a l cards. The two sets of o u t p u t — l o g d e t a i l cards (type code =» 21) and tree t o t a l cards (type code = 3 1 ) — c a n be separated by sorting on Column 1. I f no logs are missing from a tree, the highest l o g p o s i t i o n (Column 11 on tree t o t a l cards) and the number of logs i n the tree (Column 4*f) should be equal. This may be checked by s o r t i n g the tree t o t a l cards on these two columns. (One or more missing top logs w i l l of course not be detected by t h i s check.) In p a r t i c u l a r , a sequence error i n the input data could r e s u l t i n two (or more) t o t a l cards being punched f o r the same tree, of which only one could have columns 11 and hk equal. Running Time Data i s processed at the rate of about ...... logs ( i . e input cards) per minute. Operating  Procedure Card input sequence i s as follows:  1. 2.  Program deck (including modified Fortran Sub Routines). Input data deck, consisting of l o g dimension cards and l o g summary cards, sorted by TREE LOG NIJMBER, as described above.  3.  Terminating card. This card should have a negative or zero number i n Columns 7-10, the tree l o g number f i e l d (thus a blank card w i l l do). I.E. I f the terminating card i s not read, the l a s t tree t o t a l card w i l l not be punched.  k.  The deck may be followed by two blank cards.  I f the two input cards f o r any l o g have the wrong type codes or unequal tree l o g numbers, the computer w i l l h a l t a f t e r typing the message:  - 7CARD S E Q U J S E T C E ERROR, LOG MTJMBERS followed by the tree l o g numbers of the two cards i n question. (At t h i s time, these are the second and t h i r d l a s t cards i n the read stacker). This could r e s u l t from a sequence error, a nd.ssing card, or an extra card i n the input deck. Both error cards w i l l be ignored, and input w i l l be renewed i f the operator presses START a f t e r correcting the error.  

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