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The respiratory rate and volume of the guinea pig Nordan, Harold Cecil 1954

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THE RESPIRATORY RATE AND VOLUME OF THE GUINEA PIG by HAROLD CECIL NORDAN A thesis submitted in Partial fulfilment of the requirements for the degree of Master of Science in Agriculture in the Department of Animal Husbandry We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF SCIENCE IN AGRICULTURE. Members of the Department of Animal Husbandry THE UNIVERSITY OF BRITISH COLUMBIA May, 1 9 5 4 ABSTRACT The present methods for the measurement of respiratory rate and volume of laboratory animals have been reviewed. The review suggests that these methods leave much to be desired. For this reason an apparatus has been developed in the hope that i t may overcome the difficulties associated with those described in the literature. The apparatus consists of a mechanism to interrupt a beam of light in time with the animal's breathing, and the signallso produced is amplified to close a double pole double throw relay. The state of the relay, open or closed, selects an arrester on either the air supply spirometer or the air receiver spirometer. When the animal breathes in the air supply spirometer is free to move and the air receiver is locked allowing air to be taken from the air supply spirometer only. On expiration the reverse situation is in effect. A stylus attached to each spirometer records the downward or upward travel and hence the volume on a kymograph drum. An electro-magnetic stylus records each inspiration on the kymograph' and a five second timer writes a time base. A limited amount of data on female and male guinea pigs is presented to indicate the validity of the measurements made with the apparatus. Equations based on these data relating respiratory rate and volume of the guinea pigs to body weight have been derived. These equations are compared with those of other workers and suggest that the apparatus devised may be superior to those described in the literature. Acknowledgment s The writer wishes to thank Professor H. M. King, Head of the Department of Animal Husbandry for his kind permission to carry out this work and for his provision of the laboratory facilities used. To Dr. A. J. Wood, Associate Professor in the Department of Animal Husbandry, sincere gratitude is expressed, for his inspiration, enthusiastic interest and constructive criticism throughout the course of this work. The writer also wishes to thank Defence Research Board of Canada for making this problem available. Special thanks are tendered my many associates at the Animal Nutrition Laboratory for their encouragement and helpful criticisms throughout the duration of this work. TABLE OF CONTENTS page I. Introduction 1 II. Review of Literature 4 III. Experimental 13 A. Introduction to the Problem 13 B. Description of Head Piece and Restraint Box 15 C. Method of Interrupting Light Beam 15 D. Amplifiers Used 17 E. Valves Used 20 F. Use of Spirometers as Valves 27 G. Recording Apparatus 27 H. Assembly of Apparatus and Accessory Items 28 I. Operating Cycle of Apparatus 30 J. Calibration of Apparatus 31 IV. Results 32 V. Discussion 39 VI. Summary 44 VII. Appendices I. Guinea Pig Ration 46 II. Calibration Table for Respiration Apparatus 48 III. Data on Female Guinea Pigs and Preparation of Data for Fitting to a Logarithmic Equation (a) Volume 1.. 50 (b) Rate 52 IV. Data on Four Male Guinea Pigs and Preparation of Data for Fitting a Logarithmic Equation (a) Volume ." 55 (b) Rate 57 TABLE OF CONTENTS VII. Appendices (cont'd) page V. Calculation of respiratory Rate and Volume Equation and Standard Error of Estimate, Method 1 60 VI. Calculation of Respiratory Rate and Volume Equation standard Error of Estimate and Correlation Coefficient Method 2 62 VIII. Bibliography 63 LIST OF FIGURES page Figure 1 Respiration Apparatus 18 Figure 2 Component Layout . 19 Figure 3 Photo-Relay Circuit 21 Figure k Respirometer Wiring Diagram 23 Figure 5 Pulley Arrester 25 Figure 6 Guinea Pig Face Mask for Respirometer 26 Figure 7 Typical Record of Volume, Rate and Time 29 Figure 8 Weight Plotted Against Respiratay Rate and Respiratory Volume 33 Figure 9 Log of Weight Plotted Against Log of Respiratory Rate and Respiratory Volume 33 Figure 10 The Relation of Respiratory Volume to Body Weight Female Guinea Pigs • 36 Figure 11 The Relation of Respiratory Volume to Body Weight Male Guinea Pigs 36 Figure 12 The Relation of Respiratory Rate to Body Weight Female Guinea Pigs 37 Figure 13 The Relation of Respiratory Rate to Body Weight % Male Guinea Pigs 38 -1-I -Introduction Since 1777 when Lavoisier and Laplace did their classical experiment on animal calorimetry and demonstrated a definite relation-ship between the heat produced by an animal and the carbon dioxide exhaled, interest in the quantitative aspects of respiration has slowly but surely increased to i t s present day position as a major field of investigation. Present day interest in respiratory rate and volume revolves around such basic fields of investigation as animal energetics, pathology, toxicology, and homeostasis. These several branches of research may be considered to have two important aspects, namely, the fundamental and the practical, both of which are of major import-ance to the agricultural researcher. Bio-energetics or animal calorimetry falls into two major categories, direct and indirect calorimetry. In practice, since the direct method i s much more expensive and complicated; i t is rarely used, except when the caloric values of 02 and CCvj are in doubt. Indirect calorimetry was first used by Lavoisier and i s based on the fact that, normally, consumption and CO2 production are closely correlated with heat production. These studies therefore require a means of measuring respiratory volume or more important a means of measuring 02 consumption, CO2 production and hence Respiratory Quotient. -2-Animal pathology, particularly with respect to infections gaining admittance to the host via the respiratory route, e.g. Newcastle Disease, necessitate an accurate measure of respiratory volume, and also a means to partition or separate the inspired air carrying a known concentration of organisms and the expired air in which the concentration of organisms can be determined. From this data can be determined the bacterial dosage and subsequently the L.D.50 for a particular agent by the respiratory route. With the increasing use of chemical insecticides, weed killers and the ever existent possibility of a conflict involving chemical warfare, the importance of knowing the tolerance of our farm animals to these agricultural chemicals on the one hand, and having a means of assessing, by animal tests, the lethality of our chemical warfare agents on the other, adds greatly to the necessity of having at our disposal a means of measuring tidal air volume and what is more important separating inspired and expired air. The principle that a l l homeothermic organisms react to changing conditions in such a manner as to maintain constant their internal environment has long been known. However, the extent to which animals may adjust to changes in their environment, e.g. tempera-ture, humidity, and the role played by respiration in these changes is a subject of much research. The air conditioning of a dairy barn or a movie house i s closely related to data obtained on the respiratory exchange and its role in thermal regulation of the inhabitants. The many avenues of investigation cited or implied, fundamental -3-or directly practical, have their conception in the laboratory. Laboratory investigations are restricted by financial and physical limitations to workings mainly on small animals, namely the guinea pig, rabbit, white rat, white mouse and hamster. These requirements and limitations then would surely make any apparatus for directly measuring respiratory rate, respiratory volume, inspired volume and expired volume on small laboratory animals extremely useful. The fact is that much work is at present in a state of "postulative uncertainty" through lack of a suitable method of obtaining respira-tory data, and by the same limitation much work has yet to be done. -4-» II Review of Literature The few methods presently used for the determination of respiratory volume may be considered under several headings. One of the earliest methods calculated the volume indirectly from the oxygen consumption. Various methods for the determination of O2 consumption and CO2 production have been developed as a tool in the study of animal energetics. A closed-circuit-spirographic mask method originated by Fredericq (1887) and perfected by Benedict (1920) in the U. S. A. and Keogh (1923) in Europe i s now the standard Benedict-Roth-Collins clinical metabolism apparatus. The apparatus functions by connecting the pulmonary system of the subject to an oxygen spirometer, and thus measuring the rate of oxygen consumption by the rate of decline of the oxygen bell. The air i s circulated freely through porous soda-lime in one direction by valves thus removing the COg from the expired air. The oxygen bell, which floats freely in a water seal, is counterbalanced by a weight, and so will not rise or f a l l except when acted upon by the circulating air. The decline of the bell is recorded graphically on a clock kymograph drum. The rate of oxygen consumption is computed from the slope of this graphic record. This method works well for large farm animals and human beings and has been used extensively by Brody (1945) in his work on metabolic rates of steers, dairy cattle, horses, sheep and goats. -5-A closed-circuit-chamber system for small animals was originated by Hegnault and Reiset (1849)• This method involves rebreathing the same air after removing the CQ2 by circulating through soda lime, and replacing the consumed Q? by fresh Oj. In the United States Kleiber (1940) used a modification of this appara-tus for measuring the metabolism of rats, and Winchester (1940) has adapted i t for use with chickens. This apparatus consists of four parts: (1) constant-temperature cabinet, (2) burette system consisting of three tubes, two large and one ordinary titration burette, a l l interconnected so that they have the same water level, (3) Mariotte bottle, (4) COtj absorbers. There are also auxiliary items, including pressure gauge; equilibrator, which adjusts temperature of water in Mariotte bottle to that of chamber, and O2 concentration of the water to that prevailing at chamber temperature; O2 spirometer, which keeps air out of the top of the Mariotte bottle by connection with pure O 2 ; rocking mechanisms and fans. The rate of O2 consumption is measured by the rise of the water in the burette. As the O2 from the burette system is consumed, i t is replaced by water which automatically flows from the Mariotte bottle whenever the pressure at the siphon tube outlet falls below that at the inlet. The CO2 i s absorbed in the absorber battery by a saturated Ba(0H)2 solution in two sets of flat-bottomed flasks joined near the bottom by a glass tube. The battery is rocked at the rate of 40 oscillations per minute and the alkaline solutions flow from one set - 6 -of flasks to the other, alternately drawing air from and returning i t to the chamber at the rate of 12 liters per minute. The CV? consumption measurements do not begin until after the animal has been in the chamber for 1/2 hour, in order to (1) accustom the animal to the chamber, (2) bring the system to a standard temperature and (3) establish an equilibrium between the absorbing rate of the battery and the CQ2 production rate. Possible objections to these methods are: (1) the necessity of using Q2 , (2) the accumulation of water vapour which tends to depress the heat regulation by water vaporization at higher tempera-tures, (3) in the case of Winchester's apparatus i t does not permit measurement of the water vaporized. The open-circuit gravimetric method or air flow method was devised by Haldane (1892). This consfcts of a respiration chamber, in which the animal i s kept, with several H2O and GO2 absorbers. T{je H2O is usually absorbed by concentrated H2SO4 (in which lumps of pumice stone may be placed for increased area) or by such dry H2O absorbers as magnesium perchlorate. The CC2 is absorbed by alkali, such as a concentrated solution of NaOH or Ba(0H)2» or more conveniently by "shell caustic." Air is-drawn through the chamber and absorbers by a pump and a record of the rate of air passage is recorded by a wet test gas meter or similar meter. The air is freed of its CO2 and H2O by absorbers before i t enters the chamber and also as i t leaves the chamber by another set of absorbers. Thus some atmospheric Q2 is retained by the system in the form of CO2, but nothing leaves the system. Hence, while the animal loses weight during the t r i a l , i t - 7 -loses CO2 and H2O, the system as a whole, the chamber and effluent absorbers gain in weight. The gain in weight represents O2 consumed. From a t r i a l with an apparatus such as this the H2O vaporized, the GO2 produced, and the O2 consumed may be determined. Modifications of the Haldane type apparatus can be used for large farm animals but as the chamber is of necessity too large for weighing, and the CO2 production too much for absorption, air flow metering, aliquoting and gas analysis are employed. The air coming into the chamber is assumed to contain 0 . 0 3 1 per cent CO2 and 2 0 . 9 3 9 per cent O2, the outgoing air is analyzed for i t s CO2 and O2 content. The rate of circulation is measured. The percentages of O2 decrement and CO2 increment in the outgoing air are computed, the products of these and the ventilation rate is the rate of O2 consumption and CO2 production. The measurement of the ventilation rate may be done with large commerclial gas meters but the aliquoting i s a complex matter and the analysis of chamber air, which is outdoor air only slightly contaminated, one per cent, with expired air is tedious as i t must be done most accurately. An open circuit mask method for large animals involving gas analysis has long been used for measuring human metabolism, i t involves collection of a l l the expired air into a Douglas bag or into a Tissot spirometer over a short period. The analysis of directly expired air, containing several per cent CO2 increment and O2 decrement, i s very much simpler than that of chamber air containing a fraction of a per cent of CO2. -8-Kleiber (1944) motivated by an increasing need for infor-mation concerning tidal air of laboratory animals presented a general formula for such a determination on resting and fasting animals. In determining the tidal air by the formula presented i t must be assumed that animals use up the same proportion of 02 from the air as man, i.e. approximately 5 per cent. Thus animals under basal conditions inspire 20 liters of air for each l i t e r of Q2 consumed. The O2 consumption in 24 hours in animals and man can be estimated from the basal heat production which for mature homeothermic animals .75 from rats to steers averages 72W* Calories, where W is the body weight in kilograms. Since one l i t e r of O2 consumed by fasting animals represents 4.7 Calories of heat, the basal rate of O2 consumption amounts to j^W*75 = 15.3 W'75 liters 0 2 per day, or 306 W 7 5 air per day or 306 x 1000 w-75 212 W*75 c.c. of air per minute. Kleiber 1440 calculated the tidal air of 27 day old albino Swiss mice from the metabolism rate. The metabolism rate was determined by using a closed-circuit-chamber method previously described. Unfortunately Kleiber was forced to assume a decrement of 5 per cent on the one hand and had no means at his disposal to test the validity of his general formula by actual respiratory volume data. Loosli (1943) while making an estimation of the amount of air-borne virus necessary to produce infection found i t necessary to determine the tidal air of the mouse. The apparatus used consisted of two thistle tubes joined by a length of glass tubing having a side arm equidistant from each end. Over the open end of one thistle tube was stretched a latex diaphragm in which there was a hole to take the -9-animal's nose. Over the other thistle tube there was also a rubber diaphragm to which there was cemented a small mirror. The system was fil l e d with and some soda lime placed in the bottom of one thistle tube to take up the CC^ . In operation the mouse was lightly anes-thetized, tied on a board and after greasing the face piece with vase-line i ts nose was pushed through the hole in the rubber diaphragm covering the open end of the thistle tube. The side arm in the connec-ting tube was opened to allow the air pressure in the system to return to normal. A light beam was directed on to the mirror cemented to the diaphragm on the opposite thistle tube and the excursions of the reflected light beam corresponding to the breathing rhythm of the animal were recorded on a moving photographic film. After several observations the aperture for the animalfes nose was plugged and the light beam excursion calibrated by injecting and withdrawing known amounts of air with a syringe via the side arm in the tube connecting the thistle tubes. This method suffers from the disadvantages of having to use O2 and having to anesthetize the animal and then restrain i t in a somewhat unnatural position. Chapman (1944) in a modified closed circuit apparatus for measuring respiratory metabolism, attached a concave mirror to the axis of the float of a Krogh spirometer. Any change in the volume of the spirometer changed the position of the float and hence caused a rotation of the mirror. The image from a single filament bulb was focused by ahe concave mirror on an arc equipped with a centimeter scale, the radius of which was such that a 1 cm. movement of the light beam was equal to a volume change of 1 c.c. in the spirometer. - 1 0 -Guyton (1947), because data in the literature on respiratory volume of laboratory animals was very scanty, and a tremendous amount of study was being directed toward the etiology and pathogenesis of respiratory disease, did a comprehensive study of the subject. Guyton impl'es that there exists a need for a more satisfactory method of obtaining data on respiratory volume of laboratory animals and offers two methods he used to gather data and thereby augment the scanty literature. (1) Valve method: The valves used were of delicate cons-truction utilizing very minute-thin rubber discs, which were hinged loosely over the tips of polished glass inlet and outlet tubes. These valves were then connected directly by means of a glass seal either to a tight-fitting headpiece or to a tracheal cannula. Collection of air from the outlet valve was accomplished by two methods. The expired air enters a collecting chamber via a rubber tube attached to the top of the mercury fi l l e d collecting chamber, which may be connected to a water or mercury manometer on either side of the collecting column. By manipulating the stopcock at the bottom of the collecting column, mercury is allowed to f a l l at a rate which will equalize that of expired air and maintain pressure within the chamber at exactly zero. By measuring the f a l l of the mercury column for one minute while the -pressure"withiriothe chamber is maintained at atmospheric pressure, the respiratory volume per minute may be measured directly. The second device for collecting the air from the outlet valve was constructed to that no water can flow from an upper siphon -11-jar into a lower jar until an equal volume of air i s introduced into the air space above the water in the upper jar. Special precautions were taken so that the pressure against which the animal must breathe is small and always constant, approximately 1/2 cm. of water pressure, this value being considered negligible as an obstruction to respiration. The respiratory volume is read directly from the calibration of the lower bottle. (2) Oscilloscope respirograph method: In this method water flows from an upper bottle to a lower bottle forcing air from the lower bottle past the head of the animal into the upper bottle, thereby completing a closed circuit. The rate of air flow is adjusted so that the volume of air is at least five times as great as that required for norma] respiration of the animal. A third tube leads from the head piece to an airtight bellows on the top of which i s an electrical condenser made of alternate layers of insulating paper and tinf o i l . As the animal breathes in and out, pressure within the bellows alternately increases and decreases by a minute amount. The plates of the condenser likewise alternately become closer and farther apart. The changes in capacity of the condenser by the changes in distance between the plates of the condenser are measured on an oscilloscope. A syringe connected to the bellows i s used to calibrate the apparatus. All readings may be made directly from the screen of the oscilloscope, or the respiratory pattern may be accurately recorded with a continuous camera. Animals tested by this modified respirograph method were under as nearly normal physiological conditions as possible except for the matter of fear. This was overcome by allowing, the animals to -12-remain in the head piece for a long period of time before actual measurements were made. The volume of the bottles used was adjusted for different animals so that enough air was present to last usually ten minutes and so that the operating pressure within the system varied from atmospheric pressure by approximately 1/5000 of an atmosphere with each respiratory cycle. None of the methods presently reported in the literature for measuring respiratory volume adequately meet a l l the requirements of a respiratory apparatus. Early methods are based on a calculation from 0g consumption assuming a certain Q2 decrement per inspiration. The method of Loosli requires the use of O2 and also restrains the animal in a somewhat unnatural position. -The use of valves introduces an appreciable time lag and also presents surfaces upon which materials presented to the animal may impinge. Although the oscilloscopic respirograph of Guyton appears to come very close to requirements for an apparatus i t does not allow for the separation of inspired and expired air with the option of presenting anything to the animal independently of the expired air, and as is the case with many indirect methods i t i s not a simple apparatus. -13-III Experimental A. The Animal Nutrition Laboratory at the University of British Columbia has sought for the past six years to arrive at some suitable method for measuring the respiratory rate and volume of laboratory animals, particularly the guinea pig. The problem, as defined, was to devise a method of measuring respiratory rate and volume within the following limitations: 1. The method must be accurate and allow a high degree of reproducability of results. 2. The apparatus must be basically of closed-circuit design to allow for the use of toxic or pathogenic material. 3 . There must be provision to separate the expired air from the air to be inspired and a means to measure both independently of each other. k* Remembering that in the case of small animals the force that can be applied against respiratory activity is very small before and effect is obvious, the animal must be asked to do very l i t t l e work, and the work i t is asked to do must be harnessed in a subtle manner. 5. The several functions measured by the apparatus should be suitable and permanently recorded. 61 The use of valves is undesirable due to their time lag and -14-the fact that they offer points upon which air borne particulates can impinge.-7. The apparatus must be capable of measuring events occurring at a relatively high rate of speed, i.e. two respirations per second. 8. The apparatus and.method must be simple in design and operation. McQuarrie (1948) sought to solve the problem by using a Haldane type apparatus. However, this approach did not satisfy the requirements for a closed system nor did i t give a measure of rate or allow for separating expired and inspired air. Patterson (1950) measured the respiratory rate by visual observation over a definite time period. This apparatus consisted of a glass tube containing a bubble of ink into which the animal breathed. The oscillations of the bubble were counted and this gave an estimate of the rate. The animal while under test was breathing the same air over and over again and as the volume of the tube and head piece was small, the t r i a l period was short, and the animal was not altogether free from the effect of increasing CO2 concentration. The writer took up the problem in 1952 and has attempted to arrive at an apparatus f u l f i l l i n g the previously stated requirements. Several methods were tried a l l of which had one or two points in common. They are the type of head piece used on the animal and using an interrupted beam of light to activate the apparatus. -15-B. The head piece for the animal was relatively simple, being a latex mask to go over the entire head and f i t closely around the neck. Two rubber tubes led from the head piece, one bringing air to the animal, and one taking expired air away. The mask was made by applying seven successive layers of liquid latex to a 200 ml. volumetric flask which was used as a form. This gave a msk of suitable shape and size, the dead air space being very small. Figure 6 . While in the head piece the animal is placed in a restraint box. This is not absolutely necessary in most cases but some animals move around while the test i s in progress. The restraint box is of plywood construction 6^" x 5" x 4 " . The box opens longitudinally through the centre and is hinged on the back. A round opening in the front of the box allows the animal's head to protrude, while fitting close enough around the neck to prevent the head being drawn back into the box. G. It was quite obvious early in the preliminary investigations that the guinea pig was quite unable to do any useful work.in the usual sense, without imposing a considerable force against respiration. However, there existed the necessity of having the animal activate the apparatus in time with its breathing pattern. The first attempt to have the animal activate the system was by placing a "T" in the tube conducting air to the animal, and connecting to this "I" a 2 m.m. I.D. U-tube. Water was placed in the U tube to a height of 1 cm. in each leg. It was hoped that during inspiration there would be sufficient pressure drop in the leg of -16-the U connected to the air tube, and that the water level would rise in this leg by a distance sufficient to eut off a beam of light directed through the glass tube on to a photo-cell. Although the problem of water meniscus could be overcome by treating the glass tube with Desicote, the actual pressure drop was only sufficient to allow the water level to be raised 1 m.m. which was not a usable amount. Although hot enthusiastically pursued because in principle i t disregarded one of the requirements of the apparatus, namely that of having no obstruction in the air tubes, an attempt was made to have the animal move a balsa wood flap suspended in an enlarged glass section of the inlet tube. The flap while being unable to move from the vertical position on expiration was able to travel through 45° on inspiration, and i t was thought that this would allow a light beam to pass through the glass cell on inspiration and cut i t off on expiration. This system did not prove to be sufficiently positive in action or consistent in distance travelled. It also had the afore-mentioned disadvantage of being an obstruction to air flowing in the tube and a surface upon which particles of material might impinge. Finally a tambour was connected to the "T" in the tube to the animal. Although the usual rubber dam used on the tambour was under too much tension when held in place by the split ring to be moved by the animal, a satisfactory diaphragm was moulded to an air tight f i t with liquid latex. The latex diaphragm actually moved only a fraction of a millimeter on inspiration but this movement was amplified considerably by a six inch 1/8" x 1/8" balsa wood arm -17-resting on the tambour diaphragm 1" from the fulcrum-. This scheme gave a movement of 0.5 cm. at the end of the arm. To this end of the balsa arm was cemented a 1" x 1/4" flag which cut the light beam off in the normal position, expiration, and was depressed sufficiently to let light on to the photocell on inspiration. Fig. 1, 2. The pressure differential required for this movement was approximately 2 m.m. of water. Having arrived at a suitable method for interrupting the light on to the photocell i t then was necessary to amplify the signal from the photocell to a point where i t could activate a relay. D. The first amplifier built consisted of a 6SN7, 1/2 as a cathode follower, 1/2 as an amplifier, and a 6V6 as an output tube. The phototube was connected in the grid-cathode circuit of the fi r s t half of the 6SN7. The relay, a 10,000 ohm plate circuit relay, was connected in the plate circuit of the 6V6. This amplifier required a 250 volt, 90 mill power supply that was well regulated. Inasmuch as this made the apparatus very large and expensive, i t was decided to find some other photo-electric relay amplifier circuit that would f u l f i l l the requirements without the disadvantages mentioned. The amplifier finally decided upon was a photo-relay circuit using a gas tetrode as an amplifier coupled to the phototube. Fig. 3. One-half of a 6SN7 was used as a diode rectifier, the other half as an amplifier. The phototube is connected in the grid-cathode circuit of the amplifier half of the 6SM7. The output of the amplifier i s applied to the grid of the 2051 gas tetrode thereby controlling the Fig. 1 Respiration Apparatus - 2 0 -firing point by the light reaching the phototube. The gas tetrode •was used as its conduction is on a l l or none action, and after firing takes place the grid has no more control. The tube ceases to conduct on the first negative half cycle of the applied voltage, after the negative grid bias reaches a cut-off valve. A 110 volt A.C. D.P.D.T. relay i s connected in the plate circuit of the 2051 tube. This photo relay circuit appeared in the January issue of Electronics, 1941. E. (1) The second phase of development was to arrive at a method of presenting air to be inspired and collecting the expired air in a closed system. It seemed impossible at the outset to accomplish this without the use of valves, and in the face of their disadvantages several types of valves were tried. Valves for such an application have certain requirements. First they must be fast in action, they must be positive and air tight, the valve orifice must not be critical and the valve must be compact. General Electric A.30 solenoid valves were tried f i r s t . This valve has a 3/32 inch orifice, works up to 150 pounds pressure and requires 7 watts on 110 volts for operation. These valves open when the solenoid coil i s energized and close by gravity when de-energized. The distance travelled by the valve-seat piston is approximately 3/4 inch to open, and in falling the same distance to close the piston has a tendency to bounce in the seat which does not allow positive cut off. Another limitation to the use of this valve is the size of the orifice, 3/32, which was considered borderline with respect of limiting air flow. To overcome the difficulties encountered with the G. E. solenoid valve, a valve was designed at the Nutrition Laboratory. This 110V AC Fig. 3 Photo-Relay Circuit CI, C2 Rl R2 R3 R4 8 mfd 450 W. V. i 10,000 ohms 1/2 watt 10 meg. 1/2 watt 10,000 ohm 1 meg. 1/2 watt R5 1,000 ohm 20 watt 1 T 6.3 Volt Transformer Relay 115 Volt AC Coil Contacts 1.5 amp 115 Volts -22-valve consisted of two concentric chambers, a central chamber 1/4 inch in diameter with a 1/8 inch wall, and an outer chamber 1/4 inch in width around the inner one, The bottom was closed in each case but the top was open. A tube 1/4 inch I.D. led into the outer chamber and a similar size tube into the inner chamber. A latex cap was fastened over the open ends of the chambers, and on to this was cemented an iron disc 1/2 inch in diameter and 3/16 inch thick. The disc held the diaphragm tightly to the top edge of the inner chamber and air entering the outer chamber could not leave unless the iron disc, and consequently the diaphragm, was lifted, allowing the air to s p i l l over the edge into the inner chamber and exit by the tube running into i t . The disc was lifted by an electro-magnet mounted above i t . This valve satisfied most requirements but had one serious disadvantage, that of presenting a surface upon which material might collect and prevent an airtight seal. (2) Various combinations of the methods of light cut off and valves mentioned above were tried with the following two devices for separating and recording inspired and expired air volumes. A modified version of a micro-respirometer reported by Tyler (1941) was tried. This consisted of a three foot five m.m. I.D. glass tube connected to the inlet valve and a similar one connected to the outlet valve. The valves had a short 1/4 inch I.D. copper "Tn connecting them. A bubble of water was placed at the 30-inch mark 1 on the inlet tube and at the zero mark on the outlet tube. The animal and tambour were connected to one leg of the "T" joining the two valves. As the animal inspired the inlet valve was opened allowing air to be 110 V. 110V. 110V. Light—Source 6 . 5 V 2 . 7 5 A 6 . 3 Volt Transformer D.P.S.T. Switch ^ i i 6 Volt Battery 5. Second Timer 6 Volt Battery Jo.l [No.2 to.3 ,Time Marker Coil No.l No. 2 No.3 Collecting Bell Arrester Coil Air Supply Bell Arrester C o i l Plate Marker Coil i I Fig. Z| Respirometer Wiring Diagram -24-taken from the air supply tube. This would cause the water bubble, which acted as a seal, to be drawn down the tube by a distance, which multiplied by the cross sectional area of the tube, gave the volume inspired. On expiration the inspiration valve would be closed and the expiration valve open, allowing air into the collecting tube and moving the bubble a distance indicating the expired volume. Aside from the undesirable feature of being valve operated, great difficulty was experienced in holding the water bubble. The bubble tended to decrease in size, as the inside of the tube was wet, to a point where i t broke as a seal. If a non-wettable surface was put on the glass the bubble would not form at a l l . A second attempt somewhat along tbe lines of Guyton's method of providing air flow in his oscillographic respirometer was tried. This scheme employs two air-water reservoirs. One reservoir contained air, and when the inspiration valve was open water entered to equal the air removed and thereby keep the pressure equal to atmospheric. The other reservoir contained water, and as air was admitted, on expiration, water was allowed to run out equalizing the pressure in the reservoir with that outside. Volume was measured by the amount of water entering one reservoir or leaving the other. This system showed promise but aside from using valves had the difficulty that the weight of water in a system large enough for trials of any time duration presented a positive pressure against the air supply on the one hand and a negative pressure on the receiving reservoir on the other. The several methods so far described were endowed in some cases with obstacles unsurmountable, and in other cases with disadvantages - 2 5 -Fig. 5 Pulley Arrester Scale 1" A 6 Volt Relay Coil E Rubber Tip B Armature Stop F Pulley Mounting C Spring Steel_ D Armature G Pulley Mounting and Arrester Standard To Tambour Air In Air Out i O N Face Piece Fig. 6 Guinea Pig Face Mask for Respirometer t - 2 7 -with respect of the limitations originally laid down as to make further investigations on them unwarranted. r F. Finally i t was decided to try two spirometers, one to be fill e d with air at the start of the t r i a l and subsequently to be a source of air to the animal as and when required, the other spirometer to be empty at the start and be a receiver for expired air. The problem of valves again arose but i t appeared that i f at a l l possible they should not be used. After careful consideration the idea gradually developed that i f the spirometers could be fixed or arrested when not required to deliver or receive air, and the animal did not have the capacity to compress the air in the receiver or withdraw air against a pressure in the supply bell, the spirometers themselves would act as valves. To this end electro-magnetic arresters were made and mounted so as to stop or lock the pulleys that carry the balance-weight chains in phase with the breathing pattern. Fig. 5« In other words when the animal is breathing in the air supply bell is free to move and the air receiver bell is arrested. This causes the animal to obtain its air from the air supply bell. On breathing out the reverse situation is in effect, and the expired air must go into the receiver bell. This proved to be a satisfactory method of providing air to the animal, and collecting expired air without the J use of valves. The arrester coils operated on 6 volts D.C. in order to get away from vibration that often occurs in A.C. coils. G. The recording apparatus consisted of a kymograph drum mounted so that a writing stylus attached to the top of each spiro-meter would record the downward or upward travel, hence the volume -28-change in the spirometers. A stylus operated by an electro-magnet was mounted to record the respiratory rate on the kymograph. A five second contact timer was made and a five second time record drawn on the kymograph along with the volume and rate record. Fig. 7 shows a typical recording of rate, volume and time. H. -The whole apparatus was" assembled on a 17" x 12" x 3" chassis. The amplifier was built on a 10" x6" x 2" chassis that was mounted on the larger chassis. Figs. 1 and 2 show the arrangement of the components on the chassis, and Fig. 4 shows the wiring exclusive of the amplifier. As an accessory item two constant temperature cabinets were used, one in which to hold the animals over a period of time for acclimation to temperature and humidity i f experiments on the influence of these factors were to be done, and the other cabinet kept under the same conditions in which the animal was to be placed for test. These cabinets were 24" x 18" x 24" and constructed of 3/8 inch plywood. The front of the cabinet was a glass door by which the animals could be observed. Each cabinet contained the following equipment: 1. A Cenco thermostat 2. 150 watt light bulb as a heat source 3. pilot light 4. Taylor humidiguide 5. 6 volt auto-type fan. -29 1 ir. 7 T y p i c a l Record of Volume, Rate and rime - 3 0 -I. The operating cycle of the apparatus i s as follows. The head piece is put on the animal and the animal placed in the restraint box. The restraint box is placed in the constant temperature cabinet and the air tubes pushed through the holes provided for them. While the animal is adjusting to the head piece the amplifier is turned on and allowed to warm up, at the same time the air supply spirometer is fi l l e d and the air receiver emptied. Now the air tubes from the head piece are connected to their respective spirometers, and the tube leading to the tambour is connected. The light source, rate counter, arresters and timer are turned on, and when a l l components are working smoothly the kymograph motor is started. As the animal breathes in, light is allowed to strike the phototube, this extinguishes the 2051 tube and causes the relay to open. With the relay open the air supply spirometer is free and the receiver spirometer locked. Air is drawn from the supply bell by the animal and the bell descends by an amount indicating the volume of air breathed in. The stylus fastened to this spirometer bell draws a descending line on the kymograph. At the same time the rate counter coil is energized and a respiration mark is pfit on the record. When the animal exhales, the tambour returns to the normal position cutting the light off the phototube. This removes the bias on the 2051 tube allowing i t to conduct and causing the relay to close. In the closed position the arrester on the supply bell is energized locking i t in place and the receiver bell is freed allowing air to enter and raise the bell. The stylus on this spirometer draws an ascending line on the kymograph. The rate marker is returned to normal position. This -31-completes one respiratory cycle. Throughout the t r i a l period the timer is recording the time in five second intervals. The female guinea pigs to be tested were kept in the constant temperature holding cabinet for a period of three weeks and the data wa» collected over a period of one week. The male guinea pigs to be tested were kept in the holding cabinet one week and the data were collected over a period of two days. It was found to be undesirable to house male guinea pigs of such a wide weight range together for too long a period as they fought almost continuously. Whether the effect of fighting or the short holding period or both would affect the data in the case of the male guinea pigs remained to be seen. J. The completed- apparatus was calibrated with a Baltimore automatic pipette manufactured by Baltimore Biological Laboratory Incorporated, Baltimore, Maryland. This pipette is a reciprocating piston type that can be adjusted to deliver 0 to 10 c.c. per stroke at 0 to 200 strokes per minute. The inlet and outlet tubes of the pipette were attached to the head piece of the respiration apparatus and the apparatus operated by the same procedure as i f an animal were harnessed to i t . The pipette was adjusted to deliver various volumes at several delivery rates. The table for the calibration of the respiration apparatus is shown in Appendix II. - 3 2 -IV Results Sample data collected on five female guinea pigs and four male guinea pigs are presented in table form in Appendix 2. This table also gives the preparation of the data for f i t t i n g i t to a satisfactory equation. The animals tested were selected at random from the guinea pig colony at the Animal Nutrition Laboratory. The colony i s kept at a temperature of 20°C. and fed a stock ration known as U.B.G. Ration No. 8. The constituents of this ration are shown in Appendix 1. The arithmetic mean of the respiratory rate and volume of the female animals was calculated and these values plotted on an arithmetic grid, Fig. 8, and on a log-log grid, Fig. 9 . A comparison of these plots revealed that a logarithmic relationship rather than an arithmetic relationship existed between weight and rate and weight and volume. The equations for the relationship between body weight and respiratory rate and body weight and respiratory volume were calculated by the method shown in Appendix 3a and checked by the method shown in Appendix 3b. -33-:::: : His ::::i ••-— :::: : M urn ie' Hi: : la* e 00 rn.- i • . _ _ L . i I ---—- -— H © p — t i ! t i i — — - l . _ .... — t $ b o '• • • o i.. i 1... i , i ^ r i fin .. j i , • § !r 90 1—- • • ( • ; i . - • • ** • • -OO .s ._ j i ~ i AT) 1 : • t • • f • BO 7? •t I • T •: • ; • ! : . i 1 • i - • ---— - — - — Z. » • Wei i h ma .... : 11 i0:: 3( 5< 9 CO Fig. 8 Weight plotted against respiratory rate and respiratory volume. Points used are the arithmetic means of the data on female Guinea Pigs. ; ; i i 1: V Ml: 4 '.'Z. 300 - Vol ume ; J : i i : 1"-(ioo Rat 8 ' '. ! ' '. .. j . . . -1 !CO ISO " t i •t I' 1 ' — i i 4> P u. u • a. j .00 c a : 100 ! i i i i i j o 1 ! 9 'ft- • +> i i • i i i ! 1 • t ' ; . .50 ... : — i I . ; — ! i , 1 . . . . 50 200 T 1 i ! - - - - - 4 -• j • : nbo 1 1 1 : i A Weight : »i ! :6(j 0 1 i rra|m8 1000 Fig. 9 Log of weight plotted against log of respiratory rate and respiratory volume. Points used are arithmetic means of the data on female Guinea Pigs. - 3 4 -Equation relating body weight to respiratory rate for the female guinea pig. Y - 347.7W"'2 S.E.E. -+11.8$ -10.5$ /O - 0 .62 Equation relating body weight to respiratory rate for the male guinea pig. Y = 337W"*2 S.E.E. =+10.5$ - 9.5$ / ° =. 0.59 Equation relating body weight to respiratory volume for the female guinea pig. Y = 6.06W*55 S.E.E. =-+12.3$ -10.9$ /O - 0.90 Equation relating body weight to respiratory volume for the male guinea pig. Y - 13.2W44 S.E.E. =+14.00$ -12.28$ / ° ^0.78 -35-Respiratory volume as a function of body weight is shown plotted on a log-log grid in Figs. 10, 11 and respiratory rate as a function of body weight is shown plotted on a log-log grid in Figs. 12, 13. Fig. 10 The relation of respiratory volume to body weight. Plotted on a log-log grid. Female Guinea Pigs. Fig. 11 The relation of respiratory volume to body weight. Plotted on a log-log grid. Male Guinea Pigs. - 3 7 -2Q_ FEMALES Resp. Rate/Kin. = 347.7 W_ +-11.8$ -10.5$ /O = 0.62 S. E. E. — 200 400 8<>0 12p0 Fig. 12 The relation of respiratory rate to body weight. Plotted on a log-log grid. Female Guinea Pigs. -38-• - — 2C 0 • • • J 100 ^ < 1 • j ': '. r — -t . . . . . - M t ^ BO M l — - - mum s r mm 60 CO : — " — • '•• l i i i i i i i l ! — - ..... — — — 40 MALES Reap. Rate/Min. - 337 W"*2 _ + 10.5% S.E.E. - % 5 % :: :: ::::! : : : : : i i ;;;; I. i ~ 20 •L! • Ff-i -L-I M l n -.... > - — \ 1 . • . : i ; . ; i i •1 ' 1 .; ' " 2 . . . v. ><j>6 t i . .... i n " H i )0 4C ."i D l i t 6< in 0 Ch-en 0 a Fig. 13 The relation of respiratory rate of body weight. Plotted on a log-log grid. Male Guinea Pigs. -39-V Discussion It is intended that the limited data collected with the apparatus described in this thesis should provide some indication of the validity and reliability of this apparatus in measuring respiratory rate and volume, rather than establish a respiratory pattern for the experimental animals used. Guyton (1940) proposed an equation for the respiratory volume of a number of species of small animals including the • 75 guinea pig, volume equals 2.1 W* , where W is weight in grams. Table 1 below shows a comparison between the average values for respiratory volume obtained on animals of different weight and sex, and the values calculated by the equation of Guyton and that suggested by the writer. Table 1. Comparison of Respiratory Volume Obtained by Equations  of Guyton and Nordan Body Wt. Actual Guyton Equation Nordan Equation Gms. S e x Ave.Vol. Females Males Females ~ Males cd./Min. V=2.1W75 V=2.1W75 V-6.06W55 V=13.2W 300 f 144.1 144.2 140.2 485 f 186.8 206.7 184.2 725 f 234.5 293.4 230.0 900 f 264.2 345.0 259.0 1052 f 275.2 387.7 282.4 430 m 191.5 198.3 191.2 541 m 210.0 235.6 211.5 756 m 253.0 302.8 245.2 922 . m 263.0 351.4 267-7 -40-Acclose examination of Table 1 shows the effect of the different exponents used in the equations. Both equations show similar values at the lower weights but the values calculated by the Guyton equation depart from the actual values to a greater and greater extent as body weight increases. The data reported here were collected on growing animals of one species only, Guyton onthe other hand -derived his equation from growing and mature animals of a number of species. This fact may account in part for the departure from actual values his equation gives when applied to growing animals. Brody (1940) reports resting 0g consumption for several large animals in the growing and mature state. The equations for the O2 consumption of these large species appear in Table 2. Table 2. Resting O9 Consumption of Several Large Species.  Data from Brody 1945. Animal Weight Weight Respiratory Volume Equation lbs. Kgms. (W in Kgms.)  Percheron Female 200-1100 90-500 77.5 W*54 Percheron Female 1100-2000 500-900 6.22 W*97 Percheron Gelding 200-1100 90-500 84.7 w*54 1 18 Percheron Gelding 1100-2000 500-900 1.63 W Holstein 70-310 30-150 19.3 W*81 Hoistein 310-1200 150-600 53.7 W 6 0 Jersey 60-220 28-100 18.3 W*84 Jersey 220-900 100-450 61.2 W*56 Shetland Ponies 90-800 40-300 90.7 W 5 2 -41-Figures in Table 2 while admittedly not for ventilation volume as such indicate that a change in slope occurs in respira-tory volume between growing and mature animals. Further they indicate that a slope for a group of animals representing the growing and mature phases would probably be in the order of .75-This is consistent with Guyton1s value which was derived from a group of growing and mature animals. The equation for resting O2 consumption of growing horses as reported by Brody is in the order of .55. Although there appears to be some disagreement between the equations presented by the writer for female and male animals, i t is feld that the value obtained for males may have been complicated by the short acclimation period and the fact that male guinea pigs when housed together tend to fight. Guyton (1940) derived the following equation for the -.25 respiratory rate of small animals. Respiratory Rate equals 295 W where W is body weight in grams. This equation applies to a l l animals of both sexes and does not differentiate between growing and mature animals. Patterson (1950) derived the following formulae for male and female guinea pigs: Male R = 447.6 W~*22 1 Q W body weight in grams Female R - 304.1 W~,1V Patterson used a large group of growing animals and only a small -42-number that could be considered mature. Table 3 shows a comparison of respiratory rate data calculated by the equations of Guyton, Patterson and the author. Guyton has noted that mice and guinea pigs breathe somewhat faster than would be calculated by the equation. Allowing for this discrepancy as noted by Guyton, the results obtained from the equations derived by the three workers are in fairly good agreement. From a comparison of the available data on respiratory rate and volume of the guinea pig i t would appear that the apparatus described will give reasonable values for rate and volume. One of the most serious difficulties with any apparatus or method for making such determinations is certainly the care with which the animals are prepared for the experimental work. Constant temperature, humidity and acclimation to the new environ-ment and apparatus are mcast important. Table 3. Comparison of Respiratory Rate Values Obtained by Equations of Guyton, Patterson and Nordan Body Wt. Sex Actual Average Guyton Equation Patterson Equation Nordan Equation in Grams Rate per Min. R=295 W*25 Females Males Females Males R=304.iw;m R=447.6w' R=3ft7.7W' R=337.0W^ 300 f 110.3 70.88 102.9 111.1 485 f 101.5 62.86 93.88 101.0 725 f 93.5 56.85 86.98 93.14 900 f ; 88.5 53.86 83.48 89.20 1052 f 86.3 51.80 81.04 86.46 430 m 105.8 64.78 117.9 100.36. 541 m 994.75 61.17 112.1 95.72 756 m 89.4 56.26 104.1 89.52 922 m 91.2 53.54 99.69 86.00 - 4 4 -VI SUMMARY 1. A review of the literature suggests that the present methods for measuring respiratory rate and volume leave much to be desired. 2. An apparatus has been developed to overcome the difficulties associated with those described in the literature. 3 . The apparatus records on a kymograph drum volume inspired, volume expired, rate of breathing and a five second time base. 4 . The air to be inspired i s kept separate from that expired. 5. Simplicity of operation has been maintained. 6. The data obtained from the apparatus, while admittedly limited, suggest that the apparatus may be superior to those proposed by other workers. -45-VII APPENDICES APPENDIX I Guinea Pig Ration -46-U.B.C. RATION No. 8 Rolled Oat Flour 450 Flaked Wheat 140 Flaked Barley 200 Wheat Bran 350 Dehydrated Grass 100 Beet Pulp 80 Cocoanut Meal 200 Soyabean Meal 175 Oil Cake Meal '250 Mineral Pre-mix 50 Salt 20 Vitamin D o Pre-mix .... . 2015 - 4 7 -APPENDIX II Calibration Table for Respiration Apparatus Strokes/Min. Vol./Stroke Vol./Min. Delivered c.c. c.c. 80 1.00 80 80 2.00 160 ,:80 3.00 240 90 1.00 90 90 2.00 180 90 3.00 270 100 1.00 100 100 2.00 200 100 3.00 300 110 1.00 110 110 2.00 220 110 3.00 330 120 liOO 120 120 2.00 240 120 3.00 360 Strokes/Min. Recorded Vol./Min. Recorded c.c. 80 79 81 162 80 243 91 90 90 184 90 275 100 98 100 204 100 310 111 111 110 225 111 336 120 121 120 245 122 367 -49-APPEWDLX I I I Data on five female guinea pigs and preparation of data for fitting to a logarithmic equation. (a) Volume (b) Rate (a) Volume -50-No. Body wt.-x LogX Vol. /Min.Y LogY LogX.LogY Log^ Log2Y 1 300 2.47712 149 2.17318 5.38324 6.13612 4.72273 2 300 2.47712 140 2.17609 5.39044 6.13612 4.73537 3 300 2.47712 165 2.21748 5.49397 6.13612 4.91723 4 300 2.47713 150 2.17609 5.39044 6.13612 4.73537 5 300 2.47712 124 2.09342 5.18565 6.13612 4.38241 6 300 2.47712 130 2.11384 5.23649 6.13612 4.46875 7 300 2.47712 140 2.14612 5.31621 6.13612 4.60586 8 300 2.47712 140 2.14612 5.31621 6.13612 4.60586 9 300 2.47712 150 2.17609 5.39044 6.13612 4.73537 10 300 2.47712 154 2.18752 5.41875 6.13612 4.78524 11 300 2.47712 120 2.07918 5.15038 6.13612 4.32299 12 300 2.47712 140 2.14612 5.31621 6.13612 4.60586 13 300 2.47712 120 2.07918 5.15038 6.13612 5.32299 14 300 2.47712 130 2.11394 . 5.23649 6.13612 4.46875 15 300 2.47712 129 2.11059 5.22818 6.13612 4.45459 16 300 2.47712 125 2.09691 5.19429 6.13612 4.39703 17 300 2.47712 170 2.23044 5.52509 6.13612 4.97490 18 300 2.47712 190 2.27875 5.64474 6.13612 5.19271 19 300 2.47712 150 2.17609 5.39044 6.13612 4.73537 20 300 2.47712 156 2.19312 5.43263 6.13612 4.80979 21 485 2.68574 225 2.35218 6.31735 6.21321 5.53276 22 485 2.68574 232 2.36548 6.35309 7.21321 5.59553: 23 485 2.68574 225 2.35318 6.31735 7.21321 5-53276 24 485 2.68574 180 2.25527 6.05708 7.21321 5.08625 25 485 2.68574 150 2.17609 5.84441 7.21321 4.73537 26 485 2.68574 210 2.32221 6.23688 7.21321 5.39270 27 485 2.68574 209 2.32014 6.23131 7.21321 5.33972 28 485 2.68574 156 2.19312 5.89016 7.21321 4.80979 29 485 2.68574 176 . .2.24551 6.03086 7.21321 5.04232 30 485 2.68574 180 2.25527 6.05708 7.21321 5.08625 31 485 2.68574 165 2.21748 5.95558 7.21321 4.91723 32 485 2.68574' 150 2.17609 5.84441 7.21321. 4.73537 33 485 2.68574 175 2.24303 6.02422 7.21321 5.03121 34 485 2.68574 140 2.14612 5.76394 7.21321 4.60586 35 485 2.68574 235 2.37106 6.368O7 7.21321 5.62196 36 485 2.68574 225 2.35218 6.31735 7.21321 5.53276 37 485 2.68574 163 2.21218 5.94136 7.21321 4.89377 38 485 2.68574 163 2.21218 5.94136 7.21321 4.89377 39 485 2.68574 160 2.20412 5.91969 7.21321 4185814 40 485 2.68574 205 2.31175 6.20877 7.21321 5.34420 41 485 2.68574 200 2.30103 6.17997 7.21321 5.29473 42 725 2.86033 224 2.35024 6.72250 8.18153 5.52366 43 725 2.86033 200 2.30103 6.58172 8.18153 5.29473 44 725 2.86033 225 2.35218 6.72803 8.18153 5.53276 45 725 2.86033 320 2.50515 7.16557 8.18153 6.27577 46 725 2.86033 300 2.47712 7.08540 8.18153 6.13612 47 725 2.86033 240 2.38021 6.80820 8.18153 5.66540 48 725 2.86033 240 2.38021 6.80820 8.18153 5.66540 49 725 2.86033 244 2.38739 6.82874 8.18153 5.69963 50 725 2.86033 240 2.38021 6.80820 8.18153 5.66540 51 725 2.86033 200 2.30103 6.58172 8.18153 5.29473 52 725 2.86033 240 2.38021 6.80820 8.18153 5.66540 53 725 2.86033 200 2.30103 6.58172 8.18153 5.29473 (a) Volume cont'd -51© No. Body Wt.X LogX Vol. /Min.Y LogY LogX.LogY Log2X Log2Y 54 725 2.86033 200 2.30103 6.58172 8.18153 5.29473 55 725 2.86033 200 2.30103 6.58172 8.18153 5.29473 56 725 2.86033 280 2.44715 6.99969 8.18153 5.98858 57 725 2.86033 200 2.30103 6.58172 8.18153 5.29473 58 725 2.86033 244 2.38739 6.82874 8.18153 5.69963 59 725 2.86033 240 2.38021 6.80820 8.18153 5.66540 60 725 2.86033 268 2.42813 6.94528 . 8.18153 5.89583 61 725 2.86033 215 2.33243 6.67156 8.18153 5.44026 62 725 2.86033 230 2.36172 6.75534 8.18153 5.57775 63 725 2.86033 240 2.38021 6.80820 8.18153 5.66540 64 725 2.86033 225 2.35218 6.72803 8.18153 5.53276 65 725 2.86033 210 2.32221 6.64233 8.18153 5.39270 66 900 2.95424 300 2.47712 7.31801 8.72755 6.13612 67 900 2.95424 180 2.25527 6.66262 8.72755 5.08625 68 900 2.95424 .180 2.25527 6.66262 8.72755 5.08625 69 900 2.95424 300 2.47712 7.31801 8.72755 6.13612 70 900 2.95424 300 2.47712 7.31801 8.72755 6.13612 71 900 2.95424 300 2.47712 7-31801 8.72755 6.13612 72 900 2.95424 280 2.44715. 7.22949 8.72755 5.98858 73 900 2.95424 300 2.47712 7.31801 8.72755 6.13612 74 900 2.95424 280 2.44715 7122949 8.72755 5.98858 75 900 2.95424 290 2.46239 7.27452 8.72755 6.06340 76 900 2.95424 250 2.39794 7.68409 8.72755 5.75011 77 900 2.95424 250 2.39794 7.08409 8.72755 5.75011 78 900 2.95424 .- 340 2.53147 7.47860 8.72755 6.40838 79 900 2.95424 180 2.25527 6.66262 8.72755 5.08625 80'» 900 2.95424 230 2.36172 6.97711 8.72755 5.57775 81 900 2.95424 225 2.35218 6.94892 8.72755 5.53276 82 900 2.95424 300 2.47712 7.31801 8.72755 6.13612 83 900 2.95424 250 2.39794 7.08409 8.72755 5.75011 84 900 2.95424 250 2.39794 7.08409 8.72755 5.75011 85 900 2.95424 250 2.39794 7.08409 8.72755 5.75011 86 900 2.95424 278 2.44404 7.22030 8.72755 5.97335 87 900 2.95424 300 2.47712 7.31801 8.72755 6.13612 88 1052 3.02201 325 2.51188 7.59095 9.13258 6.30955 89 1052 3.02201 305 2.48430 7.50759 9.13258 6.17174 90 1052 3.02201 300 2.47712 7.48589 9.13258 6.13612 91 1052 3.02201 298 2.47421 7.47712 9.13250 '6.12174 92 1052 3.02201 250 2.39794 7.24661 9.13258 5.75011 93 1052 3.02201 300 2.47712 7.48589 9.13258 6.13612 94 1052 3.02201 240 2.38021 7.19303 9.13258 5.66540 95 1052 3.02201 275 2.43933 7.37170 9.13258 $.95034 96 1052 3.02201 280 2.44715 7.39535 9.13258 5.98858 97 1052 3.02201 260 2.41497 7.29808 9.13258 5.83209 98 1052 3.02201 250 2.39794 7.24661 9.13258 5.75011 99 1052 3.02201 250 2.39794 7.24661 9.13258 5.75011 100 1052 3.02201 235 2.37106 7.16540 9.13258 5.62196 101 1052 3.02201 310 2.49136 7.52893 9.13258 6.20688 102 1052 3.02201 300 2.47712 7.48589 9.13258 6.13612 103 1052 3.02201 330 2.34242 7.07883 9.13258 5.48694 104 1052 3.02201 250 2.39794 7.24661 9.13258 5.75011 105 1052 3.02201 278 2.44404 7.38594 8.13258 5-97335 106 1052 3.02201 272 2.43456 7.35730 9.13258 5.92712 107 1052 3.02201 306 2.48572 7.51188 9.13258 6.17880 - 5 2 -(b) Rate No. Body Wt.X Logx Rate /Min.I LogY LogX.LogY Log2x Log2? 1 300 2.47712 91 1.95904 4.85278 6.13612 3-83784 2 300 2.47712 100 2.00000 4.95424 6.13612 4.00000 3 300 2.47712 106 2.02530 5.01692 6.13612 4.10186 4 300 2.47712 108 2.03342 5.03703 6.13612 4.13481 5 300 2.47712 123 2.08990 5-17694 6.13612 4.36770 6 300 2.47712 122 2.08636 5.16816 6.13612 4.35289 7 300 2.47712 125 2.09691 . 5.19430 6.13612 4.39703 8 300 2.47712 118 2.07188 5.13230 6.13612 4.29269 9' 300 2.47712 95 1.97772 4.89906 6.13612 3.91139 10 300 2.47712 98 1.99122 4.93250 6.13612 3.96498 11 300 2.47712 120 2.07918 5.15038 6.13612 4.32299 12 300 2.47712 116 2.06445 5.11391 6.13612 4.26198 13 300 2.47712 101 2.00432 4.96494 6.13612' 4.01730 14 300 2.47712 110 2.04139 5.05677 6.13612 4.16728 15 300 2.47712 111 2.04532 5.06651 6.12612 4.18334 16 300 2.47712 109 2.03742 5.04695 6.13612 4.15110 17 300 2.47712 103 2.01283 4.98604 6.13612 4.05151 19 300 2.47712- 114 2.05690 -5.09520 6.13612 4.23085 19 300 2.47712 128 2.10721 5.21981 6.13612 4.44033 20 300 2.47712 109 2.03742 5-04695 6.13612 4.15110 21 485 2.68574 119 2.07554 5.57438 7.21321 4.30789 22 485 2.68574 116 2.06445 5-54460 7.21321 4.26198 23 485 2.68574 120 2.07918 5.58414 7.21321 4.32299 24 485 2.68574 120 2.07918 5-58414 7.21321 4.32299 25 485 2.68574 100 2.00000 5.37148 7.21321 4.00000 26 485 2.68574 105 2.02118 5.42839 7.21321 4.08520 27 485 2.68574 108 2.03342 5.46125 7.21321 4.13481 28 485 2.68574 105 2.02118 5.42839 7.21321 4.08520 29 485 2.68574 93 1.96848 5.28683 7.21321 3.87492 30 485 2.68574 94 1.97312 5.29931 7.21321 3.89323 31 485 2.68574 90 1.95424 5.24859 7.21321 3.81906 32 485 2.68574 93 1.96848 5.28683 7.21321 3.87492 33 485 2.68574 87 1.93951 5.20904 7.21321 3.76173 34 485 2.68574 92 1.96378 5.27422 7.21321 2.85646 35 485 2.68574 93 1.96848 5.28683 7.21321 3.87492 36 485 2.68574 108 2.03342 5.46125 7.21321 4.13481 37 485 2.68574 96 1.98227 5.32386 7.21321 3.92939 38 485 2.68574 96 1.98227 5.32386 7.21321 3.92939 39 485 2.68574 99 1.99956 5.37031 7.21321 3.99826 40 485 2.68574 99 1.99956 5.37031 7.21321 3.99826 41 485 2.68574 100 2.00000 5.37148 7.21321 4.00000 42 725 2.86033 80 1.90309 5.44348 8.18153 3.62175 43 725 2.86033 80 1.90309 5.44348 8.18153 3.62175 44 725 2.86033 106 2.02530 5.79306 8.18153 4.10186 45 725 2.86033 96 1.98227 5.66996 8.18153 3.92939 46 725 2.86033 9«4 1.97312 5.64381 8.18153 3.89323 47 725 2.86033 96 1.98000 5.66347 8.18153 3.92939 48 725 2.86033 100 2.00000 5.72067 8.18153 4.00000 49 725 2.86033 128 2.10721 6.02733 8.18153 4.44033 50 725 2.86033 96 1.982271 5.66996 8.18153 3.92939 51 725 2.86033 80 1.90309 5.44348 8.18153 3.62175 52 725 2.86033 86 1.93449 5.53331 8.18153 3.74228 53 725 2.86033 83 1.91907 5.48921 8.18153 3.68286 (b) Rate cont'd -53-No. Body wt.x LcgX Rate /Min.Y LogY LogX.LogY Log2X Log2Y 54 725 2.86033 88 1.94448 5.56187 8.18153 3.78101 55 725 2.86033 90 1.95424 5.58979 8.18153 3.81906 56 725 2.86033 81 1.90848 5-45891 8.18153 3.64231 57 725 2.86033 95 1.97772 5.65695 8.18153 3.91139 58 725 2.86033 83 1.91907 5.48921 8.18153 3.68286 59 725 2.86033 84 1.92427 5.50408 8.18153 3.70285 60 725 2.86033 81 1.90848 5.45891 8.18153 3.64231 61 725 r .r t2.86033 96 1.98227 5.66996 8.18153 3.92939 62 725 2.86033 92 1.96378 5.61709 8.18153 3.85646 63 725 2.86033 91 1.95904 5.60351 8.18153 3.83784 64 725 2.86033 105 2.02118 5.78128 8.18153 4.08521 65 725 2.86033 133 2.12385 6.07493 8.18153 4.51074 66 900 2.954243 96 1.98452' 5.86277 8.72755 3.93834 67 900 2.95424 70 1.84509 5.45086 8.72755 3.40438 68 900 2.95424 72 1.85733 5-48701 8.72755 3.44968 69 900 2.95424 96 1.98227 5.85611 8.72755 3.93834 70 900 2.95424 90 1.95424 5.77330 8.72755 3.81906 71 900 2.95424 105 2.02118 5.97108 8.72755 4.08520 72 900 2.95424 91 1.95904 5.78748 8.72755 3.83784 73 900 2.95424 89 1.94939 5.75897 8.72755 3.80012 74 900 2.95424 85 1.92941 5.69997 8.72755 3.72265 75 76 900 2.95424 83 1.91907 5.66942 8.72755 3.68286 900 2.95424 83 1.91907 5.66942 8.72755 3.68286 77 900 2.95424 85 1.92941 5.69997 8.72755 3.72265 78 900 2.95424 102 2.00860 5.93389 8.72755 4.03447 79 900 2.95424 72 1.85733 5.48701 8.72755 3.44968 80 900 2.95424 80 1.90309 5.62219 8.72755 3.62175 81 900 2.95424 80 1.90309 5.62219 8.72755 3.62175 82 900 2.95424 99 1.99563 5.89559 8.72755^ 3.98255 83 900 2.95424 90 1.95424 5.77330 8.72755 3.81906 84 900 2.95424 100 2.00000 5.90848 8.72755 4.00000 85 900 2.95424 • 88 1.94448 5.74447 8.72755 3.78101 86 900 2.95424 100 2.00000 5.90848 8.72755 4.00000 87 900 2.95424 91 1.95904 5.78748 8.72755 3.83784 88 1052 3.02201 92 1.96378 5.93459 9.13258 3.85450 89 1052 3.02201 84 1.92427 5.81520 9.13258 3.70285 90 1052 3.02201 84 1.92427 5.81520 9.13258 3.70285 91 1052 3.02201 83 1.91907 5.79948 9.13258 3.68286 92 1052 3.02201 90 1.95424 5.90575 9.13258 3.81906 93 1052 3.02201 108 2.03342 6.14504 9.13258 4-13481 94 1052 3.02201 92 1.96378 5.93459 9.13258 3185450 95 1052 3.02201 74 1.86923 5.64884 9.13258 3.49402 96 1052 3.02201 100 2.00000 6.04403 9.13258 4.00000 97 1052 3.02201 86 1.93449 5.84608 9.1325.8 3.74228 98 1052 3.02201 93 1.96848 5.94878 9.13258 3.87492 99 1052 3.02201 88 1.94448 5.87625 9.13258 3.78101 100 1052 3.02201 78 1.89209 5.71794 9.13258 3.58002 101 1052 3.02201 81 1.90848 5.76747 9.13258 3.64231 102 1052 3.02201 86 1.93449 5.84608 9.13258 3.74228 103 1052 3.02201 80 1.90309 5.75116 9U3258 3.62175 104 1052 3.02201 85 1.92941 5.83073 9.13258 3.72265 105 1052 3.02201 86 1.93449 5.84608 9.13258 3.74228 106 1052 3.02201 79 1.89762 5.73465 9.13258 3.60098 107 1052 • 3.02201 77 1.88649 5.70100 9.13258 3-55884 -54-APPENDIX IV Data on four male guinea pigs and preparation of data for fitting to a logarthmic equation (a) Volume (b) Rate - 5 5 -(a) Volume No. Body Wt.X LogX Vol. /Min.Y - LogY LogX.LogY Log2X Log2Y 1 541 2.73320 225 2.35218 6.42898 7.47038 5.53571 2 541 2.73320 200 2.30103 6.28918 7.47038 5.29474 3 541 2.173320 212 2.32634 6.35835 7.47038 5.41186 4 541 2.73320 250 2.38021 6.50559 7.47038 5.66540 5 541 2.73320 200 2.30103 6.28918 7-47038 5.29474 6 541 2.73320 250 2.39794 6.55405 7.47038 5.75012 7 541 2.73320 180 2.25527 6.16410 7.47038 5.08624 8 541 2.73320 192 2.28330 6.24072 7.47038 5.21346 9 541 2.73320 236 2.37291 6.48564 7.47038 5.63070 10 541 2.73320 190 2.27875 6.22828 7.47038 5.19270 11 541 2.73320 200 2.30103 6,28918 7.47038 5.29474 12 541 2.73320 190 2.27875 6.22828 7.47038 5.19270 13 541 2.73320 190 2.27875 6.22828 7.47038 5.19270 14 541 2.73320 180 2.25527 6.16410 7-47038 5.08624 15 541 2.73320 220 2.34242 6.40230 7.47038 5.48693 16 541 2.73320 220 2.34242 6.40230 7.47038 5-48693 17 541 2.73320 200 2.30103 6.28918 7.48038 5.29474 18 541 2.73320 250 2.39794 6.55405 7.46038 5.75012 19 541 2.73320 240 2.38021 6.50559 7.47038 5.66540 20 541 2.73320 240 2.38021 6.50559 7.47038 5.66540 21 756 2.87852 228 2.35793 6.78735 8.28588 5.55983 22 756 2.87852 240 2.38021 6.85148 8.28588 5.66540 23 756 2.87852 230 2.36173 6.79829 8.28588 5.57777 24 756 2.87852 230 2.36173 6.79829 8.28588 5.57777 25 756 2.87852 228 2.35793 6.78735 8.28588 5.55983 26 756 2.87852 225 2.35218 6.77080 8.28588 5.53275 27 756 2.87852 244 2.38739 6.87215 8.28588 5.69963 28 756 2.87852 245 2.38917 6.87727 8.28588 5.70813 29 756 2.87852 248 2.39445 6.89247 8.28588 5-73339 30 756 2.87852 250 2.39794 6.90252 8.28588 5.75012 31 756 2.87852 250 2.39794 6.90252 8.28588 5.75012 32 756 2.87852 250 2.39794 6.90252 8.28588 5.75012 33 756 2.87852 300 2.47712 7.13044 8.28588 6113612 34 756 2.87852 250 2.39794 6.90252 8.28588 5.75012 35 756 2.87852 290 2.46240 7C08807 8.28588 6.06341 36 756 2.87852 3:00 2.47712 7.13044 8.28588 6.13612 37 756 2.87852 . 250 2.39794 6.90252 8.28588 5.75012 38 756 2.87852 250 2.39794 6.90252 8.28588 5.75012 39 756 2.87852 280 2.44716 7.04420 8.28588 5.98859 40 756 2.87852 270 .2.43136 6.99872 8.28588 5.91151 (a) Volume (cont'd) -56-No. Body LogX Vol. LogY wt.x /Min.Y LogX.LogY Log2X Log^ Y 41 922 2.96473 273 2.43616 7.22256 8.78962 5.93488 42 922 2.96473 250 . 2.39794 7.10924 8.78962 5.75012 43 922 2.96473 240 2.38021 7.05668 8.78962 5.66540 44 922 2.96473 260 2.41497 7.15973 8.78962 5.83208 45 922 2.96473 236 2.37291 7.03504 8.78962 5.63070 46 922 2.96472 243 2.38561 7.07269 8.78962 5.69114 47 922 2.96473 230 2.36173 7.00189 8.78962 5.57777 48 922 2.96473 250 2.39794 7.10924 8.78962 5.75012 49 922 2.96473 290 2.46240 7.30035 8.78962 6.06341 50 922 2.96473 290 2446240 7.30035 8.78962 6.06341 51 922 2.96473 231 2.36361 7.00746 8.78962 5.58665 52 922 2.96473 271 2.43297 7.21310 8.78962 5.91934 53 922 2.96473 , 270::; ; 2.43136 7.20832 8.78962 5.91151 54 922 2.96473 280 2.44716 7.25517 8.78962 5.98859 56 922 2.96473 250 2.39794 7.10924 8.78962 5.75012 57 922 2.96473 230 2.36173 7.00189 8.78962 5.57777 58 922 2.96473 300 2.47712 7.34399 8.78962 6.13612 59 922 2.96473 290 2.46240 7.30035 8.78962 6.06341 60 922 2.96473 290 2.46240 7-30035 8.78962 6.66341 61 430 2.63347 165 2.21748 5.83967 6.93516 4.91722 62 430 2.63347 180 2.25527 5.93918 6.93516 5.08624 63 430 2.63347 187 2.27184 5.98282 6.93516 5.16126 64 430 2.63347 160 2.20412 5.80448 6.93516 4.85814 65 430 2.63347 150 2.17609 5.73067 6.93516 4.73537 66 430 2.63347 200 2.30103 6.05969 6.93516 5.29474 67 430 2.63347 176 2.24551 5.91348 6.93516 5.04232 68 430 2.63347 180 2.25527 5.93918 6.93516 5.08624 69 430 2.63347 200 2.30103 6.05969 6.93516 5.29474 70 430 2.63347 200 2.30103 6.05969 6.93516 5.29474 71 430 2.63347 150 2.17609 5.73067 6.93516 4.73537 72 430 2.63347 210 2.32222 6.11550 6.93516 5.39270 73 430 2.63347 200 2.30103 6.05969 6.93516 5.29474 74 430 2.63347 190 2.27875 6.00102 6.93516 5.19270 75 430 2.63347 200 2.30103 6.05969 6.93516 5.29474 76 430 2.63347 220 2.34242 6.16869 6.93516 5.48693 77 430 2.63347 230 2.36173 6.21954 6.93516 5.57777 78 430 2.63347 220 2.34242 6.16869 6.93516 5.48693 79 430 2.63347 210 2.32222 6.11550 6.93516 5.39270 80 430 2.63347 200 2.30103 6.05969 6.93516 5.29474 - 5 7 -(b) Rate No. Body wt.x LogX Rate /Min.Y LogY LogX.LogY Log?X Log2Y 1 541 2.73320 93 1.96848 5.38025 7.47038 3.87491 2 541 2.73320 86 1.93450 5.28738 7.47038 3.74229 3 541 2.73320 82 1.91381 5.23083 7.47038 3.66265 4 541 2.73320 100 2.00000 5.46640 7.47038 4.00000 5 541 2.73320 90 1.95424 5.34133 7147038 3.81905 6 541 2.73320 93 1.96848 5.38025 7.47038 3.87491 7 541 2.73320 95 1.97772 5.40550 7.47038 3.91138 8 541 2.73320 86 1.93450 5.28738 7.47038 3-74229 9 541 2.73320 101 2.00432 5.47821 7.47038 4.01730 10 541 2.73320 90 1.95424 5.34133 7.47038 3.81905 11 541 2.73320 96 1.98227 5.41794 7.47038 3.92939 12 541 2.73320 90 1.95424 5.34133 7.47038 3.81905 13 541 2.73320 89 1.94939 5.32807 7.47038 3.80012 14 541 2.73320 106 2.02531 5.53557 7.47038 4.15816 15 541 2.73320 1180 2.07188 5.66286 7.47038 4.29269 16 541 2.73320 100 2.00000 5.46640 7-47038 4.00000 17 541 2.73320 98 1.99123 5.44243 7.47038 3.96500 18 541 2.73320 93 1.96848 5.38025 7.47038 3.87491 19 541 2.73320 96 1.98227 5.41794 7-47038 3-92939 20 541 2.73320 93 1.96848 5.38025 7.47038 3.87491 21 756 2.87852 95 1.97772 5.69291 8.28588 3.91138 22 756 2.87852 100 2.00000 5.75704 8.28588 4.00000 23 756 2.87852 87 1.93952 5.58295 8.28588 3.76174 24 756 2.87852 87 1.93952 5.58295 8.28588 3.76174 25 756 2.87852 85 1.92942 5.55387 8.28588 3.72266 26 . 756 2.87852 82 1.91381 5.50894 8.28588 3.66267 27 756 2.87852 83 1.91908 5.52411 8.28588 3.68287 28 756 2.87852 89 1.94939 5.61136 8.28588 3.80012 29 756 2.87852 81 1.9.0849 5.49363 8.28588 3-64233 30 756 2.87852 90 1.95424 5.62532 8.28588 3.81905 31 756 2.87852 90 1.95424 5.62532 8.28588 3.81905 32 756 2.87852 80 1.90309 5.47808 8.28588 3.62175 33 756 2.87852 96 1.98227 5.70600 8.28588 3.92939 34 756 2.87852 100 2.00000 5.75704 8.28588 4.00000 35 756 2.87852 84 1.92428 5.53908 8.28588 3.70285 36 756 2.87852 84 • 1.92428 5.53908 8.28588 3-70285 37 756 2.87852 105 2.02119 5.81804 8.28588 4.08521 38 756 2.87852 90 1.95424 5.62532 8.28588 3.81905 39 756 2.87852 90 1.95424 5.62532 8.28588 3.81905 40 756 2.87852 90 1.95424 5.62532 8.28588 3.81905 (b) Rate ( c o n t ' d ) -58-TToT" Body Wt.X LogX Rate /Min.Y LogY LogX.LogY Log^X Log2Y 41 922 2.96473 87 1.93952 5.75015 8.78962 3.76174 42 922 2.96473 100 2.00000 5.92946 8.78962 4.00000 43 922 2.96473 100 2.00000 5.92946 8.78962 4.00000 44 922 2.96473 85 1.92942 5-72021 8.78962 3.72266 45 922 2.96473 100 2.00000 5.92946 8.78962 4.00000 46 922 2.96473 87 1.93952 5.75015 8.78962 3.76174 47 922 2.96473 91 1.95904 5.80802 8.78962 3.83784 48 922 2.96473 95 1.97772 5.86340 8.78962 3.91138 49 922 2.96473 90 1.95424 5.79379 8.78962 3.81905 50 922 2.96473 90 1.95424 5.79379 8.78962 3.81905 51 922 2.96473 74 1.86923 5.54176 8.78962 3.49402 52 922 2.96473 95 1.97772 5.86340 8.78962 3.91138 53 922 2.96473 98 1.99123 5.90346 8.78962 3.96500 54 922 2.96473 90 1.95424 5.79379 8.78962 3.81905 55 922 2.96473 75 1.87506 5.55905 8.78962 3.51585 56 922 2.96473 100 2.00000 5.92946 8.78962 4.00000 57 922 2.96473 98 1.99123 5.90346 8.78962 3.96500 58 922 2.96473 90 1.95424 5.79379 8.78962 3.81905 59 922 2.96473 90 1.95424 5.79379 8.78962 3.81905 60 922 2.96473 90 1.95424 5.79379 8.78962 3.81905 61 430 2.63347 104 2.01703 5.31179 6.93516 4.06841 62 430 2.63347 101 2.00432 5.27832 6.93516 4.01730 63 430 2.63347 104 2.01703 5.31179 6.93516 4.06841 64 430 2.63347 101 2.00432 5.27832 6.93516 4.01730 65 430 2.63347 102 2.00860 5.28959 6.93516 4.03447 66 430 2.63347 105 2.02119 5-32274 6.93516 4.08521 67 430 2.63347 105 2.02119 5.32274 6.93516 4.08521 68 430 2.63347 109 2.03743 5.36551 6.93516 4.15112 69 430 2.63347 106 2.02531 5.33359 6.93516 4.10188 70 430 2.63347 111 2.04532 5.38629 6.93516 4.18333 71 430 2.63347 111 2.04532 5.38629 6.93516 4.18333 72 430 2.63346 115 2.06070 5.42679 6.93516 4.24648 73 430 2.63347 112 2.04922 5.39656 6.93516 4.19930 74 430 2.63347 110 2.04139 5.37594 6.93516 4.16727 75 430 2.63347 96 1.98227 5.22025 6.93516 3.92939 76 430 2.63347 108 2.03342 5.35495 6.93516 4.13480 77 430 2.63347 106 2.02531 5-33359 6.93516 4.10188 78 430 2.63347 104 2.01703 5.31179 6.93516 4.06841 79 430 2.63347 105 2.02119 5.32274 6.93516 4.08521 80 430 2.63347 102 2.00860 5.28959 6.93516 4.03447 APPENDIX V Calculation of respiratory rate and volume equation and standard error of estimate, Method 1. - 6 0 -Method 1 Y = aXb or log Y = log a +- b log X (1) €(log Y) = N log a -+• b£(log X) (2) Z(log X x log Y) = log ai(log X) + bi(log 2X) (1) 249.37155 = 1071og a + 300.02468b (2) 701.41291 =• 300.024681og a + 845.21453b Divide each equation by coefficient of log a (1) 2.33057 = log a + 2.80396b (2) 2.33785 = log a + 2.81715b .00728 =.01319b b = .55215 Substitute value "b" in equation (1) solve for "a" 2.33057 = log a + 2.80396(.55) 2.33057 - log a + 1.54758 log a = .78236 a = 6.06 equation Y = 6.06X*55 • mm. " Slog y v log x - (log 2Y)-log a^Iog Y)-b£(log X x log Y) N 1 _ 582.65608 - (.78236 x 249.37155)-.55215 x 701.41291 105. - 582.65608 - 195.098325 - 387.285138 _. .272617 _ .00259 105 105 slog y . log x - *°5°2 + S r - 2 f .0502 = 2.0502 = 112.3 = 12.3$ -Sr = 2 - .0502 = 1.9498 =• 89.9 - 10.91$ N^" is the "degrees of freedom". The "degrees of freedom" are the number of data points less the number of constants in the equation. -61-APPENDIX VI Calculation of respiratory rate and volume equation, standard error of estimate and correlation coefficient, Method 2. - 6 2 -Method 2 \ N / ^log X = 300.02468 (jaoz Xj = 2.803 96 ilog X = 841.25720 log2X = 845.21453 tlog^X = 3.95733 ^ log Y =• 249.37155 ^ l o g Yj=. 2.330575 log2Y - 582.65608 (ilg&2)aog Y = 581.17910 £log^Y - 1.47698 N ^107 ^log X x log Y = 701.41291 ^ l o g glog Y = 699.22785 l l o g Xx log Y = 2.18506 log Y = U o ^ g , Y £ l o g x log Y = 2.330575 + 2.18506 ± x . ( 2 . 8 0 3 9 6 ) 3.95733 2.330575 1- .552151og X - 1.54820 .782369 +.55215log X Y = 6.06X .55 b(qog X x log Y) _ .55(2.18506) _ 1.20178 _ .813 £ log2Y 1.47698 ~ 1.47698 /o =. .901 Slog v log x - *log2Y - b(?log x x log Y) _ 1.47698 - 1.20648  6 s N - 2 " 105 - .2705 - .002528 105 Slo g"y . log x = '°502 + Sy > x - ^ (antilog .0502) - l] 100 = (1.123 - 1)100 = 12. X - 12.3 - 10.95? 1.123~ -63-BIBLIOGRAPHY Benedict, F.G. and Collins, W.E., Boston Medical and Surgical Journal, 183:449, (1920) Original not available, cites in Brody (1945) Brody, S., Bio-energetics and Growth, Reinhold Publishing Co., New York, (1945) Chapman, A., Baldes, E.J., Higgins, G.M., "A closed c i r c u i t apparatus for the measurement of respiratory metabolism," Science, 99:329, (1944) Fredericq, L., Arch, de Biol., 3:687, (1887) Original not available, cited in Brody (1945) Guyton, A.C, "Measurement of the respiratory volumes of laboratory animals," The Americal Journal of Physiology, 150:70, (1947) Guyton, A.C, "Analysis of respiratory patterns in laboratory animals," The American Journal of Physiology, 150:78, (1947) Haldane, J.S., J. Physiol., 13:419, (1892) Original not available, cited in Brody (1945) Kleiber, M., "A respiration apparatus for ser i a l work with small animals, particularly rats," Univ. Calif. Publ. Physiol., 8:207, (1940 Kleiber, M., "The t i d a l a i r of laboratory animals," Science, 99:542,(194$ Krogh, A., Boston Medical and Surgical Journal, 189, 313 (1923) Original not available, cited in Brody (1945) Loosli, C.G., Robertson, O.H., Puck, T.T., "The production of experimental influenza in mice by inhalation of atmospheres containing Influenza virus dispersed as fine droplets," Journal of Infectious Diseases, 72_:147, (1943) McQuarrie, K., Unpublished (1948) Personal communication Patterson, E.B., "The respiration rate of the guinea pig under inimical conditions," Term essay, University of British  Columbia, (1950) Regnault, V., and ReiSet, J., "Recherches chimiques sur l a respiration des animaux des deverses classes," Annals Chimique et de Physique, 26:299, (1849) Tyler, A., and Berg, Wm., "A new type of Micro-respirometer," Science, 94: 347, (1941) Winchester, C.F., "Seasonal metabolic and endocrine rhythms in the domestic fowl," University of Missouri Agriculture  Research Station Bulletin, 315, (1940) 

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