Metabolic Rate Determinations BOOTHBY - SAUDI FORD UNIVERSITY OF CALIFORNIA MEDICAL CENTER LIBRARY SAN FRANCISCO FROM THE LIBRARY OF HERBERT C. MOFFITT, SR, Laboratory Manual of the Technic of Basal Metabolic Rate Determinations By Walter M.^Boothby, A. M., M. D. and Irene Sandiford, Ph. D. Section on Clinical Metabolism The Mayo Clinic, Rochester, Minnesota and The Mayo Foundation, University of Minnesota Illustrated Philadelphia and London W B. Saunders Company 1920 Copyright, ig2o, by W. B. Saunders Company PRINTED IN AMERICA PRESS OF B. SAUNDERS COMPANY PHILADELPHIA B72.L 1924 TO J. S. H. H. C. H. S. P. PREFACE NEW methods of precision for the study of disease are con- tinuously passing from the purely scientific to the more prac- tical clinical application. The most recent of these methods of precision and probably the most difficult technically is indirect calorimetry. This manual has been prepared in the effort to render this valuable diagnostic method available to any well- equipped and scientifically conducted clinical aboratory, and with the hope that the results of indirect calorimetry will not be thrown into general discredit by a neglect of the details requisite for obtaining a true basal metabolic rate. ROCHESTER, MINNESOTA. August, 1920. CONTENTS SECTION I GENERAL DISCUSSION 11 Basal Metabolic Rate 11 Normal Standards 14 Clinical Calorimetry 17 Direct and Indirect Calorimetry. The Respiration Calorimeter 18 Agreement of Direct and Indirect Calorimetry 20 Indirect Calorimetry 20 Unit Apparatus 20 Portable Unit Apparatus 21 Gasometer 22 SECTION II DETAILS OF TECHNIC 24 THE PATIENT 24 Postabsorptive Condition 24 Muscular Activity ' 24 Preliminary Rest Period 25 Effect of Body Temperature 29 Character of Respiration 30 Effect of Sleep 30 Body Position 31 Observer's Chart 32 Repetition of Test 34 THE GASOMETER AND ACCESSORY APPARATUS 35 Mask 35 Valves 37 Intake Pipe 41 Outdoor Air 41 Room Air 41 Connections 42 Gasometer 42 Barometer 49 Calibration of Gasometer 49 Collection of Expired Air in Gasometer 50 Sampling Tubes 52 Stratification of Air in Gasometer 53 Effect on the Carbon Dioxid and Oxygen Content of the Expired Air from Standing in the Gasometer 55 7 8 CONTENTS I'AGK THE HALDANE GAS ANALYSIS APPARATUS 56 Description of Haldane Apparatus 56 Calibration of Haldane Buret 60 Assembling the Haldane 65 Electric Glass Cutter 66 Control Tube 68 Management of Haldane Apparatus 68 Preliminary 68 Sampling 70 Analysis 72 Care of Haldane 73 Filling Haldane 77 Analysis of Outdoor Air 78 Shaker 79 SOLUTIONS 80 Potassium Pyrogallate Solution (Haldane) 80 Potash Solution for Carbon Dioxid Absorption 80 Black Rubber Grease 81 Cleaning Solution ... 81 Cleaning Mercury 81 SECTION III CALCULATION OF BASAL METABOLIC RATE 82 Volume of Expired Air 82 Correction of Barometer to C 83 Correction for Water Vapor 83 Reduction to Standard Pressure 83 Reduction to Standard Temperature 83 Ventilation Rate 84 Carbon Dioxid Production , 84 Oxygen Absorption 84 Respiratory Quotient 85 Calories per Square Meter per Hour 86 Basal Metabolic Rate (B. M. R.) 86 Checking Calculations 86 Non-protein Respiratory Quotient 87 Calculation of Metabolic Rate of a Diabetic 88 BIBLIOGRAPHY 89 APPENDIX 94 Explanation of Tables 94 Table I, Equivalent of Seconds in Decimal Parts of a Minute 94 Table II, Log Factor for Reducing Volume of Gases to Standard Temperature and Pressure, Dry 96 CONTENTS 9 Table III, Correction Inspired Oxygen Percentage to Basis of Ex- pired Volume 104 Table IV, Calorific Value of One Liter of Oxygen for Various Res- piratory Quotients 105 Table V, Du Bois Height- weight Chart 106 Table VI, Aub and Du Bois Normal Standards 107 Table VII, Four-place Logarithms 108 Form 1, Observer's Chart facing page 1 12 Form 2, Calculation Sheet facing page 112 Form 3, Summary Card facing page 112 Form 4, Outdoor Air Analysis facing page 112 INDEX.. . 113 TECHNIC OF BASAL METABOLIC RATE DETERMINATIONS SECTION I GENERAL DISCUSSION 1. Basal Metabolic Rate. "In each mammal there is a basal metabolism." 55 By the term "basal metabolism" or "basal meta- bolic rate" of an organism is meant the minimal heat production of that organism, measured from twelve to eighteen hours after the ingestion of food and with the organism at complete muscular rest. This minimal heat production may be determined directly by actual measurement by means of a calorimeter, or indirectly by calculating the heat production from an analysis of the end- products which result from oxidation within the organism, or specifically from the amount of oxygen used and the corresponding amount of carbon dioxid produced, together with the total nitrogen eliminated in the urine. The physiologic importance of oxygen for the needs of the body was recognized by Lavoisier (1780), who identified and named the gas. It is remarkable how clear was his conception of the problem of animal combustion both qualitatively and quantitatively. He determined the oxygen requirement with the subject fasting both at rest and at work, and also carried on experiments on the effect of food ingestion, showing that the oxidative processes within the body were thereby increased. It was not until 1850 that serious attempts were made to ad- vance the work of Lavoisier. At this time Regnault and Reiset ii 12 BASAL METABOLIC RATE devised an apparatus for the measurement of the respiratory ex- change, that is, the amount of oxygen absorbed by the subject and the simultaneous determination of the carbon dioxid produced. The apparatus was of the closed-circuit type, in which the subject re- breathed air from a closed system from which the carbon dioxid produced was removed by absorption in potash solution and the oxygen consumed was replaced as it was used by a known amount of oxygen. A respiration apparatus which measured only the amount of carbon dioxid produced was constructed by Pettenkofer in 1862, under Carl Voit's direction. The latter, using the heat values de- termined in his laboratory by Rubner for protein, fat, and carbo- hydrate, calculated the quantity of heat arising from the burning of these substances within the body, thus developing the method of indirect calorimetry. Rubner in 1894 constructed the first successful respiration calorimeter for experimental work on dogs. In connection with the calorimeter he used the respiration apparatus of Pettenkofer and Voit, and so was able to show the agreement between the methods of direct and indirect calorimetry, and to prove that the law of conservation of energy holds for the living organism. In 1894 the United States Government began a series of inves- tigations on problems of nutrition. Funds were granted by our government to Professor Atwater, of Wesleyan University, who had been associated with Voit for a number of years, and in 1897 an account of the Atwater-Rosa respiration calorimeter was pub- lished. The respiration apparatus of Pettenkofer and Voit was used in connection with the calorimeter, so that it was possible to de- termine on man the carbon dioxid production together with the actual heat elimination. Later the Carnegie Institute granted a fund to Atwater for the perfection of the apparatus, and in 1905 the Atwater-Benedict BASAL METABOLIC RATE 13 respiration calorimeter for the simultaneous determination of the heat elimination, carbon dioxid production, and oxygen absorp- tion of a subject was completed. The accurate measurement of the oxygen absorption was an important improvement, for it was now possible to apportion accurately the quantity of oxygen used for the combustion of protein, fat, and carbohydrate if, in addition, the urinary nitrogen were determined. As a result of another generous grant of funds from the Carnegie Institute the Carnegie Nutrition Laboratory was built in Boston, and Professor Francis G. Benedict, then of Wesleyan University, was placed in charge. Under his direction careful investigations have been made of the accuracy of the various types of respiration apparatus, 14 ' 29 and the respiration calorimeter was improved still further. Moreover, many fundamental problems in nutrition have been worked out in this laboratory in the greatest detail and with the highest degree of accuracy. The studies on prolonged fasting 11 and on restricted diet, 21 the investigations on the metabolism of normal persons, 15 ' 19 of infants, 25 and of diabetics 20 are particularly valuable. Professor Graham Lusk, with the aid of Dr. H. B. Williams, in 1912 constructed a small respiration calorimeter at Cornell Medical College for the investigation on dogs (and on infants) of various metabolic problems. The results of this work were pub- lished by Lusk and his co-workers in a series of papers on Animal Calorimetry. 53 This great contribution by Lusk has done much to clear up many fundamental problems and to stimulate and direct along definite lines further researches on metabolism. Lusk and Du Bois and their co-workers in 1915 began the publi- cation of a series of papers on Clinical Calorimetry, 54 having con- structed, through funds from the Russell Sage Institute of Path- ology, a respiration calorimeter at Belle vue Hospital, New York, with Dr. Eugene Du Bois as medical director. 67 In these papers 14 BASAL METABOLIC RATE they showed definitely the close agreement between direct and in- direct calorimetry in the normal as well as in all the pathologic conditions investigated by them. 2. Normal Standards. A very important contribution was made by Du Bois in determining the heat production in normal con- trols. Rubner 69 had suggested that the heat production of an in- dividual was proportional to his surface area. For the determina- tion of the surface area Meeh proposed the formula : Surface area (sq. cm.) = 12.3 (a constant) X weight (gm.) 5 However, using the surface area obtained by this formula as a basis of comparison, the heat production of normal controls still showed quite wide variations, although not as great as when compared on the basis of weight alone. By exact measurements of the surface area of several bodies Du Bois demonstrated an error in the above formula due in greater part to the fact that the height of the sub- ject was neglected. 34 ' 40 As a result of further studies Eugene F. Du Bois and Delafield Du Bois 35 ' 70 devised a formula based on height and weight by means of which the surface area can be calculated with an average error of 1.7 per cent. This formula is A = W- 425 X HO-725 X 71.84 where A is the surface area in square centimeters, W is the weight in kilograms, and H is the height in centimeters, and 71.84 is a con- stant. On the basis of this formula they 34 then constructed a height- weight chart by means of which the surface area can be estimated at a glance. Du Bois, using this new height-weight chart for the determination of the surface area in conjunction with his standards of normal basal metabolism for age and sex, 4 ' 36> 40 ' 63 further showed that the metabolism of normal persons could be predicted with an accuracy of =*= 10 per cent. This fact has been confirmed both by Means and by Boothby. Benedict has severely criticized the method of predicting the heat NORMAL STANDARDS production from the unit of surface area, maintaining u that the metabolism or heat output of the human body even at rest does not depend on Newton's law of cooling and, therefore, is not pro- portional to the body surface." 8 Harris and Benedict in a very exhaustive treatise have reconsidered the entire problem of the pre- diction of the normal basal metabolic rate, and show that by proper biometric formulas, based on stature, body weight, sex, and age (the same factors as used by Du Bois), "results as good as or better than those obtainable from the constant of basal metabolism per square meter of body surface can be obtained by biometric formulas in- volving no assumption concerning the derivation of surface area, but based on direct physical measurements." Since their publica- tion we have not had time to study in detail the accuracy of the two methods of prediction. We have, however, tabulated 404 deter- minations of the basal metabolic rate expressed in percentages above and below normal, using both the standards of Du Bois and of Harris and Benedict. The average rates of all the cases show that the rates obtained by Harris and Benedict's method are 6.5 points higher than those obtained by Du Bois' method. The par- allelism between the results obtained by the two methods is strik- ingly shown in Table 1, in which it is seen that 195 of the 404 de- terminations are within ="=2.5 of the average variation. Only 52 TABLE 1. COMPARISON OF METABOLIC RATES OBTAINED BY HARRIS 1 AND BENEDICT'S METHOD WITH THOSE OBTAINED BY DU BOIS 1 METHOD Difference between Harris 1 and Benedict's rates from Du Bois' rates as standard Number of determinations for each range -10 to -6 - 5 to -1 to +3 + 4 to +9 +10 to +14 +15 to +19 +20 to +25 3 20 88 195* 69 24 5 Average of 404 determinations +6.5 within 2.5 of this average 1 6 BASAL METABOLIC RATE of the entire 404 rates deviate more than 7.5 from the average variation. The comparative agreement, therefore, of the two methods is very satisfactory, indicating as it does the similarity of both methods of comparison, and supporting in a large propor- tion of the cases the clinical conclusions based on the Du Bois and Du Bois height-weight chart and the Du Bois normal standards for comparison. The fact that the metabolic rate decreases with progressive inanition, as in Benedict's thirty-day fasting man, and in prolonged restricted diet is, in our opinion, an argument in favor of the clinical value of a knowledge of the heat production. The conditions cited by Benedict are abnormal and the data presented both from the metabolic and clinical viewpoint substantiate observations (not yet published) made by us that a decrease in the metabolic rate occurs in certain types of undernutrition. Such conditions cannot be considered normal either by the clinician or the physiologist, and therefore cannot be rightly used as an argument against the validity of a proposed standard of normality. Nevertheless, Benedict's 13 statement that "There is no inflex- ible standard for normal metabolism for any given age, weight, height, and sex, from which all normal individuals never vary," is true. It would also be true if applied to other physiologic data of clinical value commonly determined, such as the temperature, 15 the systolic and diastolic blood-pressure, the pulse-rate, the acuity of hearing and vision, and the like. For instance, in the evalua- tion of the temperature clinicians are rarely concerned by variable readings between 97 and 99 F. Yet, they properly consider an elevation above 99 F. as indicative of febrile disease, usually of a bacterial character, in spite of the fact that occasionally normal and healthy people have temperatures, under certain conditions, of over 99 F. During the past three years we have made more than 10,000 CLINICAL CALORIMETRY 17 metabolic rate determinations both on healthy people and on patients suffering from various diseases. Our results will be re- ported in detail elsewhere, but it is in place here to state that only occasionally have we found patients who had metabolic rates be- yond the normal limits established by Du Bois which could not be accounted for by the presence of a definite pathologic condition. Furthermore, we are convinced that certain pathologic conditions always produce characteristic variations in the metabolic rate and, in addition, that there is a much larger group of diseases in which there is no abnormal variation in the heat production, just as there are many diseases which have a normal temperature. We con- sider, therefore, that the metabolic rate differentiates with exact- ness three clinically characteristic groups of cases: (1) those with increased rates, (2) those with normal rates, and (3) those with de- creased metabolic rates, just as surely and just as definitely as the thermometer divides diseases into the febrile and afebrile groups. 3. Clinical Calorimetry. As a result of the work briefly out- lined above the extended use of indirect calorimetry in clinical practice has been rendered feasible. In the clinic of Profes- sor Edsall, at the Massachusetts General Hospital in Boston, Means and his associates, 31 ' 44j 57 > 58 > 59j 60 using Benedict's unit ap- paratus, investigated the metabolism in various pathologic condi- tions and in normal controls. At the Peter Bent Brigham Hospital, Boston, in the clinic of Professor Harvey Gushing, metabolism studies were begun in 1914 by Boothby and Sandiford, using the gasometer method originally introduced by Tissot in 1904. Both normal and various pathologic conditions were studied, 27 but most important were the investigations of the metabolic findings in dis- orders of the pituitary gland, publication of which has been delayed by the war. In March, 1917 a metabolism laboratory was opened at the Mayo Clinic by Boothby and Sandiford under the clinical direction 1 8 BASAL METABOLIC RATE of Professor Henry S. Plummer. In the treatment of the large number of thyroid cases seen at the clinic our results have definitely shown how essential is the knowledge of the basal metabolic rate in pathologic conditions of the thyroid. It is as essential as a knowl- edge of the temperature in febrile cases. With the wide-spread recognition of the importance of the basal metabolic rate in thyroid disorders it seems advisable, for the benefit of the clinician and surgeon, to give briefly a description of the methods of direct and indirect calorimetry, of the various kinds of apparatus used in indirect calorimetry, and finally to give in detail a description of the apparatus and technic used in our laboratory for the routine determination of the basal metabolic rate. 4. Direct and Indirect Calorimetry. The Respiration Calorim- eter. In the combined method of direct and indirect calorimetry the production and elimination of heat are determined by means of a respiration calorimeter 54 which may be denned as "an appa- ratus designed for the measurement of the gaseous exchange be- tween a living organism and the atmosphere which surrounds it and the simultaneous measurement of the quantity of heat pro- duced by that organism." 55 A complete respiration calorimeter, therefore, combines within one apparatus two separate and entirely distinct methods : the one determining the heat production and the other, the heat elimination, thus allowing a comparison of the two principles. Heat is eliminated from the body in two ways : first, by evapora- tion of water from the lungs and skin, and second, by radiation and conduction. The amount of water of evaporation is deter- mined by passing the air in the calorimeter, in which the subject is at rest, through weighed sulphuric acid the gain in weight of the acid is the weight of this water. Since 1 gram of vaporized water contains as latent heat 0.586 cal., the gain in weight of the sulphuric acid multiplied by this factor is the amount of heat lost DIRECT AND INDIRECT CALORIMETRY 19 by evaporation of water approximately one-fourth of the total heat elimination. The calorimeter itself measures the heat given off from the body by radiation and conduction. The apparatus is so constructed that there is no heat loss through the walls of the calorimeter, and consequently, to prevent the temperature within the chamber from rising to that of the body, a continuous stream of water is kept circulating through copper pipes within the calorimeter; by this means the heat eliminated from the body by radiation and conduc- tion is removed and its amount calculated by multiplying the total quantity of water passed through the calorimeter during the test by the difference in temperature (measured to 0.01 C. by electric resistance thermometers) between the outgoing and the incoming streams of water. The heat thus calculated is subject to correc- tion, however, if the temperature of the subject changes during the test, or if the temperature of the wall of the calorimeter varies. The measurement by the calorimeter of the heat eliminated by radiation and conduction together with the measurement of the heat eliminated by evaporation of water from the lungs and skin constitutes the method of direct calorimetry. In connection with the calorimeter a respiration apparatus of the Benedict "unit," 6 or closed-circuit type (more fully described below), is used to determine the respiratory exchange, that is, the oxygen absorbed and the carbon dioxid produced by the subject in a known time. From these two factors, together with the amount of nitrogen eliminated in the urine, it is possible to calculate not only the heat production but also to apportion the amount of oxygen used for the burning of protein, fat, and carbohydrate in the body. This is the method of indirect calorimetry. The respiration calorimeter requires the full attention of at least three skilled observers, and with the constant repair and check- ing of the apparatus and the long preliminary and experimental 20 BASAL METABOLIC RATE periods each of at least one hour's duration it can readily be seen that the combined method of direct and indirect calorimetry is quite beyond extensive clinical use, and, moreover, of the two methods, the indirect is to be preferred, since it is less complicated than the direct. It was necessary, however, first to determine the agreement between the two methods in normal and in pathologic conditions before indirect calorimetry could be used to measure heat production. 5. Agreement of Direct and Indirect Calorimetry. Rubner showed the agreement between direct and indirect calorimetry on dogs for long periods and Lusk 53 for short hourly periods; Atwater and Benedict demonstrated this for man at rest and at woik, and Rowland for babies both normal and atrophic. Lusk and Du Bois 54 have shown the close agreement between the two methods in normal and in all pathologic conditions investigated by them, and have pointed out the difficulties involved in the direct method and of the comparative simplicity of the indirect. Gephart and Du Bois 39 con- clude that, because of the many possible sources of error in direct calorimetry, especially in short or isolated experiments, "it is more desirable to use the method of indirect calorimetry as the standard, and to check its accuracy by the level of the respiratory quotient and the agreement with the direct calorimetry." 6. Indirect Calorimetry. Krogh, of Copenhagen, and Car- penter, of the Carnegie Nutrition Laboratory, have described and compared in great detail the various kinds of respiration apparatus used in indirect calorimetry. Carpenter has shown that for indirect determinations two types of apparatus are suitable the closed circuit and the gasometer. (a) Unit Apparatus. By far the best apparatus of the closed- circuit type is the Benedict unit apparatus. 6 By means of a mask, mouth-, or nose-piece the subject rebreathes air from a closed system in which the carbon dioxid produced is absorbed by soda lime, and INDIRECT CALORIMETRY 21 as the oxygen is consumed it is replaced by oxygen in known amounts. The air within the apparatus is kept in constant circula- tion by means of a blower. A small spirometer is inserted in the circuit as an expansion chamber and records volumetrically on a smoked drum the respiratory movements. Knowing the weights of oxygen used and carbon dioxid produced, one can readily cal- culate the heat production. As pointed out by Carpenter, this apparatus is very satisfactory and, indeed, the best for many pur- poses, especially when used in conjunction with a calorimeter or with the "cot-chamber calorimeter" described by Benedict and Tompkins. We have found, however, that for clinical work the unit apparatus is rather cumbersome. It requires constant checking to see that it is absolutely air tight, for a leak even of a few cubic centimeters either in the apparatus or in the adjustment of the mask, during a fifteen-minute determination, will appreciably affect the result, because such a leak in this type of apparatus will be equivalent to the loss of so much oxygen and not equivalent to the loss of so much air, as is the case in the gasometer method, thus magnifying the error five times. Furthermore, the accumula- tive errors of the apparatus fall on the oxygen and not on the car- bon dioxid determination, thus causing errors in the calculation of the respiratory quotient and heat production. The absorbing chemicals must be changed frequently, and with the repairing and constant checking of the apparatus it is, on the whole, difficult to use in clinical work, particularly if many determinations are to be made. (b) Portable Unit Apparatus. The portable respiration ap- paratus recently devised by Benedict 12 ' 13) 21 for clinical work is a modification of his unit apparatus described above. It is designed primarily to give a rapid and at the same time a comparatively accurate measurement of the oxygen consumption without involv- ing analyses or weighing. We have not adopted this apparatus for 22 BASAL METABOLIC RATE routine work, as we prefer to determine with greater accuracy not only the oxygen consumption but also the carbon dioxid elim- ination, since the heat production can thereby be more exactly cal- culated. Moreover, the difficulties inherent in the closed-circuit type of apparatus mentioned above are still present in the portable unit. In addition, in the early models there is the danger of the oxygen-rich mixture catching on fire, which, although it may not injure the patient, is at least disconcerting. The chief objection to the apparatus for clinical work is the fact that it cannot be cleaned and the patient is exposed to the serious danger of infection by rebrea thing contaminated air. (c) Gasometer. For clinical work the gasometer method in- troduced by Tissot in 1904 is considered by us the most satisfactory. Briefly, the determinations are made in the following manner: A mask is tightly adjusted over the patient's mouth and nose and, by means of expiratory and inspiratory valves, the total volume of the patient's expired air is collected in a gasometer for a known period of approximately ten minutes. Duplicate determinations are made of the carbon dioxid and oxygen content of the expired air, the analyses being done in the Haldane gas analysis apparatus. Since the ventilation rate for each minute is known and the per- centages of carbon dioxid produced and oxygen absorbed, it is pos- sible to calculate by means of calorie tables the total calories pro- duced each hour. The gasometer method is particularly suitable for clinical work because each step in the procedure can be checked by a second assistant, reducing to a minimum the chance of technical errors. Unlike in the work with the closed-circuit apparatus, no appre- ciable error is introduced by failing either to start or to stop the experimental period at exactly the end of a normal respiration, a difficult thing to do with accuracy in the case of patients who breathe irregularly. Furthermore, the air inspired by the patient INDIRECT CALORIMETRY 23 is fresh, clean air and not the exhalations of previous patients, as in the closed-circuit type of apparatus. Moreover, all parts of the apparatus that come in contact with the patient or with the air that he breathes can be thoroughly cleaned. Although the method requires care and accuracy in every part of the procedure, it is pos- sible to teach the technic to laboratory workers who have had no preliminary scientific training other than that obtained in high school. The most difficult step in the procedure is the analysis of the expired air. This, however, we have found to be inconsiderable. Our assistants can obtain routinely duplicate analyses agreeing within 0.04 per cent, for carbon dioxid and 0.06 per cent, for oxygen, and they are able also to take entire care of their gas analysis apparatus. The equipment necessary for this method is simple and inexpensive, and if properly constructed is rarely out of order and, except for cleaning, requires very little mechanical care. Fur- thermore, the apparatus is free from the many mechanical difficulties inevitably inherent in a closed-circuit system in which the air cur- rent is driven by an electric pump. In the metabolism laboratory at the Mayo Clinic we have done more than 12,000 tests and are now averaging 32 cases a day, and have developed a very definite and routine procedure which has decreased the probability of a technical error occurring in less than 1 per cent, of the tests. SECTION II DETAILS OF TECHNIC A. THE PATIENT 1. Postabsorptive Condition. Since the time of Lavoisier the influence of food on the metabolic processes has been recognized. In a series of investigations on food ingestion Benedict and Car- penter 16 conclude "that the ingestion of all kinds of food in any amount results in an increment in the metabolism." The mechan- ical work of chewing and even the drinking of liquids, especially in large amounts, increase the metabolism, although the increases are small. Lusk found that in man the increase in heat production after a large protein meal amounted to 46 per cent, and the effect did not disappear for about twelve hours; with carbohydrate and fat the result was less striking, but a rise of 20 per cent, was not uncommon. Soderstrom, Barr, and Du Bois studied the effect on the metabolism of a small breakfast of bread, coffee, milk, and sugar, totaling 222 cal., and showed that there was an average increase of 7 per cent, in the first hour after such a breakfast, and in the second and third hours, 2 per cent. In other words, the effect was small and of short duration. Benedict, however, rightly insists that the subject should be in the so-called "postabsorptive" state when absorption of material from the alimentary tract has ceased, this being with adults generally twelve hours after the last meal. For this reason we require all our patients to go without breakfast and caution them not to eat heartily the night before the test. 2. Muscular Activity. Much of the earlier work on metabolism was vitiated because the subjects were not quiet during the test. 24 PRELIMINARY REST PERIOD 25 Benedict and Carpenter 15 have repeatedly emphasized the impor- tance of complete muscular repose, and, in fact, they use a recording device to obtain graphic records of the degree of activity of the subject. For a time we made use of similar graphic records, but have found it more satisfactory to have one of our laboratory assistants with the patient to record any body movements and to evaluate their significance at the time of the observation instead of attempting later to interpret a tracing. 3. Preliminary Rest Period. Benedict and Carpenter 16 advise, furthermore, that there should be a preliminary rest period of at least thirty minutes or preferably longer, so that one may be cer- tain that the basal level has been reached. We require a prelim- inary rest period of at least twenty minutes before the mask is adjusted. It is obviously desirable when many cases are being studied to make this rest period as short as possible and yet of sufficient length to obtain the basal rate. With this point in view we have studied 44 cases in which the metabolic rate was deter- mined after varying preliminary periods of rest. The data are summarized in Tables 2 and 3. It will be seen that in these 44 cases there is no material difference in the average metabolic rate produced by the prolongation of the preliminary rest period beyond twenty minutes. Sixteen of the patients showed a decrease in the metabolic rate as a result of resting over one-half hour; 7 cases showed no change, and 21 cases showed not a decrease but an increase in the metabolic rate by prolonging the rest period, pos- sibly due to the tendency of certain patients to be annoyed and irritated by the delay. Du Bois also found "a distinct tendency for the patient to become more restless as the observation progresses," 37 and showed that the metabolism is usually higher in the second hour than in the first. In another group of 20 cases we determined the metabolic rate directly the patient went to bed, and then made a second determi- 26 BASAL METABOLIC RATE nation after the patient had been resting quietly for at least twenty minutes. The average metabolic rate of these 20 cases determined I (V J Jed o Jed uj) jnoq jed pof Jed aed ^.ueo aed potasd xeg > o fe o: o M S Q <: o s^ s (V JO ^ueo aed uj) T TOqq.9W S I* t, m o> ) tfj O O 4l>CiCi)C) t 1 t I 1 * *-lf4.4 #4 (- t- c~-t-OrOrH co coco o> =* mn o coococo co o> -s| co O o CO 00 Tj< Tf 00 M r- c>J CMW N W H|f>4 Ct C 33 34 BASAL METABOLIC RATE misreading of the latter. When the mask is on, a complete record of the patient's mental and physical condition is kept, as ^ell as of the pulse and respiration rates. Thus the observer notes whether the patient is quiet, records any movements, whether slight or marked, and whether the patient was apparently asleep or nervous and worried. At the end of the test the patient's height (bare feet) in centimeters and weight (without clothing) in kilograms are recorded and checked. 9. Repetition of Test. The necessity for a repetition of the test is dependent on two distinct considerations the avoidance of technical laboratory mistakes and the elimination of physiologic errors. Laboratory errors are best detected and avoided by doing two complete determinations each time the patient comes to the labora- tory until the laboratory routine has become so perfected that material variations in the results of the duplicate tests do not occur. Physiologically, however, in an extremely nervous person a basal rate occasionally cannot be obtained the first time the patient comes to the laboratory. In order to rule out the effect of nervous- ness or temporary slight indisposition the patient is instructed to return the following morning for a second test, instead of repeating the determination on the same day. In such instances the meta- bolic rate will occasionally be as much as 10 points lower than that obtained at the first test when the patient was unduly nervous and frightened about an unknown procedure, often aggravated by rest- lessness during the preceding night. A check reading is particularly important in those patients who have, on their preliminary tests, metabolic rates between +10 and +20 per cent, because slight errors in this range have a greater relative significance, and there- fore even the slight effect of nervousness must be ruled out. In conclusion it must be said that it is essential to secure the co- operation of the patients for correct metabolic rates, and one must MASK 35 impress on them the necessity of lying absolutely quiet by explaining that muscular movement increases the metabolism and so renders their test inaccurate. B. THE GASOMETER AND ACCESSORY APPARATUS* 1. Mask. Hendry, Carpenter, and Emmes have shown that the oxygen consumption is practically the same regardless of the breathing appliance used. We have found, however, that in clin- ical work the patients object strenuously to the mouth-piece, and furthermore, that it requires intelligent co-operation on their part to introduce it correctly and to keep it air-tight throughout the observation. Once the mouth-piece is in place there is a tendency to excess saliva, the drooling of which is most disagreeable. A gas mask (Fig. 1) of the type used for mine rescue work is much more satisfactory. The mask is made of rubber fitted over a flex- ible metal framework, so that it is possible to mold it to the shape of the individual face. The face-piece has a pneumatic rim around its edge, but it is much safer not to inflate it, for the air valve attached to the rim tends to leak, thus altering the pressure of the mask against the face, with the consequent result that it may not be air-tight. The mask should be fitted to the patient's face and held securely in place by means of tapes tied in various positions across the mask. For convenience twelve tapes are sewed on each side of a narrow towel which is about 6 inches wide and 18 inches long. The towel is placed on the pillow under the patient's head and the various tapes can be used to tie the face-piece securely without disturbing the patient. One pair of tapes is tied over the mask at the nose and another pair around the chin (Fig. 2). Two pairs of tapes are then tied crosswise over the mask, a pair over the nose, and a final pair * The entire apparatus may be obtained from H. N. Elmer, 1135 Monad- nock Building, Chicago, 111. BASAL METABOLIC RATE Expiratory valves C orvrve c "bi on, s Mask/" Towel u/itH tapS--j Fig. 1. Mask and connections showing valves and intake pipe. around the chin (Fig. 3). The most frequent source of leaks is around the nose and at either of the two corners of the mask, and MASK 37 extreme care must be taken to avoid them. Smearing the face with vaselin is, however, unnecessary. The mask and connections are kept clean by washing thor- oughly with soap and water and finally by rinsing with bichlorid solution (1 : 1000). The mask itself should be frequently tested Fig. 2. Mask with two pairs of tapes adjusted. for tightness. To do this rubber corks are inserted in the connec- tions and both face-piece and connections are then completely filled with water and allowed to stand one-half hour. It will be found that the mask usually gives way first at the nose. 2. Valves. Carpenter has given an excellent discussion of the various types of air valves and of their relative efficiency. Up to 38 BASAL METABOLIC RATE the present time we have preferred the Douglas valves with mica flaps, although, as Carpenter has shown, they may have an effi- ciency of only 75 per cent. We overcome this defect by using two of these valves on the inspiratory side at about 2 feet distant from the mask and one valve on the expiratory side (Fig. 1). With this Fig. 3. Mask with six pairs of tapes adjusted. arrangement the loss of any expired air can be completely avoided, because if a slight leak in the valves should occur the expired air would pass back a short distance into the inspiratory tubes, but would not reach the double inspiratory valves; this expired air would be rebreathed on the next inspiration and, therefore, would not be lost. There is very little resistance from these valves to the VALVES 39 passage of air, so that they cause no respiratory discomfort to the patient, and they are, moreover, sufficiently large to take care of any volume of air that a patient breathes, even under conditions of Fig. 4. Rubber flutter valve assembled. extreme muscular exertion. A distinct improvement has been made recently in the Douglas valve by the substitution of a rubber in place of a mica flap. By far the most efficient air valve is the rubber flutter valve 40 BASAL METABOLIC RATE devised by the British during the war for use on the antigas masks. Fig. 5. Various parts of rubber flutter valve. The valve offers very slight and negligible resistance to the passage of air and yet is absolutely tight, as proved repeatedly by the fact INTAKE PIPE 41 that the men were able to stay without any danger in extremely high concentrations of the most deadly gases when the slightest leak would have been fatal. As used on the British and American gas masks the valve opened into the atmosphere. To adapt the valve to our work necessitated the construction of a metal air- tight container suitably designed to insert in the air circuit (Figs. 4 and 5). 3. Intake Pipe. -(a) Outdoor Air. With the stationary gas- ometers in the laboratory the two inspiratory valves are mounted on a large intake pipe (Fig. 1) about 2 inches in diameter which leads out of doors so that the subject inspires outdoor air which has a known constant composition: 0.04 per cent, carbon dioxid and 20.93 per cent, oxygen (page 78). The intake pipe can easily be put up in any laboratory and, if possible, should always be used. (b) Room Air. The air in patients' rooms in one of the Roch- ester Hospitals varied on analysis between 0.04 per cent, carbon dioxid and 20.93 per cent, oxygen to 0.34 per cent, carbon dioxid and 20.70 per cent, oxygen; the average of 100 determinations of the air from different rooms was 0.11 per cent, carbon dioxid and 20.84 per cent, oxygen. In case room air of this average composi- tion is used and no correction made for it in the calculations the resulting metabolic rate will be too high by 3 to 6 points; if there is more than 0.30 per cent, of carbon dioxid with a corresponding decrease in the oxygen content the error in the metabolic rate may be as high as 16 points. On the other hand, analyses of the room air made before and after opening the window wide show that three to five minutes is sufficient to render the composition of the room air within 0.02 per cent, of that of out-door air, a neglect of which will produce no appreciable error in the calculated metabolic rate. With the movable gasometer it is more convenient in routine work to air the room by opening the window wide from three to five 42 BASAL METABOLIC RATE minutes during the preliminary period than to carry an extra long inspiratory tube that will reach out-doors. When using room air the inspiratory tube consists of corrugated tubing, 2 or 3 feet long, with double inspiratory valves; the tubing is hung over the top of the bed so that the valves are upright. It must be remembered that variations in the metabolic rate of 3 or 4 points cannot be con- sidered significant unless either out-door air has been used or con- trol analyses made of the composition of the room air at the site of the opening of the inspiratory tube at the time of the test. 4. Connections are made from the valves to the mask by corru- gated tubing (Fig. 1) which does not tend to collapse or kink and thus cut off the air supply to the patient. They are made sufficiently long to meet the needed requirements by joining various lengths of the corrugated tubing by brass connections. With the movable gasometer the connections are long enough so that the apparatus during a test may be stationed just outside the patient's room. When using a long connecting tube additional time is necessary to wash out the increased dead space with the expired air (page 51). The tubing must be carefully watched for leaks, because the car- bon dioxid of the expired air tends to rot the rubber. To do this the tubes should be filled with water and hung up for ten minutes. A leak in the tubing will allow the water to trickle through on to the dry outer linen covering and so is readily detected. 5. Gasometer. The gasometer method of determining the respiratory exchange was introduced by Tissot in 1904, and has been extensively used in French and in American laboratories. A complete description of the original apparatus and the technic used in Chauveau's laboratory is given by Carpenter. Although the fundamental principles of the Tissot spirometer have not been changed, a few alterations in detail render the form of apparatus used by us more convenient for clinical use. Figures 6, 7, and 9 illustrate the design of our apparatus as perfected by GASOMETER 43 _ - -T h, er m om eter Rubbev stoppev Sampling pet To room, Outer* wall oj" water ssal ,Y Patieut to room a,i,T' patieut Patiervt to gasorrueber Drainage pet-cock.--' Fig. .6 Cross-section of gasometer . Fig. 7. Stationary gasometer. 44 GASOMETER 45 Mr. George Little of the clinic instrument shop. The gasometers Fig. 8. Gasometer room. in the laboratory are stationary and, in addition, we have a gasom- eter mounted on wheels and of slightly smaller capacity (Fig. 9) Fig. 9. Movable gasometer." GASOMETER 47 With this movable apparatus it is possible to test the patients in their rooms, which is of considerable advantage. The gasometer (Figs. 6, 7, 9) consists of a thin copper bell, of approximately 125 liters capacity, suspended in a water-bath be- tween double walls of a hollow cylinder which is closed at the top, except for the inlet and outlet tubes. The counterpoise of the bell is hung over ball-bearing wheels by means of steel piano wire. The main weight of the bell is balanced by a long, hollow brass tube (counterpoise tube) on the lower end of which are placed the necessary lead weights to counterbalance the bell exactly. To compensate for the increase in weight of the gasometer bell as it. rises out of the water seal a quantity of water equal to the increase in the weight of the bell siphons from a small reservoir into the hollow counterpoise tube. When the lead weights are on the coun- terpoise tube the bell is in perfect equilibrium at any point in its course, so that when the valve C (Fig. 6) is opened to room air the bell will not change its position. One of the lead weights (the balancing weight) is removable, and when it is not on the counter- poise tube the bell will gradually drop if the valve C is opened to room air. Whenever readings are taken of the volume of the gasometer this weight must be on the counterpoise tube. For the purpose of sampling, however, the weight is removed and the bell allowed to drop by opening valve C until about half the volume of air collected has escaped, thus washing the sampling connections with the expired air. An extra weight (the negative pressure weight) of approximately 300 gm. is placed on the counterpoise tube after the preliminary readings are taken and just before the test is started. This causes a slight negative pressure between the gasometer and the patient and so overcomes the resistance of the air passing through tubes. The position of the bell is determined by means of two fixed steel pointers reading against a steel tape attached to the counter- 48 BASAL METABOLIC RATE poise tube. The object of the two pointers is to give two readings of the position of the bell, both at the start and at the end of the test, thus giving an excellent check on the readings of the difference in the position of the bell at the beginning and at the end of the experiment. The use of the steel tape attached to the counterpoise tube for reading is preferable to a fixed scale with a movable pointer attached to the bell itself (as is the arrangement on the Tissot spirometer), for a slight swing or tip of the bell might make a dis- tinct change in the level of the pointer, and consequently result in incorrect reading of the volume of air. To obtain the temperature of the air in the bell a thermometer is inserted through a rubber stopper in the top of the float. The thermometer projects about 4 inches inside the bell, and it is so placed that when the bell is completely down resting on the top of the inner copper cylinder the thermometer fits into the air inlet tube. The thermometer is graduated to one-fifth of a degree Cen- tigrade. Separate outlet and inlet tubes are arranged on the gasometer as indicated in Fig. 6. The valves are arranged as follows: On the inlet tube leading from the patient to the gasometer there is a three-way valve which when set in position B closes the gasometer and allows the expired air from the patient to escape into the room ; when set in position A the former opening is closed and the expired air passes into the gasometer. When the three-way valve on the outlet tube is put in position C the gasometer is open to room air; when in position D, the gasometer will be closed if the sampling pet-cock is closed; the latter is open only while taking a sample of air. On the portable apparatus a two-way valve is used at C and the sampling pet-cock is inserted directly into the outlet tube below the valve. The water seal is kept at the level indicated in Fig. 6. It never covers the incline of the inner cylinder, consequently the expired CALIBRATION OF GASOMETER 49 air is not exposed to a large surface of water, since there might be an appreciable loss of carbon dioxid by water absorption. The level of the water seal drops as the bell rises ; this introduces a very small and negligible error in the readings. The water in the tank need be changed only occasionally, for the copper salts from the walls of the gasometer prevent bacterial growth. To test the bell for tightness the outlet and inlet valves are closed with the bell counterpoised. The bell is put under a fairly heavy positive pressure by placing a weight of 2 kg. on the top of it. Readings are then taken of the gasometer volume and its tempera- ture, also the barometer reading. At the end of half an hour, if no changes have occurred either in the temperature or in the barom- eter, the gasometer volume should be unchanged. We are care- ful to test our gasometers frequently, and have found that when- ever leaks occurred they could always be traced to faulty greasing of the outlet or inlet valves. 6. Barometer. In all volumetric work with gases it is necessary to reduce the observed volume of the gas from the experimental temperature and pressure to the standard temperature C. and the standard barometric pressure of 760 mm. dry. A good barom- eter,* such as supplied to the United States Weather Bureau for ordinary observatory work, is necessary. This barometer should have a metric scale with a vernier reading to tenths of a millimeter, and a thermometer graduated in degrees Centigrade. 7. Calibration of Gasometer. The gasometer readings are made on a steel tape, fixed on the counterpoise tube. The tape is grad- uated to 0.10 cm. and is read by means of stationary markers to 0.05 cm. It is, therefore, necessary to determine the factor of the gasometer in order to convert the linear rise of the bell into a unit of volume. This factor is derived in the following manner: The *A suitable barometer may be obtained from Henry J. Green Co., 1911 Bedford Avenue, Brooklyn. N. Y., Catalogue: No. 1. 50 BASAL METABOLIC RATE bell of the gasometer is a cylinder, and the circumfeience of it is determined by measurement at several points from top to bottom, either with the bell in position or removed entirely from the gas- ometer. On our gasometer A the following measurements of the circumference were taken with the bell in position: Reading on tape, Circumference of bell, cm. cm. 97 126.0 87 126.0 72 125.9 59 125.9 45 125.8 33 125.8 17 125.8 9.. ..125.8 Average. 125.9 Since the radius of a circle = ^~ X the circumference, then the radius to the outside of the wall of the bell = 2 * U16 X 125.9 = 20.038 cm. The radius to the inside of the bell is, therefore, equal to 20.038 cm. minus the thickness of the copper wall as de- termined by calipers. This radius of the inside of the bell is, there- fore, 20.038 cm. - 0.046 cm. = 19.992 cm. Since the area of a circle equals TtR 2 , then 3.1416 X 19.992 2 cm. = 1256 sq. cm. Therefore, the capacity of the bell corresponding to a rise of 1 cm. measured by the tape will be equal to 1 cm. X 1256 sq. cm. = 1256 c.c. or 1.256 1., the factor of the gasometer. We read the centimeter scale to the nearest half-millimeter corresponding to a change in volume of 63 c.c. 8. Collection of Expired Air in Gasometer. The gasometer bell is dropped to the bottom of the tank by removing the balancing weight and opening valve C, thus forcing out all the air save what is left in the dead space at the top of the tank and in the connecting pipes. When the patient has rested sufficiently to start the test, the mask is tied on with one pair of tapes around the upper part of COLLECTION OF EXPIRED AIR IN GASOMETER 51 the mask and a second pair over the chin. One of the assistants then turns the gasometer inlet valve so that the expired air passes into the tank. While the remaining four tapes are being tied the patient is filling the gasometer and the connections with his expired air. When the gasometer bell has risen to 6 cm. on the tape the valve C (Fig. 6) is opened and the bell dropped to the bottom with- out turning the patient off from the machine. Valve C is then closed and the gasometer filled with expired air to a volume corre- sponding to 3 cm. on the tape. Valve B is then turned so that the patient breathes into room air. Valve C is opened and the gas- ometer allowed to drop to about 1.50 on the tape, so that a small air cushion of the patient's expired air is left at the top of the inner tank. The bell should not be lowered so far that it rests on the inner copper cylinder, as its equilibrium is thereby disturbed. The balancing weight is replaced on the counterpoise tube. The po- sition of the bell at the start of the test is taken by reading the level of the two pointers on the steel tape. These readings are recorded to the nearest 0.05 cm., and then the negative pressure weight is added to the counterpoise tube. The inlet valve is quickly turned, so that the patient is once more breathing into the gasometer, and at the same instant the stop-watch is started and the time independently recorded by the observer sitting with the patient. At the end of approximately ten minutes the inlet valve is turned off from the patient, the stop-watch stopped, and the time recorded by the observer. While the mask is removed by the observer, the other assistant removes the negative pressure weight from the counterpoise tube, makes the two final readings on the tape to the nearest 0.05 cm., records the temperature of the gasometer to the nearest half-degree Centigrade, and finally the barometer to the nearest millimeter. All the readings mentioned are checked by the observer. If the differences in the two sets of readings of the position of the bell at the beginning and at the end 52 BASAL METABOLIC RATE of the experiment do not agree, the test is repeated. Likewise, if the duration of the test noted by the observer using an ordinary Ingersoll watch does not agree within five seconds of the time on the stop-watch, the test is repeated. The object of the additional time determination by the observer is to prevent gross misreadings of the stop-watch. The balancing weight on the counterpoise tube is then taken off and the outlet valve C and sampling pet-cock opened to room air to wash the connections with the expired air. The gasometer is allowed to drop about one-half its volume, the outlet valve C is closed, thus shunting the air current through the open sampling pet-cock and so allowing it to be thoroughly washed (Fig. 8). At the end of one minute the four sampling tubes are filled with the expired air. 9. Sampling Tubes. The sampling tubes (Figs. 8, 11) are those described by Krogh and Lindhard. They have a volume of 30 or 35 c.c. with a two-way tap and small bored tip about 4 cm. long above the tap for the purpose of making connections with the gasometer in sampling. A piece of rubber tubing about 15 inches long connects the sampling tube to its mercury reservoir of about 40 c.c. capacity. The sampling tubes are mounted in fours on a rack, and four sam- ples of expired air are always taken for each test; two are analyzed, and this leaves two extra samples in case of accident. The sam- pling tubes are filled to the tip with mercury. In sampling, con- nection is made to the pet-cock on the gasometer by means of heavy walled 3-mm. bore rubber tubing. The tubing is tightly adjusted to the tip of the sampling tube, the mercury reservoir lowered, and the tap on the sampling tube opened. The sampling tube is washed twice with the expired air and the sample collected after the second rinsing. The tap is closed and the mercury reservoir hung up to keep the sample under positive pressure. The tap must be well greased and for this purpose we use a "black rubber" grease, the formula for which is given on page 81. When the sampling tubes STRATIFICATION OF AIR IN GASOMETER 53 become dirty they are cleaned with concentrated nitric acid, rinsed with distilled water, and thoroughly dried. This is sufficient for the purpose, although it will be found that the "etching" that eventually develops on the inside of the tubes cannot be removed. 10. Stratification of Air in Gasometer. On account of the well- known tendency of air to stratify and, therefore, not form a uni- form mixture throughout, doubt has often been expressed as to the possible variation of the percentages of carbon dioxid and oxy- gen at different levels in the gasometer. Carpenter reviewed the existing evidence on this point and, in addition, published a few new experiments. He concluded that the "uniformity in the com- position of the air throughout the spirometer depends on the char- acter of the respiration. . . . When the respiration was quiet and uniform the good agreement of the results indicates that the composition of the expired air was uniform in all parts of the spi- rometer." As the accuracy of the gasometer method depends fundamen- tally on obtaining samples of expired air from the gasometer that represent at least with a negligible error the mean composition of the expired air, we have investigated the question of stratification in considerable detail. The method of procedure was as follows: Samples were taken from the gasometer according to the usual routine described on page 50, with the exception that in addition to the regular sample taken from the middle of the gasometer two additional samples were taken, the one after the bell had been allowed to drop 10 cm. from the top, and the other after the bell had been dropped to within 10 cm. of the bottom. This gave three sets of samples of air collected first from the lower segment of the gasometer, second from the middle segment, and third from the top segment. Analyses were made in duplicate according to our usual custom. Forty-nine experiments were done, in 14 of which no note was made of the length of time elapsing between the collec- 54 BASAL METABOLIC RATE eouoaejjfp e2t3JGAT3 sift -xe jo -OH jo oStMSAB JJ 'B'VTJjq.S STPpTtn jo <0 -9Q 90UGJ9J -JTQ <0 H^> OJ 3 a 8- rf * Crt t-l 5l jo COMPOSITION OF AIR IN GASOMETER 55 tion of the expired air and the sampling; in 10, samples were taken as soon as possible after the collection of the expired air ; in 11, they were taken after a lapse of five minutes, and in 14, after a lapse of ten minutes. A study of the experiments summarized in Table 6 shows that the expired air collected in a gasometer has a tendency to stratify. However, if the samples used for calculating the metabolic rate are taken from the middle of the gasometer, the error caused by such stratification is negligible, especially if a few minutes are allowed to elapse between the collection of the expired air and the taking of the samples in order that the gas mixture may become more uniform by diffusion. Furthermore, the cases given in Table 6 were taken indiscriminately and, therefore, represent with reasonable probability the usual variations in the type of respira- tion that one naturally meets in the course of routine work. We conclude, therefore, that the accidental error that might be intro- duced by the slight stratification that exists in the expired air col- lected in a gasometer does not invalidate the calculation of the metabolic rate, since such changes that are thereby produced fall within the total experimental error of the method. 11. Effect on the Carbon Dioxid and Oxygen Content of the Expired Air from Standing in the Gasometer. It was likewise im- portant to know whether or not variations in the carbon dioxid and oxygen content of expired air collected in a gasometer changed after prolonged standing, as theoretically it might be thought that the water seal of the gasometer might either take up or give off carbon dioxid. Therefore, we carried out 22 experiments in which three hours elapsed between the collection of the first and second samples. A second set of 16 experiments was done in which the samples were collected the next morning, about twenty hours after the collection of the first sample. All of the analyses were done in duplicate, according to our usual routine. The results are summarized in BASAL METABOLIC RATE TABLE 7 % EFFECT ON THE C0 2 AND 2 CONTENT OF EXPIRED AIR FROM STANDING IN GASOME 1 ] ER a/ o i " * K tj S , 3 2 Q V. g s V "SS2 . ^ -g ^ 00 OJ ^J Vi O VH r-4 C bO fc. TJ bO a R a 2 %, a TS > o ts JB -H o . .-1 t, O t O +> U C SJ - t! So n 1 fc a fet t-t O Q, ^, +a o t4 J5 - tH P. 4* 5 o> |o> -p b w* c . w oho *> H rH S Ir3 CO C-'-v D 3 o m o rH (-* oj O CO O4 ^ J> CQ JM O O rH rH ' CO O> O> K ^ CO OOJiO C- l/> O> ^H CO , | o ej oo to \*& rH L gtf . c^^ISS H to ico in rH COJt- Scolm O ^lin oo rH COlt- CO to g Q . * COltO Oi ^ ^lOl Oi CO COlOJ 05 co cold to Q 0= t rH e ^ CH . i-i I-H |oi d) to > 1 I 1 1 i i c- tolo X ^ rH W C * 1 ^Ln] to - 1 lO OIiD CO leO d x o> colco rH |rH (X CO co co lii oJ X '"^ -p c in Ojco "2 2 ^ O> |0i ? oj 05 oi a. o> o ^ -p Gi oS -P cj O> -P eo CO 4) ^ ^ t- to oo cj i * tolc- co ^Ito Oi cojc- CO CO IS c- to jo c "d -5 .S *~s rH O Q) (/} +> CO * OIco in ojto m Olin >i K s z II II II -P o lo to ho +> w C C C rH II-H 3 H -H .H ^ rl hD hO tO t. ^ r = a O K X K S C-i o c- ojc- co CVJ glCA hO t- rH|O> O rH OOJCJ 'o> s s a co tolin e o< o< 1 a a c O JO) TJ 0) a) a$ c .p *> +> Cj f^4 m << co m co TJI co p tf O colcj o> co|o co col^ O tolc^ aJ C C ^P C -H -|H rl 3 bO feO c? ^ co cojto O CO |rH rH tOW K E C !-. Cl 15 s 3 cHo w H ~ > I > 6 S ^E et "J i-H II-H rH JrH rH JfH fll o is* c o *J i i w c-t t o " H hO v" o olo ^ M K n C- OICO w O 0>|O O O i-i * C CO O>lcO 5*2 * c = |rH 0,2 I to rH in cn g * H.33S 0) -0 1 2 CO 1 05 10 C- O> CJ O> C rH rH O> -n ( -P oj m oj to rH JO K 3 rH P< ^f o to Q o Q 3 CO CO co CO "at O*= = > H CO CO CO CO V J the moisture makes it somewhat difficult to obtain check calibra- tions, and so we prefer to calibrate the buret dry. The calibration ASSEMBLING THE HALDANE 65 tap must be fused to the buret and not attached by rubber tubing, because changes in level of the mercury from the top to the bottom of the buret will produce variations in pressure against the rubber tubing, and consequently the latter will not always have the same bore, and an appreciable error in the calibration results. As has been suggested by Haldane, it is possible to calibrate the gas analysis apparatus by determining the percentage error found on analyz- ing pure outdoor air which has a constant composition of carbon dioxid and oxygen. This method is only applicable if the buret has an absolutely even bore throughout its entire length, and we have found this frequently not to be the case. 3. Assembling the Haldane. The mounting of the various parts of the Haldane is not difficult. If the duplicate calibrations agree the calibration tap is cut off and the end of the buret carefully fire- polished. To clearly define the graduations of the buret, the stem is cautiously warmed over a low flame and a blue skin pencil rubbed hard over the surface of the buret to fill in the figures and markings with "the blue lead; the excess is wiped off with a soft cloth. The length of the water-bath (1) is cut so that it will reach from just below the buret tap (8) to about 5 cm. below the 10 c.c. mark on the buret. The control tube should fit in the water-bath with its bulb 1 cm. below the bulb of the buret. A right-angle bend is made in the control tube about 2.5 cm. above the buret tap (8). The end of the control tube is sealed at a point projecting 2 cm. below the water-bath and it is then filled about half-way up its stem with dis- tilled water. By means of a sharp cork borer, moistened with soap solution, two holes are bored in a rubber stopper which should not be more than 1.5 cm. thick. The stopper is fitted into one end of the water-bath and the control tube and buret are put inside the water-bath and through the stopper. The rubber tubing (5), after being thoroughly cleaned of talc and moistened with water, is slipped on the buret. The water-bath, with the buret and control tube in 5 66 BASAL METABOLIC RATE position, is placed on the Haldane board in front of the glazed glass (4) and is supported by two long screws. It is securely held in place by wires, covered with rubber tubing, across the top and bottom of the water-bath. One by one the taps and pipets are measured, cut off to the proper lengths, fire-polished, and mounted with proper rubber connections. For this purpose heavy 3 mm. bore pressure tubing is used, except on the lower part of the potash (16) and pyro (21) pipets where black sulphid-free tubing is necessary. The pressure tubing must be thoroughly cleaned of its talc. A piece of tubing (10) of 1 mm. bore and 30 cm. long, connected at each end by 1 mm. bore glass tubing to two pieces of the 3 mm. bore pressure tubing, is attached at one end to the arm of the sampling tap (9). Finally, the various parts are supported by appropriately placed 2-inch screws, covered with rubber tubing, and held firmly by copper wire covered with rubber tubing. The taps must not be allowed to rest on or press against the Haldane board, as they are thereby loosened from their bores, causing them to leak. Care should be taken not to fasten the glass parts too rigidly, as with changes in temperature the glass may break. In case the level markings are not cut into the glass on the potash and pyro pipets and manometer tube a linen thread may be tightly tied on and held in place by a tiny drop of glue on either side. The line drawings and photographs (Figs. 11, 12) indicate quite accurately the gen- eral set up and position of the supporting screws, clamps, and so forth. A convenient way of cutting glass tubing the size of the water- bath or even larger is to use an electric glass cutter (Fig. 13). It consists of 2 or 3 feet of nichrome or chromel wire (No. 22 or 24, B. & S.) supported by three or four 2-inch screws as binding-posts on an asbestos board. To the binding-post at one end is attached one of the wires from an ordinary electric circuit; to the binding- post at the other end is fastened another piece of nichrome wire ELECTRIC GLASS CUTTER 67 about 18 inches long to the free end of which is attached an ordi- nary thumb snap switch which is connected with the other in- sulated wire from the electric'circuit. When the current is on the Fig. 13. Electric glass cutter. wire should become red hot, but should not reach a white heat; the proper degree of heating is regulated by varying the length of the nichrome wire between the binding-posts. A single deep cut 68 BASAL METABOLIC RATE is made on the glass tubing with a sharp triangle file and the ni- chrome wire is passed through this cut and around the tube. The wire must be kept taut and no short circuit made by contact be- tween the loops of wire. The switch, which acts as a handle, is pressed with the thumb, the wire becomes red hot, and expands. It is necessary, therefore, to keep sufficient tension on the wire to take up the slack. After thirty to sixty seconds the tube will crack off evenly. With very hard glass it may be occasionally necessary to turn off the electricity and dash on a glass of cold water. 4. Control Tube. By means of the control tube, first employed in gas analysis by Williamson and Russell in 1868, the effects of changes in temperature, pressure, and water vapor on the gas volume may be compensated. The control tube (3) has approxi- mately the same shape and volume as the gas buret; it is sealed at the lower end and filled about half-way up its stem with distilled water. It is placed in the water-bath beside the buret and the pressure of the air within is balanced against that in the buret through the potash absorption pipet (16), the potash tube (25) acting as a manometer. A three-way tap (18) on the control tube permits connection with the room air, so that before an analysis the pressure in the control tube may be made the same as that in the room. Since the control tube is in the water-bath (1) beside the buret any changes in pressure or temperature will affect alike the air in both the buret and the control tube, and their effect on the air in the buret can be compensated by altering the level of the potash reservoir (17) and the mercury reservoir (6) to bring the potash to the standard level in the manometer (25) and in the potash pipet (15), thereby maintaining the volume of air in the control tube con- stant and the pressure in the control tube and buret alike. There- fore the readings of the buret are compensated by mechanical means for variations of temperature and barometric pressure dur- ing the analysis. MANAGEMENT OF HALDANE APPARATUS 69 5. Management of Haldane Apparatus. (a) Preliminary. Compressed air is slowly bubbled through the water-bath (1) in which the buret (2) and control tube (3) are mounted to keep the water constantly stirred and thus maintain the entire column of water at a uniform temperature. As a result the air in both the con- trol tube and the buret has the same temperature. Instead of hav- ing a constant stream of compressed air circulating through the water-bath the water can be stirred just before any of the readings on the buret are made by using a blood-pressure bulb attached to the tube leading into the water-bath. Before the machine is ready for an analysis it must be checked to see that it is air-tight and that there is no carbon dioxid or oxygen in the buret. For this the fol- lowing procedure is necessary: The buret tap (8) and the potash tap (14) are turned so that the buret is closed to room air and is in connection with the potash pipet (16). With the control tap (18) open to room air and in connection with the potash manometer (25) and the control tube (3) the levels of the potash in the absorbing pipet (15) and in the manometer tube (25) are set at the levels marked thereon. The control tap (18) is closed to room air. The air in the buret is shunted into the pyro (21) by properly turning the tap (14) and by raising the mercury reservoir (6) attached to the buret. After passing back and forth in the pyro ten times, the air is shunted into the potash pipet in order to remove all traces of oxygen by bringing the air above the potash level to the same com- position as the air in the buret. This procedure is called "washing or rinsing" the connections. After rinsing in the potash twice the air is then passed back and forth in the pyro ten times. This pro- cedure, rinsing in the potash and absorption in the pyro, is repeated three times. The preliminary nitrogen reading can now be taken. To do this the pyro is brought to the level (20), and when carefully adjusted the tap (14) is turned so that the air in the buret is in con- nection with the potash solution only. The levels in the potash 70 BASAL METABOLIC RATE (15) and manometer (25) tubes are now set, using the potash (17) and mercury (6) reservoirs for this. The potash reservoir is ad- justed by sliding through its spring clamp and the mercury reser- voir by means of a ratchet and pinion (7). The reading of the mercury meniscus is then made with all the precautions mentioned on page 61 : to hold the lens properly and to have the eyes on the correct level and the various levels carefully adjusted. The volume is recorded to the nearest 0.001 c.c. An electric light (with a 12- inch Mazda Fostoria bulb) placed behind the Haldane is turned on by the switch (24); the light shining through the glazed glass (4) sharply defines the mercury meniscus so that accurate readings are quickly obtained. The light is immediately turned off when the reading has been made. The potash tube is again washed twice and the air then shunted into the pyro, and, after passing back and forth ten times, the reading of the volume is again determined, setting the various levels described above. If the machine had been left full of nitrogen from the previous analysis these nitrogen readings should now check. If the readings do not check within 0.002 c.c., the process above is repeated until check readings of the volume are obtained, after which the machine is ready for an analysis. (b) Sampling. Connection is made by a 1-mm. bore rubber tubing (10) from the sampling tap (9) to the sampling tube (12). The tap (11) on the sampling tube is opened, care being taken that the sampling tap (9) is closed so that none of the sample can escape. The potash and pyro levels are carefully set and the buret tap is closed to the potash and opened to room air. At this point in the procedure acidified water is put in the buret with a medicine-dropper if it appears dry, for the air sample must be thoroughly saturated with water vapor throughout the analysis. For this purpose dis- tilled water slightly acidified with sulphuric acid is used (about 2 drops of concentrated sulphuric acid in 50 c.c. of distilled water). It is most important to have sufficient water in the buret, enough MANAGEMENT OF HALDANE APPARATUS 71 so that the inside appears moist and there is a very small amount on the mercury meniscus. If the buret is too dry, readings simulat- ing a leak in the machine will be obtained because of the variation in saturation of the air sample with water vapor. The buret is washed twice with room air, thus diluting the nitrogen and bring- ing the air in the buret more nearly to the composition of the sample to be analyzed. The index-finger of the left hand is moist- ened with water and placed on the top of the buret, and with the right hand holding the mercury reservoir (6), and securely sup- ported on the upper edge of the Haldane board, the mercury in the buret is brought up to the buret tap (not into it), the air is allowed to escape slowly from beneath the index-finger, and then the sampling may be started. The sampling tap (9) is cautiously turned by the thumb and middle finger of the left hand to the sampling tube (12) and buret (2), and, since the sample is under positive pressure, it will run into the buret. When 3 c.c. of the sample have passed into the buret the sampling tap (9) is turned off from the sampling tube (12) and the air in the buret is permitted to escape into the room by cautiously allowing it to flow from under the moistened index- finger in position on the top of the buret. The air escapes until the mercury in the buret has reached the buret tap (8) . This process must be carried out slowly so that there is no back lash of the mer- cury which might introduce room air into the buret and so vitiate the sample. This is the first rinsing. Three subsequent rinsings of about 3 c.c. each are cautiously and carefully made without re- moving the index-finger of the left hand from its position at the top of the buret, and then the sampling tap (9) is completely opened to the buret and sampling tube. The left land is removed from its position at the top of the buret and the right hand slowly lowered and again raised to pass the sample back into the sampling tube. This process is repeated twice and the mercury reservoir (6) then hung on the ratchet at about 9.0 c.c. With the left hand the mer- 72 BASAL METABOLIC RATE cury reservoir (13) on the sampling tube is taken from its holder and lowered, together with the mercury reservoir (6) on the buret, to such a position that the amount of sample in the buret is 9.5 c.c. or more. The mercury reservoir (6) is hung up on the ratchet. Care is taken to level exactly the mercury in the sampling tube (12) and its reservoir so that the air in the buret will be at atmospheric pressure; the tap (11) of the sampling tube is closed and the mer- cury reservoir of the sampling tube hung up on its rack. The buret tap (8) is then turned to close the connection with the sampling tube and put the air in the buret in connection with the potash tube (16). (c) Analysis. If the mercury levels of the sampling tube (12) and its reservoir have been properly adjusted, the potash levels will change very little when the buret tap (8) is turned into the potash solution (16). The rubber tubing of the potash tube (16) and also the tubing (5) attached to the buret should be pressed gently to see that the potash levels (15, 25) respond, to make certain that the small openings in the taps are not stopped up with grease. The potash levels (15, 25) are set by carefully adjusting the mercury (6) and potash (17) reservoirs, and, with the precautions mentioned above, the total volume of the air sample is read and recorded. A readjustment of the levels is made as quickly as possible after again gently pressing the mercury tube and the rubber potash tube to insure free communication and the check reading of the total volume of air taken. The air sample is then passed back and forth eight times in the potash solution and a reading of the volume recorded after setting the potash levels with great care. Again the sample of air is passed five times into the potash solution and the check reading made. If the readings do not agree within 0.002 c.c., the procedure is re- peated until check readings are obtained. The tap (14) is then turned so that the sample is passed into the pyro about eighteen times. The potash tube by turning tap (14) properly is rinsed MANAGEMENT OF HALDANE APPARATUS 73 twice and the sample again shunted into the pyro and passed back and forth ten times. This complete procedure is repeated twice again before a reading is taken of the volume. In making a read- ing the pyro level is set by means of the mercury reservoir (6) and then the tap (14) is turned to the potash tube and the two potash levels (15, 25) set. A check reading is made after rinsing in the potash and again passing the air back and forth in the pyro ten times. A duplicate analysis is made, using, if possible, another Haldane and following the procedure above. A complete analysis and its duplicate follow: Case 100,490. March 5, 1918. Haldane No. V. Reading Corr. Corr. Diff. Per cent. buret. reading. 9.377 9.377 + 0.003 = 9.380 9.137 9.136 + 0.007 = 9.143 = 0.237 = 2.53% C0 2 7.443 7.444 + 0.020 = 7.464 = 1.679 = 17.90% 2 Reading buret. 9.548 9.548 + 9.303 9.303 + 7.589 7.579 7.579 + Corr. 0.004 0.006 Haldane No. III. Corr. Diff. reading. Per cent. 9.552 9.309 0.243 2.54% C0 2 0.023 = 7.602 = 1.707 = 17.87% O 2 (d) Care of the Haldane. Several of the steps in the analysis and management of the gas analysis apparatus deserve further dis- cussion. Whenever check readings on carbon dioxid or oxygen absorp- tion cannot be obtained within a reasonable time, the difficulty is usually due to the following causes: A leaky tap from faulty greasing ; an insufficiency of water in the buret to saturate the air, or pieces of grease or mercury obstructing the taps or capillary tubing, or inaccuracy in adjusting the levels. 74 BASAL METABOLIC RATE In transferring the sample into the buret the "dead space" of the connections from the sampling tube to the sampling tap and the upper part of the buret are thoroughly rinsed with the sample to be analyzed. After each rinsing the small portion of sample used for this purpose is allowed to escape into the room in the manner described above. The escape of the air must be slow and gradual so as to prevent any back-lash of the mercury. When the sample is taken into the buret it should be transferred slowly, so that the air may become thoroughly saturated with water vapor and also prevent any mercury from sticking to the sides of the buret. The importance of having sufficient acidulated water in the buret must be emphasized. The presence of acid prevents the water from becoming alkaline from contact with the glass buret and, therefore, from absorbing carbon dioxid. When the buret is dry it is impossi- ble to get constant readings; the potash levels change, and the readings, which show a slight continual decrease in the volume of the air, apparently indicate that the machine is leaking. If at this point the sample is allowed to stand for a few minutes in the buret and in connection with the potash solution it will take up moisture and so increase in volume; in this way it is sometimes possible to obtain check readings and so prevent the loss of the analysis. As Haldane states: "If the buret is allowed to become dry- very appreciable errors are produced. A sample of pure air will, for instance, probably increase in volume when passed over into the potash pipet, as the air will take up more moisture than it loses of carbon dioxid in contact with the potash solution." An excess of water insures that under all conditions the volume of the gas meas- ured is completely saturated with water vapor, and, therefore, the contractions from absorption of carbon dioxid and oxygen will be proportional to those obtained had the gas been absolutely dry. On the other hand, too much water in the buret decreases the volume of air and so gives incorrect, although constant, readings. MANAGEMENT OF HALDANE APPARATUS 75 A dirty buret vitiates the analyses, especially the oxygen deter- mination, causing the latter to be appreciably higher, and if very dirty, amounting to an error of 0.10 per cent. If the buret is cleaned before it becomes very dirty the process is much easier. In cleaning, the buret is filled through the top with concentrated nitric acid diluted with an equal amount of distilled water and al- lowed to stand for one-half hour. The nitric acid is then removed and a long pipe-stem cleaner is very carefully run down the length of the buret. After removing the pipe -stem cleaner the buret is washed thoroughly and repeatedly with distilled water and finally with distilled water containing a few drops of sulphuric acid. A very dirty buret, however, must be cleaned with warm cleaning solution, or concentrated nitric acid, and for this it is necessary to disconnect the rubber tubing (5) and suck the acid up into the buret. Alcohol and ether should never be used for cleaning gas analysis apparatus, because it is very difficult to remove the last traces and their vapor may cause serious analytic errors. The control tap (18) is closed to room air during an analysis, but on account of changes in the temperature of the room it is often necessary between analyses to open the tap and reset the tw6 pot- ash levels (15, 25) at room air pressure. It is not necessary at this point to get check readings of the nitrogen. There must be free connection between the potash manometer (25) and the control tube (3); otherwise there is no longer a correct compensation for temperature and pressure changes and the analyses will be incor- rect; grease in the tap bore is usually the cause of this error. Occa- sionally during an analysis the temperature changes are such that the range of adjustment of the potash reservoir (17) is insufficient to properly set the level in the manometer tube (25), and to over- come this difficulty potash solution is either added to or removed from the reservoir (17) by means of a capillary pipet. When through using a machine the control tap (18) should be 76 BASAL METABOLIC RATE opened to room air, manometer, and control tube; otherwise tem- perature changes may suck the potash up into the taps. The pot- ash tap (14) should also be turned so that the solutions are not in connection with the buret, to prevent them from getting into the taps or buret in case of any accident to the apparatus. The absorption of the last traces of oxygen is slow and, if the check reading is taken too soon, the readings may be practically unchanged from the preceding reading and yet all the oxygen may not be absorbed; at least two minutes of shaking by the me- chanical shaker should be allowed between check readings. The use of tubes in the pyro pipet materially increases the rapidity of the oxygen absorption because of the increased surface area. With their use the pyro, especially when it has become thick from use, is liable to form air bubbles which must be carefully watched for, and the pyro changed as soon as their tendency to develop is no- ticed. If the pyro is either very new or nearly used up it absorbs the last traces of oxygen very slowly. Since the liquids are controlled by the movements of the mercury reservoir, it sometimes happens that they are sucked over into the buret. The machine should be cleaned as soon as the accident happens. In such a case the buret and connections must be thor- oughly washed first with dilute sulphuric acid (1 part sulphuric to 3 parts distilled water) and finally with distilled water, slightly acidified with sulphuric acid. The presence of 'the strong alkaline solutions on the taps may cause them to be frozen into their bores, and for this reason they must be carefully cleaned of the alkaline solution. Sulphid-free black rubber tubing must be used on the potash absorption pipet. The ordinary black tubing contains various sulphur compounds, which are more or less soluble in potash, giving a yellowish tinge to the solution. Such a solution tends to absorb oxygen so that the carbon dioxid reading in consequence will be MANAGEMENT OF HALDANE APPARATUS 77 too high. It is also better to use this black sulphid-free tubing on the pyro pipet. The rest of the connections which do not come in contact with the absorbing liquids are made with heavy red pressure tubing. The bore of the pressure tubing is covered with talc which should be carefully removed before using to prevent any leaks. To remove the talc the tubing is soaked in soap and water and the bore carefully scrubbed with a pipe-stem cleaner; it should then be thoroughly rinsed in distilled water slightly acidi- fied with sulphuric acid. Practically the only source of leaks on a Haldane that is care- fully set up is due to the improper greasing of the taps. In greas- ing, the tap and its bore should be thoroughly wiped off with a soft cloth and the tap covered with a very thin layer of grease, avoiding an excess which might clog the openings. When the greased tap is turned in its bore there should be no stria tions and the tap should turn smoothly. In cleaning the bore pipe-stem cleaners are very satisfactory, but care must be taken not to scratch the glass with the uncovered wire. In manipulating a tap the handle is turned by the thumb and index-finger at the same time pressing gently inward; care, however, must be used not to press too hard, as thereby the grease is squeezed out, causing binding of the tap and so necessitating regreasing. Beginners have a tendency to pull the tap out in turning it and so causing a leak. (e) Filling the Haldane. The solutions in the machine are changed whenever the pyro gives an oxygen content of outdoor air below 20.90 per cent., or whenever the pyro becomes thick and tends to catch air bubbles. The potash solution is readily changed by taking out the taps (14) and (18), and by removing the potash container (17) from its holder, to allow the solution to run out. The pipet is rinsed with dilute hydrochloric acid to dissolve the thin film of carbonate formed, and then repeatedly washed with distilled water. Fresh potash solution of specific gravity 1.15 is 7 8 BASAL METABOLIC RATE then put in the pipet through the potash reservoir. The potash should stand at the two levels (15) and (25) and half-way up in the stem of the potash reservoir when the latter is placed in its holder. In filling the pyro pipet the tap (19) is taken out and then the solid glass rod (30) is removed from the lower end of the rubber tubing attached to the pipet. By means of a glass funnel and an extra piece of rubber tubing and glass connection the pipet (21) is thor- oughly cleaned with water and finally filled to its proper level with the pyro solution, and the solid glass rod is reinserted in the end of the rubber tube. It is not necessary to change the potash solution in the seal, although water must be added from time to time to replace that lost by evaporation, and so prevent breaking of the seal. The buret should be thoroughly cleaned whenever the solu- tions are changed. The water-bath should be kept clean and com- pletely filled with distilled water. If the bulbs of the buret or con- trol tube are only partly covered with water, temperature changes will affect the readings of the air volume. About 20 c.c. of mercury are introduced into the buret through the reservoir (6) attached to the buret by means of rubber tubing (5). The mercury should be changed whenever it becomes dirty. 6. Analysis of Outdoor Air. The limit of accuracy attainable by a skilled analyst using a Haldane gas analysis apparatus with a perfectly clean buret is ^O.Ol per cent. In routine work, however, this error increases to 0.03 per cent, for oxygen. In all work done in our laboratory analyses are made in duplicate and must agree in the carbon dioxid determination within 0.02 per cent, and in the oxygen determination within 0.03 per cent of the average. Haldane has found with this apparatus that outdoor air con- tains 0.03 per cent, carbon dioxid and 20.93 per cent, oxygen, and with his large apparatus the carbon dioxid was 0.030 per cent, and the oxygen 20.928 per cent. Benedict 7 found that the average result of 212 analyses of out-door air using the Sonden apparatus SHAKER 79 was 0.031 per cent, carbon dioxid and 20.938 per cent, oxygen, the balance being due to nitrogen and inert gases. In one series of 349 analyses of out-door air nearly equally divided among 18 Haldane gas analysis apparatus which had been calibrated in duplicate by mercury, as described on page 60, we found the average carbon dioxid content to be 0.037 per cent, and the oxygen content 20.930 per cent. In a second series of 343 analyses the average carbon dioxid was 0.035 per cent, and the average oxygen 20.930 per cent. The average of the two series of 692 analyses was 0.036 per cent, for carbon dioxid and 20.930 per cent, for oxygen. The outdoor air for these analyses was taken from the fire escape outside the laboratory \vindow and in the center of Rochester, Minnesota. On account of the large number of chimneys in the neighborhood vary- ing amounts of smoke drifted toward the laboratory; this probably accounts for the differences in the carbon dioxid and oxygen per- centages found by us as compared with the results obtained both by Haldane and Benedict. Therefore in our calculations and in Table III of the Appendix we have adopted as an average for out- door air 0.04 per cent, of carbon dioxid and 20.93 per cent, of oxygen. Room air, however, has a variable composition (page 41) with an increase in the carbon dioxid and a corresponding decrease in the oxygen content, the variations depending mainly on the size of the room, the number of occupants, and the efficiency of the ventilating system. As a routine procedure an outdoor air analysis is done once a week on every Haldane machine and a record kept on file. We consider it essential that such control air analyses be made regularly to indicate the accuracy of the apparatus, the efficiency of the absorbing solutions, and the skill of the analyst (Form IV, Appendix). 7. Shaker. When many analyses are being done, using several machines, some mechanical device should be used to raise and lower the mercury reservoirs (6). For this purpose we have beside 80 BASAL METABOLIC RATE each of our 18 Haldanes an arm (28) about 12 inches long which rises and falls at its outer end from 3^2 to 4 inches ten to twelve times a minute. This arm is driven by light shafting (27) from an eccentric geared down from a one-sixth horse-power electric motor. The exact throw for each Haldane is obtained by varying the posi- tion of the hook (26) on the arm upon which the mercury reservoir is hung. The level of the arm (28) is adjusted by a thumb-screw by means of which it is clamped to the shafting (27). The most efficient throw is one which keeps the mercury in the bulb, never in the stem of the buret. While a single analysis cannot be done as quickly by this method as by hand, it allows one person to run from four to six machines and at the same time to calculate the analyses. An experienced analyst can thus do from twelve to sixteen complete analyses and their calculations in a morning. D. SOLUTIONS 1. Potassium Pyrogallate Solution (Haldane). To 600 gm. of stick potassium hydroxid (not purified by alcohol) are added 300 c.c. of distilled water. The specific gravity of the resulting solution should be exactly 1.55 (this can be determined by using a hydrom- eter or by finding the weight of 100 c.c. of the solution, which should be 155 gm.). If the specific gravity is too low, potassium hy- droxid should be added until the desired concentration is obtained. To 100 c.c. of this concentrated potash solution 10 gm. of Merck's pyrogallic acid are added in a bottle with a greased stopper. Hal- dane states that the solution should be made exactly in the manner described. The resulting solution of potassium pyrogallate should have a brownish-green tint and should become a deep wine color immediately on exposure to air. The pyro should be at least a month old before using, although it improves with greater age. This "aging" can sometimes be hastened by exposing the pyro for a few minutes to air and thus giving it a "start." CLEANING MERCURY 8 1 2. Potash Solution for Carbon Dioxid Absorption. For the ab- sorption of carbon dioxid we use a dilute solution of potassium hydroxid of specific gravity of about 1.15, approximately a 17 per cent, solution. 3. Black Rubber Grease. Ordinary black rubber tubing of small diameter is washed in water to remove the talc. Then it is cut into very small pieces and slowly added to an equal quantity of lanolin which has been melted (about 2 tablespoonfuls of finely cut tubing and of lanolin). The rubber is allowed to melt, using a slow flame until the resulting liquid is free from any lumps. The grease should be very smooth and of a consistency slightly firmer than lanolin. While still melted the grease is poured into a small "cold cream' 7 jar. It is a very satisfactory grease for glass taps, it wears well, and if sufficiently thin it will not clog the tap. 4. Cleaning Solution. This should be used to remove grease from glass apparatus like the sampling tubes and occasionally the buret of the Haldane. It is a supersaturated solution of potassium bichromate in concentrated sulphuric acid. It is more efficient when warm and can be used over and over until the solution has become green, when it should be discarded. 5. Cleaning Mercury. The mercury used in the type of gas analysis described becomes very dirty from grease, dust, and from forming an amalgam with the copper wire used to wire the connec- tions of the Haldane and sampling tubes. In cleaning, the mercury should be first wrung through several layers of close meshed towels. It is then covered with nitric acid (1 part concentrated nitric acid to 1 part distilled water) and air bubbled through it for several hours. The same procedure is repeated, using distilled water, so that the mercury is no longer acid. The excess water is removed with filter-paper and the mercury is allowed to stand until all the water has evaporated, leaving the mercury dry. 6 SECTION III CALCULATION OF BASAL METABOLIC RATE WHILE the patient is in the laboratory the following data are obtained: The gasometer readings at the start and at the end of the test, and the duration of the test in minutes and seconds; the temperature of the expired air at the time of the final volumetric readings and the barometric pressure, and finally, the patient's height, weight, pulse, and blood-pressure. A detailed calculation of the basal metabolic rate step by step is given below. On Form II, Appendix, is shown a routine calculation in the same case in which our forms and calculation tables devised to simplify the procedure are used. 1. Volume of Expired Air. 5-14-18. Case A 172,918; F. 50; wt. 53.7 kg.; ht. 159.4cm. Barometer 738.8 mm. Temperature gasometer 21.6 C. I. II. Gasometer reading at end 63.90 cm. 65.90 cm. Gasometer reading at start 1.50 cm. 3.50 cm. Gasometer difference 62.40cm. 62.40cm. Since by calibration we have found that a rise of 1 cm. on the steel tape corresponds to 1.256 1. (the factor of the gasometer), the volume of the expired air is 62.4 cm. X 1.256 = 78.38 1. at 738.8 mm. and 21.6 C. In order to compare the volumes of gases with each other, a standard pressure and temperature have been universally adopted, and the volumes of all gases are expressed under the standard con- ditions at a pressure of 760 mm. of mercury and at a temperature of C. (or at absolute temperature 273+ C.) and dry. 32 The gas volume, 78.38 1., has, therefore, to be reduced to standard 82 REDUCTION TO STANDARD TEMPERATURE 83 conditions of temperature and pressure. To do this the following steps are necessary, and the various factors are obtained from Lan- dolt, Bornstein, and Roth: 2. Correction of Barometer to C. The barometer reading must first be corrected for the temperature of the mercury, since the density of the mercury varies with variations in temperature. The temperature of the barometer is 21.6 C., and at this tempera- ture the correction for the density of mercury for a barometer read- ing recorded on a brass scale is 2.6 mm. The corrected barometer reading is 738.8 mm. 2.6 mm. = 736.2 mm. 3. Correction for Water Vapor. The expired air is saturated with water vapor; therefore the volume of the air, if dry, would be smaller. The pressure of water vapor for the temperature at which the volume is read must be deducted from the barometer reading. At the temperature of 21.6 C. this correction is 19.4 mm. Con- sequently the pressure of the dry expired air is 736.2 mm. 19.4 mm. = 716.8 mm. 4. Reduction to Standard Pressure. According to Boyle's law the volume of a gas is inversely proportional to the pressure, provided the temperature remains constant. To correct to the standard pressure of 760 mm. the following procedure is necessary: 78.38 : x = 760 : 716.8 716.8 or 78.38 X = 73.93 1. at 760 mm. and 21.6 C., dry. 760 5. Reduction to Standard Temperature. Charles' law states that, provided the pressure remains constant, the volume of a gas will change ^73- of its volume at for each degree of change of temperature. To reduce the above gas volume to standard tem- perature the following calculation must be done : 73.93 : x = 273 + 21.6 : 273 + 273 + or 73.93 X = 68.52 1. at 760 mm. and C., dry. 273 + 21.6 84 BASAL METABOLIC RATE 6. Ventilation Rate. This volume at standard pressure and temperature dry has been expired by the patient in 11 minutes and 4 seconds (or 11.07 minutes). The volume per minute or, as it is called, the ventilation rate per minute is, therefore, 68.52 1. = 6.191. per minute. 11.07min. 7. Carbon Dioxid Production. Duplicate analyses show that the expired air from the above test contained 3.00 per cent. CO 2 17.53 per cent. O 2 79.47 per cent. N 2 Outdoor air has the following composition (page 78) : 0.04 per cent. CO 2 20.93 per cent. O 2 79.03 per cent. N 2 (including all the inert gases). The carbon dioxid produced by the patient per minute is, there- fore, 3.00 - 0.04 X 6.191. = 0.1831. or 183 c.c. 100 8. Oxygen Absorption. The volume of oxygen absorbed is more difficult to calculate than the carbon dioxid elimination, since the inspired air during the process of respiration has decreased in volume due to the fact that more oxygen has been absorbed from it than carbon dioxid has been given off. From a comparison of the analyses of the expired with the inspired air it will be seen that the nitrogen readings have changed, the nitrogen of the expired air being larger, although nitrogen is in no way involved in physiologic processes, and should, therefore, remain unchanged. Since nitrogen is neither taken up nor given off in respiration, it is evident that for RESPIRATORY QUOTIENT 85 every 100 volumes of expired air there corresponded in the inspired air not 20.93 volumes of oxygen, but 79.47 20.93 X = 21.05 volumes. 79.03 Hence the oxygen absorption is 21.05 - 17.53 100 X 6.191. = 0.2181. or 218 c.c. If instead of outdoor air the patient inspires room air it is obvious that the figures found on analysis of the latter must be substituted in those places where the composition of the inspired air enters into the calculation. The values for the correction of the inspired oxygen percentage given in Table III can be utilized by subtracting from them the difference between the percentage of oxygen in outdoor air (20.93) and the percentage of oxygen in the inspired room air. 9. Respiratory Quotient. The respiratory quotient is the ratio between the volume of the carbon dioxid produced and the corresponding volume of oxygen absorbed, 183 c.c. CO 2 or = 0.84, the respiratory quotient. 218 c.c. O 2 The respiratory quotient when not affected by abnormal respi- ration indicates the kind of material being burned in the body. Thus when pure carbohydrate is burned the reaction is C 6 H 12 O 6 + 6O 2 = 6CO 2 + 6H 2 O And the ratio of the volume of carbon dioxid produced to the volume of oxygen absorbed is 6CO 2 = 1.00 60 2 86 BASAL METABOLIC RATE For protein the respiratory quotient is 0.80 and for fat 0.71, and for a mixed diet consisting of all three substances the quotient will average about 0.84. It is necessary to know the value of the respiratory quotient since the calorific value of 1 liter of oxygen is 5.047 when the respiratory quotient is 1.00, but is only 4.690 when the respiratory quotient is 0.71. Consequently, the number of calories produced when 1 liter of oxygen is absorbed will depend on the food substances being burned. 10. Calories per Square Meter per Hour. For a quotient of 0.84 the calorific value of 1 liter of oxygen is 4.850 (using the value for the non-protein respiratory quotient, a negligible error which will be explained later) . Therefore, the number of calories produced per hour will be 0.218 1. X 60 min. X 4.850 cal. = 63.4 cal. per hour. Du Bois has shown that the heat production is proportional to the surface area. From Du Bois' height- weight chart the surface area corresponding to a height of 159.4 cm. and a weight of 53.7 kg. is 1.54 sq. m. The number of calories produced per square meter of body surface per hour is 63.4 cal. 1.54 sq. m. 41.2 cal. per sq. m. per hour. 11. Basal Metabolic Rate (B. M. R.). The normal standard for a woman aged fifty is 35.0 cal.; therefore, this patient has a basal metabolic rate of 41.2 - 35.0 = +18 per cent. 35.0 12. Checking Calculations. In order to avoid technical errors all original observations are made by two independent sets of read- ings, as will be noted throughout the description of the technic, and checked by a second observer. The calculations are carried NON-PROTEIN RESPIRATORY QUOTIENT 87 out as on Forms I and II of the Appendix, and completely checked by a second calculator before the results are reported. The follow- ing morning all the calculations of the previous day are rechecked by a third calculator. 13. Non-protein Respiratory Quotient. The calorific value of 1 liter of oxygen when protein is burned is 4.485 ; when fat is burned, 4.686; when carbohydrate is burned, 5.047. To apportion the quan- tity of heat derived from the combustion of protein, fat, and car- bohydrate the following additional steps are necessary: The amount of heat produced from protein can be calculated if the total nitrogen in the urine is known, because every gram of nitrogen appearing in the urine indicates a heat production of 26.51 cal., dur- ing which process 5.91 1. of oxygen are consumed and 4.76 1. of carbon dioxid given off. To obtain the amount of heat by the method of indirect calorimetry resulting from the combustion of fat and car- bohydrate the amount of carbon dioxid and oxygen due to protein combusion must be subtracted from the respiratory carbon dioxid and oxygen, and the oxygen difference then multiplied by the calo- rific value of oxygen for the resultant respiratory quotient from the combustion of fat and carbohydrate (non-protein respiratory quotient). The total metabolism will be the sum of the heat pro- duced by the combustion of protein added to that from the com- bustion of carbohydrate and fat. Magnus-Levy has shown that the calculation of the protein and non-protein heat separately rarely makes a difference of 3 per cent, in the amount of heat found by neglecting this refinement and cal- culating directly the heat from the average respiratory quotient and total carbon dioxid elimination and oxygen consumption. Furthermore, the inability to obtain exact urinary nitrogen deter- minations for short periods such as used in indirect calorimetry renders the refinement of questionable value. Therefore in all our calculations we neglect this step. 88 BASAL METABOLIC RATE A complete calculation from the protein and non-protein factors to obtain the non-protein respiratory quotient and to apportion 55 the heat due to the combustion of protein, fat, and carbohydrate in the case given above is a's follows : CO 2 = 183 c.c. per min. or 10.98 1. per hour. Oz = 218 c.c. per min. or 13.08 1. per hour. Urinary nitrogen per hour = 0.333 gm. Non-protein CO 2 per hour = 10.98 1. (0.333 X 4.76) = 9.39 1. Non-protein O 2 per hour = 13.08 1. (0.333 X 5.91) = 11.11 1. 9.39 Non-protein respiratory quotient = = 0.85. Calories derived from protein combustion = 0.333 X 26.51 = 8.83 Calories derived from non-protein combustion = 11.11 X 4.863 = 54.03 Total calories per hour = 62.86 62.86 Calories per square meter per hour = = 40.8. 1 .U~r 40.8 35.0 Basal metabolic rate = - - -- = +17 per cent. Combustion due to carbohydrate = 54.03 X 49 per cent. = 26.48 cal. Combustion due to fat = 54.03 X 51 per cent. = 27.55 cal. Combustion due to protein = 8.83 cal. 14. Calculation of Metabolic Rate of a Diabetic. The calcula- tion of the metabolic rate of a diabetic is much more difficult. The diabetic organism is more or less unable to burn sugar, depending on the severity of the disease. The relation between the urinary nitrogen and sugar elimination in the fasting and meat-fed diabetic? the dextrose (D) to nitrogen (N) ratio, is the key to the quantity of sugar which can be derived from protein metabolism. Allen and Du Bois have given the calculation of the metabolism of a dia- betic when there is sugar formation from protein the details of which are given below: "In the normal metabolism each gram of nitrogen in the urine indicates the combustion of 6.25 gm. protein, with the liberation from this protein of 26.51 cal., 9.35 gm. carbon dioxid, and the ab- sorption of 8.45 gm. oxygen. It is obvious that if part of this pro- BIBLIOGRAPHY 89 tein molecule is unoxidized in the diabetic organism and is excreted in the urine, all of these figures will be lowered by exactly the num- ber of calories and grams of carbon dioxid and oxygen lost in the glucose. With the dextrose-nitrogen ratio of 3.65 to 1, 1 gm. of nitrogen in the urine indicates the combustion of 6.25 gm. protein with the liberation of 26.51 minus 13.47 cal., 9.35 minus 5.35 gm. carbon dioxid, and the absorption of 8.45 minus 3.89 gm. oxygen. When the dextrose-nitrogen ratio is lower, the calculation is easily made, as follows: The calories, carbon dioxid, and oxygen ascribed to the metabolism of protein are calculated from the number of grams of nitrogen excreted per hour by using the normal factors given by Lusk. 76 Knowing the number of grams of glucose excreted per hour, one can make the proper subtractions, since each gram of glucose represents a loss of 3.692 cal., 1.467 gm. carbon dioxid, and 1.067 gm. of oxygen. In this way it is possible to determine the non-protein respiratory quotient and the heat production by the method of indirect calorimetry. If there is no glycosuria, or if the sugar in the urine is all derived from ingested carbohydrate, the calculations are exactly the same as for normal persons." BIBLIOGRAPHY 1. Allen, F. M., and DuBois, E. F.: Clinical Calorimetry. Paper XVII- Metabolism and Treatment in Diabetes, Arch. Int. Med., xvii, 1010, 1916. 2. Atwater, W. O., and Benedict, F. G.: A Respiration Calorimeter with Ap- pliances for the Direct Determination of Oxygen, Carnegie Inst., Wash- ington, Publication No. 42, 1905. 3. Atwater, W. O., and Rosa, E. B.: First Report of Respiration Calorimeter, U. S. Dept. of Agriculture, Office of Experiment Stations Bull., xliv, 1897. 4. Aub, J. C, and Du Bois, E. F.: The Basal Metabolism of Old Men. Clinica 1 Calorimetry. Paper XIX, Arch. Int. Med., xix, 823-831, 1917. 5. Barr, D. P., and Du Bois, F.: The Metabolism in Malarial Fever. Clinical Calorimetry. Paper XXVIII, Arch. Int. Med., xxi, 627-658, 1918. 6. Benedict, F. G.: Ein Universalrespirationsapparat, Deutsch. Arch. f. klin. Med., cvii, 156, 1912. 7. Benedict, F. G. : The Composition of the Atmosphere with Special Reference to its Oxygen Content, Carnegie Inst., Washington, Publication No. 166, 1912. 8. Benedict, F. G.: Factors Affecting Basal Metabolism, Jour. Biol. Chem., xx, 263-313, 1915. QO BASAL METABOLIC RATE 9. Benedict, F. G. : A Photographic Method for Measuring the Surface Area of the Human Body, Amer. Jour. Physiol., xli, 275-291, 1916. 10. Benedict, F. G. : The Relationship Between Body Surface and Heat Pro- duction, Especially During Prolonged Fasting, Amer. Jour. Physiol., xli, 292-308, 1916. 11. Benedict, F. G. : A Study of Prolonged Fasting, Carnegie Inst., Washington, Publication No. 203, 1915. 12. Benedict, F. G.: A Portable Respiration Apparatus for Clinical Use, Boston Med. and Surg. Jour., clxxviii, 567, 1918. 13. Benedict, F. G. : Notes on the Use of the Portable Respiration Apparatus, Boston Med. and Surg. Jour., clxxxii, 243-245, 1920. 14. Benedict, F. G., and Carpenter, T. M.: Respiration Calorimeters for Study- ing the Respiratory Exchange and Energy Transformations of Man, Carnegie Inst., Washington, Publication No. 123, 1910. 15. Benedict, F. G., and Carpenter, T. M.: Metabolism and Energy Trans- formation of Healthy Man During Rest, Carnegie Inst., Washington, Publication No. 126, 1910. 16. Benedict, F. G., and Carpenter, T. M.: Food Ingestion and Energy Trans- formation with Special Reference to the Stimulating Effect of Nutrients, Carnegie Inst., Washington, Publication No. 261, 1918. 17. Benedict, F. G., and Cathcart, E. P.: Muscular Work, Carnegie Inst., Wash- ington, Publication No. 187, 1913. 18. Benedict, F. G., and Emmes, L. E.: A Comparison of the Basal Metabolism of Normal Men and Women, Jour. Biol. Chem., xx, 253-262, 1915. 19. Benedict, F. G., Emmes, L. E., Roth, P., and Smith, H. M.: The Basal, Gaseous Metabolism of Normal Men and Women, Jour. Biol. Chem., xvii, 139-155, 1914. 20. Benedict, F. G., and Joslin, E. L.: Metabolism in Diabetes Mellitus, Car- negie Inst., Washington, Publication No. 136, 1910. A Study of Metab- olism in Severe Diabetes, Carnegie Inst., Washington, Publication No. 176, 1912. 21. Benedict, F. G., Miles, W. R., Roth, P., and Smith, H. M.: Human Vitality and Efficiency Under Prolonged Restricted Diet, Carnegie Inst., Wash- ington, Publication No. 280, 1919. 22. Benedict, F. G., and Murschhausen, H.: Energy Transformations During Horizontal Walking, Carnegie Inst., Washington, Publication No. 231, 1915. 23. Benedict, F. G., and Roth, P.: The Metabolism of Vegetarians as Compared with the Metabolism of Non-vegetarians of Like Weight and Height, Jour. Biol. Chem., xx, 231-241, 1915. 24. Benedict, F. G., and Smith, H. M. : The Metabolism of Athletes as Compared with Normal Individuals of Similar Height and Weight, Jour. Biol. Chem., xx, 243-252, 1915. 25. Benedict, F. G., and Talbot, F. B.: The Gaseous Metabolism of Infants, Carnegie Inst., Washington, Publication No. 201, 1914. The Physiology of the Newborn Infant, Carnegie Inst., Washington, Publication No. 233, 1914. 26. Benedict, F. G., and Tompkins, E. H.: Respiratory Exchange, with a Des- cription of a Respiration Apparatus for Clinical Use, Boston Med. and Surg. Jour., clxxiv, 857, 1916. BIBLIOGRAPHY 9 1 27. Boothby, W. M.: The Clinical Value of Metabolic Studies of Thyroid Cases, Boston Med. and Surg. Jour., clxxv, 564, 1916. 28. Boothby, W. M.: Absence of Apnea after Forced Breathing, Jour. Physiol., xlv, 328, 1912. 29. Carpenter, T. M.: A Comparison of Methods for Determining the Res- piratory Exchange of Man, Carnegie Inst., Washington, Publication No. 216, 1915. 30. Coleman, W., and Du Bois, E. F.: Calorimetric Observations on the Metab- olism of Typhoid Patients. Clinical Calorimetry. Paper VII, Arch. Int. Med., xv, 887-938, 1915. 31. Denis, W., and Means, J. H.: The Influence of Salicylate on Metabolism in Man, Jour. Pharm. and Exper. Therap., viii, 273-283, 1916. 32. Dennis, L. M.: Gas Analysis, New York, MacMillan, 1913. 33. Douglas, C. G., and Haldane, J. S.: The Regulation of Normal Breathing, Jour. Physiol., xxxviii, 420, 1909. 34. Du Bois, D., and Du Bois, E. F. : Clinical Calorimetry. Paper X. A Formula to Estimate the Approximate Surface Area if Height and Weight Be Known, Arch. Int. Med., xvii, 863, 1916. 35. Du Bois, D., and Du Bois, E. F.: The Measurement of the Surface Area of Man. Clinical Calorimetry. Paper V, Arch. Int. Med., xv, 868-881, 1915- 36. Du Bois, E. F. : The Metabolism of Boys Twelve and Thirteen Years Old Compared with the Metabolism at Other Ages. Clinical Calorimetry, Paper XII, Arch. Int. Med., xvii, 887-901, 1916. 37. Du Bois, E. F.: Metabolism in Exophthalmic Goiter. Clinical Calorimetry. Paper XIV, Arch, Int. Med., xvii, 915-964, 1916. 38. Emmes, L. E., and Riche, J. A.: The Respiratory Exchange as Affected by Body Position, Amer. Jour. Physiol., xxvii, 406-413, 1910-11. 39. Gephart, F. C., and Du Bois, E. F.: Clinical Calorimetry, Paper IV. The Determinations of the Basal Metabolism of Normal Men and the Effect of Food, Arch. Int. Med., xv, 835, 1915. 40. Gephart, F. C., and Du Bois, E. F.: The Basal Metabolism of Normal Ad- ults with Special Reference to Surface Area. Clinical Calorimetry, Paper XIII, Arch. Int. Med., xvii, 902-914, 1916. 41. Haldane, J. S.: Methods of Air Analysis, London, Griffin, 1912. 42. Harris, J. A., and Benedict, F. G. : A Biometric Study of Basal Metabolism in Man, Carnegie Inst., Washington, Publication No. 279, 1919. 43. Hendry, M. F., Carpenter, T. M., and Emmes, L. E.: Gaseous Exchange with Unpractised Subjects and Two Respiration Apparatus Employing Three Breathing Appliances, Boston Med. and Surg. Jour., clxxxi, 285-296; 334-344; 368-371, 1919. 44. Higgins, H. L., and Means, J. H.: The Effect of Certain Drugs on the Res- piration and Gaseous Metabolism in Normal Human Subjects, Jour. Pharm. and Exper. Therap., vii, 1-30, 1915. 45. Howland, J.: Der Chemismus und Energieumsatz bei schlafenden Kindern., Ztschr. f. physiol. Chem., Ixxiv, 1-12, 1911. Also: Tr. XV Internat. Cong, of Hygiene, ii, Pt. 2, 438, 1912. 46. Huntington, E. V.: Four Place Tables (Abridged Ed.). Harvard Co- operative Society, Cambridge, Mass. 92 BASAL METABOLIC RATE 47. Johansson, J. E.: Ueber das Verhalten der Kohlensaure-Abgabe und der Korpertemperatur bei moglichst vollstandiger Auschliessung der Muskel- thatigkeit, Nordisk. Med. Arkiv., xxx, 1897. Ueber die Tagesschwan- kungen des Stoffwechsel, Skand. Arch. Physiol., viii, 85. 48. Krogh, A.: The Respiratory Exchange of Animals and Man (with excellent Bibliography), London, Longmans, Green & Co., 1916. 49. Krogh, A., and Lindhard, J.: The Volume of the Dead Space in Breathing and Mixing of Gases in the Lungs of Man., Jour. Physiol., li, 59, 1917. 50. Landolt, Bornstein, and Roth: Tabellen, Berlin, Springer, 4 ed., 1912. 51. Lavoisier, A. L., and Laplace: Memoire sur la chaleur, Mem. de math, et de phys. de 1'Acad. d. Sc., 355, 1780. 52. Lavoisier, A. L., and Seguin: Premier memoire sur la respiration des animaux, Mem. de math, et de phys. de 1'Acad. d. Sc., 566, 1789. (Also: "(Euvres de Lavoisier," 1862). 53. Lusk, G.: A series of papers on Animal Calorimetry by Lusk and his as- sociates appearing in Jour. Biol. Chem., beginning in 1912, xii. 54. Lusk, G.: A series of papers on Clinical Calorimetry by Lusk and his as- sociates appearing in Arch. Int. Med., beginning in 1915, xv. 55. Lusk, G.: Science of Nutrition, Philadelphia, Saunders, 3 ed., 641 pp., 1917. 56. Magnus-Levy, A.: Physiologic des Stoffwechsels, v. Noorden's Handbuch des Stoffwechsels, i, 207, 1896; also Von Noorden's Metabolism and Practical Medicine, Vol. I: The Physiology of Metabolism. Keener & Co., Chicago, 1907. 57. Means, J. H.: Studies of the Basal Metabolism in Obesity and Pituitary Disease, Jour. Med. Research, xxxii, 121-158, 1915. 58. Means, J. H.: Basal Metabolism and Body Surface. A Contribution to the Normal Data, Jour. Biol. Chem., xxi, 263-268, 1915. 59. Means, J. H.: Studies of the Basal Metabolism in Disease and their Importance in Clinical Medicine, Boston Med. and Surg. Jour., clxxiv, 864-870, 1916. 60. Means, J. H., and Aub, J. C.: A Study of Exophthalmic Goiter from the Point of View of the Basal Metabolism, Jour. Amer. Med. Assoc., Ixix, 33- 37, 1917. 61. Means, J. H., and Aub, J. C.: The Basal Metabolism in Exophthalmic Goiter, Arch. Int. Med., xxiv, 645-677, 1919. 62. Meeh, K.: Oberflachenmessungen des menschlichen Korpers, Ztschr. f. Biol., xv. 425-458, 1879. 63. Olmstead, W. H., Barr, D. P., and, Du Bois E. F.: The Metabolism of Boys Twelve and Fourteen Years Old. Clinical Calorimetry, Paper XXVII, Arch. Int. Med., xxi, 621-626, 1918. 64. Pettenkofer, M.: Ueber die Respiration, Ann. d. Chem. u. Pharm., ii, Suppl. 1, 1862. 65. Pettenkofer, M., and Voit, O.: Untersuchungen iiber die Respiration, Ann. d. Chem. u. Pharm., Suppl. 52, 1862. 66. Regnault, V., and Reiset, J.: Recherches cliniques sur la respiration des animaux des diverses classes, Ann. de chim. et de phys., 3.s., xxvi, 299, 1849. Also: Ann. d. chem. u. pharm., Ixxiii, 92, 129, 257, 1850. 67. Riche, J. A., and Soderstrom, G. F.: Clinical Calorimetry. Paper II. The Respiration Calorimeter of the Russell Sage Institute of Pathology in Bellevue Hospital, Arch. Int. Med., xv. 805, 1915. BIBLIOGRAPHY 93 68. Rubner, M.: Die Quelle der tierischen Warme (Comparison of direct and indirect calorimetry), Ztschr. f. Biol., xxx, 73, 1894. Die Biokalorimetrie, Tigerstedt's Handbuch der physiologischen Methodik, Bd. i, Abt. 3. 69. Rubner, M.: Die Gesetze des Energieverbrauchs bei der Ernahrung, Leipsic, Deuticke, 426 pp., 1902. 70. Sawyer, M., Stone, R. H., and Du Bois, E. F.: Further Measurements of the Surface Area of Adults and Children. Clinical Calorimetry, Paper IX, Arch. Int. Med., xvii, 855-862, 1916. 71. Soderstrom, G. F., Barr, D. P., and Du Bois, E. F.: Clinical Calorimetry, Paper XXVI. The Effect of a Small Breakfast on Heat Production, Arch. Int. Med., xxi, 613-620, 1918. 72. Soderstrom, G. F., Meyer, A. L., and Du Bois, E. F.: Clinical Calorimetry. Paper XI. A Comparison of the Metabolism of Men Flat in Bed and Sitting in a Steamer Chair, Arch. Int. Med., xvii, 872, 1916. 73. Tissot, J.: Nouvelle methode de mesure et d'inscription du debit et des mouvements respiratiores de rhomme et des animaux, Jour, de phys. et de path, gen., vi, 688. 74. Von Noorden, C.: Metabolism and Practical Medicine, 3 vols., W. T. Keener & Co., Chicago, 1907. Excellent bibliography; sections by Magnus- Levy, A.; Von Noorden, C.; Kraus, Fr.; Schmidt, A.; Weintraud, W.; Matthes, M.; Strauss, H.; Salomon, H.; Czerny, A.; Steinitz, H.; Dapper, C.; Neuberg, C.; Loewi, O.; Mohr, L. 75. Williams, H. B.: Animal Calorimetry. Paper I. A Small Respiration Calorimeter, Jour. Biol. Chem., xii, 317, 1912. 76. Williams, H. B., Riche, J. A., and Lusk, G.: Animal Calorimetry. Paper II. Metabolism of the Dog Following the Ingestion of Meat in Large Quantity, Jour. Biol. Chem., xii, 349-376, 1912. 77. Williamson and Russell: Jour. Chem. Soc., 238, 1868. 78. Zuntz, N., and Schumburg,: Studien zu einer Physiologic des Marsches, Berlin, 1901. APPENDIX EXPLANATION OF TABLES A CALCULATION of the basal metabolic rate is appended (Forms I, II). The form adopted by us involves the use of tables which we have compiled to simplify the calculations detailed above. Table /. The duration of the test is recorded in minutes and to the nearest second, and used in the calculations as minutes and decimal parts of a minute. Table I is used to convert seconds into decimal parts of a minute. Table I* Equivalent of Seconds in Decimal Parts of a Minute. Sec . Min. Sec. Min. Sec . Min. 1 0.02 21 .35 41 .68 2 .03 22 .37 42 .70 5 .05 23 .38 43 .72 4 .07 24 .40 44 .73 5 .08 25 .42 45 .75 6 .10 26 .43 46 .77 7 .12 27 .45 47 .78 8 .13 28 .47 48 .80 9 .15 29 .48 49 .82 10 .17 30 .50 50 - .83 11 .18 31 .52 51 .85 12 .20 32 .53 52 .87 13 .22 33 .55 53 .88 14 .23 34 .57 54 ,90 15 .25 35 .58 55 .92 16 .27 36 .60 56 .93 17 .28 37 .62 57 .95 18 .30 38 .63 58 .97 19 .32 39 .65 59 .98 20 .33 40 .67 60 1.00 Table II. In this table are given the log factors for converting in one step the gas volumes to standard temperature and pressure, dry, including the correction of the observed barometer readings for the variations in the density of mercury from changes in tem- perature. The table gives the factors for a barometric range from 700 to 780 mm. and for temperatures between 15.0 and 32.0 C. 94 APPENDIX 95 As an example the derivation of the factor used in the experiment given in the preceding pages is as follows : Barometer = 738.8 mm. = 739 mm. Temperature of the barometer = temperature of the gasom- eter = 21.6 (21.5). We assume the temperature of the barom- eter to be the same as the temperature of the gasometer; as they are in adjoining rooms, the error thus introduced is negligible and the calculation greatly simplified (a variation of 2 degrees causes a change of only 0.1 mm. in the correction). The barometer read- ing is corrected for the density of mercury at 21.5 C. thus: 739.0 mm. 2.6 mm. correction for density of mercury 736.4 mm. corrected barometer. The vapor tension of water at 21.5 C. is 19.2 mm. and must be subtracted from the corrected barometer reading to get the pressure of the air dry. 736.4 mm. 19.2 mm. 717.2 mm. = 717 mm. In reducing the gas volume from 21.5 to C. it is necessary to multiply the gas volume by the ratio 273 ~'~- 21 5' ^ ne ^S" arithm of this ratio is 0.96702-1 as given by Landolt, Bornstein, and Roth. In the same way the volume is reduced to standard barometric pressure by multiplying it by the ratio ^, the log of which ratio is 0.97471-1. We have combined these log factors for the correction of the temperature and pressure into one, thus: 0.96702-1 0.97471-1 1.94173-2 or 0.94173-1 The log factor for the experimental data of 738.8 mm. (739) and 21.6 (21.5) combining (1) the correction for the density of mercury, 96 BASAL METABOLIC RATE Table II. Log Factor for Reducing Volume of Gases to Standard Temperature and Pressure, Dry; Including Reduction of Barometric freight to Standard Temperature (brass scale). Barometer in Millimeters. Temp. C 700 701 702 703 704 705 706 707 708 709 710 15.0 1.9319 9325 9331 9338 9344 9351 9357 9363 9369 9375 9382 15.5 9308 9314 9320 9327 9333 9340 9346 9352 9359 9365 9372 16.0 9298 9304 9310 9317 9323 9329 9335 9341 9348 9354 9361 16.5 9287 9293 9299 9306 9312 9318 9324 9330 9337 9343 9350 17.0 9277 9283 9289 9296 9302 9308 9314 9320 9327 9333 9340 17.5 9266 9272 9278 9284 9290 9297 9303 9309 9316 9322 9329 18.0 9255 9261 9267 9273 9279 9286 9292 9298 9305 9311 9318 18.5 9244 9250 9256 9262 9268 9275 9281 9287 9294 9300 9307 19.0 9233 9239 9245 9251 9257 9264 927.0 9276 92.83 9289 9296 19.5 9222 9228 9234 9240 9246 9253 9259 9265 9271 9278 9285 20.0 9211 9217 9223 9230 9236 9242 9248 9254 9260 9266 9273 20.5 9200 9206 9212 9218 9224 9230 9236 9242 9248 9255 9262 21.0 9188 9,194 9200 9206 9212 9219 9225 9231 9237 9243 9251 21.5 9176 9182 9188 9194 9200 9207 9213 9219 9225 9232 9239 22.0 9164 9171 9177 9183 9189 9196 9202 9208 9214 9221 9228 22.5 9152 9159 9166 9172 9 ITS 9185 9191 9197 9203 9210 9217 23.0 9141 9147 9153 9159 9166 9173 9179 9186 9192 9198 9205 23.5 9129 9135 9141 9147 9154 9161 9167 9173 9179 9186 9193 24.0 9117 9123 9129 9135 9142 9149 9155 9161 9167 9174 9181 24.5 9105 9111 9117 9123 9130 9137 9143 9149 9155 9162 9169 25.0 9093 9099 9105 9111 9118 9125 9131 9137 9143 9150 9157 25.5 9080 9086 9092 9098 9105 9112 9118 9124 9130 9137 9144 26.0 9068 9074 9080 9086 9093 9100 9106 9112 9118 9125 9132 26.5 9056 9062 9068 9074 9081 9088 9094 9100 9106 9113 9120 27.0 9044 9050 9056 9062 9069 9076 9082 9088 9094 9101 9108 27.5 9030 9037 9043 9050 9056 9062 9068 9074 9080 9087 9094 28.0 9017 9023 9029 9035 9042 9049 9055 9061 9067 9074 9081 28.5 9004 9010 9016 9022 9029 9036 9042 9048 9054 9061 9068 29.0 8991 8997 9003 9009 9016 9023 9029 9035 9041 9048 9055 29.5 8977 8983 8989 8995 9002 9009 9015 9021 9027 9034 9041 30.0 8964 8970 8976 8982 8989 8996 9002 9008 9014 9020 9027 30.5 8950 8956 8962 8968 8975 8982 8988 8994 9000 9007 9014 31.0 8937 8943 8949 8955 8962 8969 8975 8981 8987 8994 9001 31.5 8923 8929 8935 8941 8948 8955 8961 8967 8973 8980 8987 32.0 8910 8916 8922 8928 8935 8942 8948 8954 8960 8967 8974 (2) for aqueous vapor, (3) for barometric pressure, and (4) for tem- perature is 0.9417-1. As shown above, the patient expired 78.38 liters at the experi- mental temperature and pressure. To reduce the volume to and APPENDIX 97 Table II (Con't.) Log Factor for Reducing Volume of Gases to Standard Temperature and Pressure, Dry; Including Reduction of Barometric Height to Standard Temperature (brass scale). Barometer in Millimeters. 710 711 712 713 714 715 716 717 718 719 7^0 15.0 1.9382 9388 9394 9400 9406 9413 9419 9425 9431 9437 9444 15.5 9372 9377 9384 9389 9396 9403 9409 9415 9421 9426 9433 16.0 9361 9367 9373 9379 9385 9392 9398 9404 9410 9416 9423 16.5 9350 9356 9362 9368 9374 9381 9387 9393 9399 9405 9412 17.0 9340 9346 9352 9358 9364 9371 9377 9383 9389 9395 9402 17.5 9329 9335 9341 9347 9353 9360 9366 9372 9378 9384 9391 18.0 9318 9324 9330 9336 9342 9349 9355 9361' 9367 9373 9380 18.5 9307 9313 9319 9325 9331 9338 9344 9350 9356 9362 9369 19.0 9296 9302 9308 9314 9320 9327 9333 9339 9345 9351 9358 19.5 9285 9291 9297 9303 9309 9316 9322 9328 9334 9340 9347 20.0 9273 9279 9285 9291 9298 9305 9311 9317 9323 9329 9336 20.5 9262 9268 9274 9280 9287 9294 9300 9306 9312 9318 9325 21.0 9251 9257 9263 9269 9275 9282 9288 9294 9300 9306 9313 21.5 9239 9245 9251 9257 9263 9270 9276 9282 9288 9294 9301 22.0 9228 9234 9240 9246 9252 9259 9265 9271 9277 9283 9290 22.5 9217 9223 9229 9235 9241 9248 9254 9260 9266 9272 9279 23.0 9205 9211 9217 9223 9229 9236 9242 9248 9254 .9260 9267 23.5 9193 9199 9205 9211 9217 9224 9230 9236 9242 9248 9256 24.0 9181 9187 9193 9199 9206 9212 9218 9224 9230 9237 9244 24.5 9169 9175 9181 9187 9194 9200 9206 9212 9218 9225 9232 25.0 9157 9163 9169 9175 9181 9188 9194 9200 9206 9213 9220 25.5 9144 9150 9156 9162 9169 9176 9182 9188 9194 9200 9207 26.0 9132 9138 9144 9150 9157 9164 9170 9176 9182 9188 9195 26.5 9120 9126 9132 9138 9145 9152 9158 9164 9170 9176 9183 27.0 9108 9114 9120 9126 9133 9140 9146 9152 9158 9164 9171 27.5 9094 9100 9106 9112 9119 9126 9132 9138 9144 9151 9158 28.0 9081 9087 9093 9099 9106 9113 9119 9125 9131 9138 9145 28.5 9068 9074 9080 9086 9093 9100 9106 9112 9118 9125 9132 29.0 9055 9061 9067 9073 9080 9087 9093 9099 9105 9112 9119 29.5 9041 9047 9054 9061 9067 9074 9080 9086 9093 9099 9106 30.0 9027 9033 9040 9047 9054 9061 9067 9073 9080 9087 9093 30.5 9014 9020 9026 9033 9040 9047 9053 9059 9065 9072 9079 31.0 9001 9008 9015 9021 9027 9034 9040 9046 9052 9059 9066 31.5 8987 8994 9000 9006 9013 9020 9026 9032 9038 9045 9052 32.0 8974 8980 8987 8994 9000 9007 9013 9019 9025 9032 9059 760 the log factor 0.9417-1 is added to the log of 78.38 (0.8944+1), giving the log 0.8361 + 1, the antilog of which is 68.57 liters. Throughout our calculations we use four place logs without the characteristics. 7 9 8 BASAL METABOLIC RATE Table II (Con't.) Log Factor for Reducing Volume of Gases to Standard Temperature and Pressure, Dry; Including Reduction of Barometric Height to Standard Temperature (brass scale)* Barometer in Millimeters. 720 721 722 723 724 725 726 727 728 729 730 15.0 1.9444 9450 9456 9462 9468 9474 9480 9486 9492 9498 9505 15.5 9433 9439 9445 9452 9457 9464 9470 9476 9482 9488 9494 16.0 9423 9429 9435 9441 9447 9454 9460 9466 9472 9478 9484 16.5 9412 9418 9424 9430 9436 9443 9449 9455 9461 9467 9473 17.0 9402 9408 9414 9420 9426 9433 9439 9445 9451 9457 9463 17,5 9391 9397 9403 9409 9415 9421 9427 9433 9439 9445 9452 18.0 9380 9386 9392 9398 9404 9410 9416 9422 9428 9434 9441 18.5 9369 9375 9381 9387 9393 9399 9405 9411 9417 9423 9430 19.0 9358 9364 9370 9376 9382 9388 9594 9400 9406 9412 9419 19.5 9347 9353 9359 9365 9371 9378 9384 9390 9396 9402 9409 20.0 9336 9342 9348 9354 9360 9367 9373 9379 9385 9391 9398 20.5 9325 9331 9337 9343 9349 9356 9362 9368 9374 9380 9387 21.0 9313 9319 9325 9331 9337 9344 9350 9356 9362 9368 9375 21.5 9301 9307 9313 9319 9325 9332 9338 9344 9350 9356 936$ 22.0 9290 9296 9302 9308 9314 9321 9327 9333 9339 9345 9352 22.5 9279 9285 9291 9297 9303 9310 9316 9322 9328 9334 9341 23.0 9267 9273 9279 9285 9291 9298 9304 9310 9316 9322 9329 23.5 9256 9262 9268 9274 9280 9286 9292 9298 9304 9310 9317 24.0 9244 9250 9256 9262 9268 9274 9280 9286 9292 9298 9305 24.5 9232 9238 9244 9250 9256 9262 9268 9274 9280 9286 9293 25.0 9220 9226 9232 9238 9244 9250 9256 9262 9268 9274 9281 25.5 9207 9213 9219 9225 9231 9238 9244 9250 9256 9262 9269 26.0 9195 9201 9207 9213 9219 9226 9232 9238 9244 9250 9257 26.5 9183 9189 9195 9201 9207 9214 9220 9226 9232 9238 9245 27.0 9171 9177 9183 9189 9195 9202 9208 9214 9220 9226 9233 27.5 9158 9164 9170 9176 9183 9190 9196 9202 9208 9214 9221 28.0 9145 9151 9157 9163 9170 9177 9183 9189 9195 9202 9208 28.5 9132 9138 9144 9150 9157 9164 9170 9176 9182 9188 9195 29.0 9119 9125 9131 9137 9144 9151 9157 9163 9169 9175 9182 29.5 9106 9112 9118 9124 9130 9137 9143 9149 9155 9161 9168 30.0 9093 9099 9105 9111 9117 9124 9130 9136 9142 9148 9155 30.5 9079 9085 9091 9097 9103 9110 9116 9122 9128 9134 9141 31.0 9066 9072 9078 9084 9090 9097 9103 9109 9115 9121 9128 31.5 9052 9058 9064 9070 9076 9083 9089 9095 9101 9107 9114 32.0 9039 9045 9051 9057 9063 9070 9076 9082 9088 9094 9101 APPENDIX 99 Table II (Con't.) Log Factor for Reducing Volume of Gases to Standard Temperature and Pressure, Dry; Including Reduction of Barometric Height to Standard Temperature (brass scale). Barometer in Millimeters. 'Temp. C 730 731 732 733 734 735 736 737 738 739 740 15.0 1.9505 9511 9517 9523 .9529 9535 9541 9547 9553 9559 9565 15.5 9494 9500 9507 9512 9518 9524 9531 9536 9542 9549 9554 16.0 9484 9490 9496 9502 9508 9514 9520 9526 9532 9538 9544 16.5 9473 9479 9485 9491 9497. 9503 9509 9515 9521 9527 9533 17.0 9463 9469 9475 9481 9487 9493 9499 9505 9511 9517 9523 17.5 9452 9458 9464 9470 9476 9483 9489 9495 9500 9507 9513 18.0 9441 9447 9453 9459 9465 9472 9478 9484 9490 9496 9502 18.5 9430 9436 9442 9448 9454 '9461 9467 9473 9479 9485 9491 19.0 9419 9425 9431 9437 9443 9450 9456 9462 9468 9474 9480 19.5 9409 9415 9421 9427 9433 9439 9445 9451 9457 9463 9470 20.0 9398 9404 9410 9416 9422 9428 9434 9440 9446 9452 9459 20.5 9387 9393 9399 9405 9411 9417 9423 9429 9435 9441 9448 21.0 9375 9381 9387 9393 9399 9405 9411 9417 9423 9429 9436 21.5 9563 9569 9375 9381 9387 9393 9399 9405 9411 9417 9424 22.0 9352 9358 9364 9370 9376 9382 9388 9394 9400 9406 9413 22.5 9341 9347 9353 9359 9365 9371 9377 9383 9389 9395 9402 23.0 9329 9335 9341 9347 9353 9359 9365 9371 9377 9383 9390 23.5 9317 9323 9329 9335 9342 9348 9354 9360 9366 9372 9379 24.0 9305 9311 93l7 9323 9329 9336 9342 9348 9354 9360 9367 24.5 9293 9299 9305 9311 9317 9324 9330 9336 9342 9348 9355 25.0 9281 9287 9293 9299 9305 9312 9318 9324 9330 9336 9343 25.5 9269 9275 9281 9287 9293 9300 9306 9312 9318 9324 9330 26.0 9257 9263 9269 9275 9281 9288 9294 9300 9306 9312 9318 36.5 9245 9251 9257 9263 9269 9276 9282 9288 9294 9300 9306 27.0 9233 9239 9245 9251 9257 9264 9270 9276 9282 9288 9294 27.5 9221 9227 9233 9239 9245 9251 9257 9263 9270 9276 9285 28.0 9208 9214 9220 9226 9232 9238 9244 9250 9256 9262 9268 28.5 9195 9201 9207 9213 9219 9225 9231 9237 9243 9249 9255 29.0 9182 9188 9194 9200 9206 9212 9218 9224 9230 9236 9243 29.5 9168 9174 9180 9186 9192 9199 9205 9211 9217 9223 9229 SO.O 9155 9161 9167 9173 9180 9186 9192 9198 9204 9210 9216 30.5 9141 9147 9153 9159 9166 9173 9179 9185 9191 9197 9203 31.0 9128 9134 9140 9146 9153 9160 9166 9172 9178 9184 9190 31.5 9114 9120 9126 9132 9139 9146 9152 9158 9164 9170 9176 32.0 9101 9107 9113 '9119 9126 9133 9139 9145 9151 9157 9163 100 BASAL METABOLIC RATE Table II (Con't.) Log Factor for Reducing Volume of Gases to Standard Temperature and Pressure, Dry; Including Seduction of Barometric Height to Standard Temperature (brass scale)* Barometer in Millimeters. Temp. C T40 15.0 1.9565 15.5 9554 16.0 9544 16.5 9533 17.0 9523 17.5 9513 18.0 9502 18.5 9491 19,0 9480 19.5 9470 20.0 9459 20.5 9448 21.0 9436 21.5 9424 22.0 9413 22.5 9402 23.0 9390 23.5 9379 24.0 9367 24.5 9355 25.0 9343 25.5 9330 26.0 9318 26.5 9306 27.0 9294 27.5 9283 28.0 9268 28.5 9255 29.0 9243 29.5 ' 9229 30.0 9216 30.5 9203 31.0 9190 31.5 9176 32.0 9163 741 742 743 744 9571 9577 9583 9589 9560 9566 9572 9579 9550 9556 9562 9569 9539 9545 9551 9558 9529 9535 9541 9547 9519 9525 9531 9537 9508 9514 9520 9526 9497 9503 9509 9515 9486 9492 9498 9504 9476 9482 9488 9494 9465 9471 9477 9483 9454 9460 9466 9472 9442 9448 9454 9460 9430 9436 9442 9448 9419 9425 9431 9437 9408 9414 9420 9426 9396 9402 9408 9414 9385 9391 9397 9403 9373 9379 9385 9391 9361 9367 9373 9379 9349 9354 9360 9366 9336 9342 9348 9354 9324 9330 9336 9342 9312 9318 9324 9330 9300 9306 9312 9318 9289 9295 9301 9307 9274 9280 9286 9292 9261 9267 9273 9280 9249 9255 9261 9267 9236 9242 9248 9254 9222 9228 9234 9241 9209 9215 9221 9227 9196 9202 9208 9214 9182 9188 9194 9200 9169 9175 9181 9187 745 746 747 748 749 750 9595 9601 9607 9613 9619 9624 9584 9590 9596 9602 9608 9614 9574 9580 9586 9592 9598 9603 9563 9569 9575 9581 9587 9593 9553 9559 9565 9571 9577 9583 9542 9548 9554 9560 9566 9572 9531 9537 9543 9549 9555 9561 9521 9527 9532 9538 9544 9550 9510 9516 9522 9528 9534 9540 9499 9505 9511 9517 9523 9529 9488 9494 9500 9506 9512 9518 9477 9483 9489 9495 9501 9507 9466 9472 9477 9483 9489 9495 9455 9461 9467 9473 9479 9485 9443 9449 9455 9461 9467 9473 9432 9438 9444 9450 9456 9461 9420 9426 9432 9438 9444 9450 9408 9414 9420 9426 9432 9438 9397 9403 9409 9415 9421 9427 9385 9391 9397 9403 9409 9415 9373 9379 9385 9391 9397 9403 9361 9367 9373 9379 9385 9391 9349 9355 9361 9367 9373 9379 9337 9343 9349 9355 9361 9367 9325 9331 9337 9343 9349 9355 93.13 9319 9325 9331 9337 9342 9299 9305 9311 9317 9324 9330 9287 9293 9299 9305 9311 9317 9274 9280 9286 9292 9298 9304 9261 9267 9273 9279 9286 9292 9248 9254. 9260 9266 9272 9278 S234 9240 9246 9252 9258 9264 9281 9227 9233 9239 9245 9251 9207 9213 9219 9225 9231 9238 9194 9200 9206 9212 9218 9225 APPENDIX 101 Table ll (Con't.) Log Factor for Reducing Volume of Cases to Standard Temperature and Pressure, Dry: Including Reduction of Barometric Height to Standard Temperature (brass scale). Barometer in Millimeters. Temp. C 750 751 752 753 754 755 756 757 758 759 760 15.0 1.9624 9630 9636 9642 9648 9654 9660 9665 9671 9677 9683 15.5 9614 9620 9626 9632 9637 9643 9649 9655 9661 9667 9673 16.0 9603 9609 9615 9621 9627 9633 9639 9645 9651 9656 9662 16.5 9593 9599 9605 9611 9617 9622 9628 9634 9640 9646 9652 17.0 9583 9588 9594 9600 9606 9612 9618 9624 9630 9636 9641 17.5 9572 9578 9584 9590 9595 9601 9607 9613 9619 9624 9630 18.0 9561 9567 9573 9579 9585 9591 9596 9602 9608 9614 9620 18.5 9550 9556 9562 9568 9574 9580 S586 9591 9597 9603 9609 19.0 9540 9546 9551 9557 9563 9569 9575 9581 9587 9593 9598 19.5 9529 S534 9540 9546 9552 9558 9564 9570 9576 9582 9588 20.0 9518 9524 9530 9536 9541 9547 9553 9559 9565 9571 9577 20.5 9507 9513 9518 9524 9530 9536 9542 9548 9554 9560 9566 21.0 9495 9501 9507 9513 9.519 9525 9531 9537 9542 9548 9554 21.5 9485 9491 9497 9502 9508 9514 9520 9526 9531 9537 9543 22.0 9473 9479 9485 9491 9497 9503 9509 9515 9521 9526 9532 22.5 9461 9467 9473 9479 9485 9491 9497 9503 9509 9515 9521 23.0 9450 9456 9462 9468 9474 9480 9486 9492 9498 9503 9509 23.5 9438 9444 9450 9456 9462 9468 9474 9480 9486 9492 9498 24.0 9427 9433 9439 9445 9451 9456 9462 9468 9474 9480 9486 24.5 9415 9421 9427 9433 9439 9445 9451 9457 9463 9468 9474 25.0 9403 9409 9415 9421 9427 9433 9439 9445 9450 9456, 9462 25.5 9391 9397 9403 9409 9415 9421 9427 9433 9439 9445 9450 26.0 9379 9385 9391 9397 9403 9409 9415 9421 9427 9433 9439 26.5 9367 9373 9379 9385 9390 9396 9402 9408 9414 9420 9426 27.0 9355 9361 9367 9373 9379 9385 9391 9397 9403 9409 9415 27.5 9342 9348 9354 9360 9366 9372 9378 9384 9390 9396 9402 28.0 9330 9336 9342 9348 9354 9360 9366 9372 9377 9383 9389 28.5 9317 9323 9329 9335 9341 9347 9353 9359 9365 9371 9377 29.0 9304 9310 9316 9322 9328 9334 9340 9346 9352 9358 9364 29.5 9292 9298 9304 9310 9316 9322 9328 9534 9340 9346 9351 30.0 9278 9284 9290 9297 9303 9309 9315 9321 9327 9333 9339 30.5 9264 9270 9276 9282 9288 9295 9301 9307 9313 9319 9325 31.0 9251 9257 9263 9269 9275 9282 9288 9294 9300 9306 9312 31.5 9238 9244 9250 9256 9262 9268 9274 9280 9286 9292 9298 32.0 9225 9231 9237 9243 9249 9255 9261 9267 9273 9279 9285 102 BASAL METABOLIC RATE Table II (Con't.J Log Factor for Reducing Volume, of Gases to Standard Temperature and Pressure, Dry; Including Reduction of Barometric Height to Standard Temperature (brass scale). Barometer in Millimeters, Terap. (0 C 760 15.0 1.9683 15.5 9673 16.0 9662 16.5 9652 17.0 9641 17.5 9630 18.0 9620 18.5 9609 19.0 9598 19.5 9588 20.0 9577 20.5 9566 31.0 9554 21.5 9543 22.0 9532 22.5 9521 23.0 9509 23.5 9498 24.0 9486 24*5 9474 25.0 9462 25.5 9450 26.0 9439 26.5 9426 .27.0 9415 27.5 9402 28.0 9389 28.5 9377 29.0 9364 29.5 9351 '30.0 9339 30.5 9325 31.0 9312 51.5 9298 32.0 9285 761 762 763 764 765 9688 9694 9700 9706 9712 9678 9684 9690 9696 9702 9668 9674 9680 9685 9691 9658 9663 9669 9674 9680 9647 9653 9659 9665 9670 9636 9642 9648 9654 9659 9626 9632 9637 9643 9649 9615 9621 9626 9632 9638 9604 9610 9616 9621 9627 9593 9599 9605 9611 9617 9582 9588 9594 9600 9606 9572 9577 9583 9589 9594 9560 9566 9572 9578 9583 9549 95'55 9561 9567 9573 9538 9544 9550 9556 9562 9527 9533 9538 9544 9550 9515 9521 9~526 9532 9538 9504 9510 9516 9521 9527 9492 9498 9504 9509 9515 9480 9486 9492 9498 9503 9468 9474 9480 9486 9492 9456 9462 9468 9474 9480 9445 9451 9457 9463 9468 9432 9438 9444 9450 9456 9421 9427 9432 9438 9444 9408 9414 9420 9426 9432 9395 9401 9407 9413 9419 9383 9389 9395 9401 9407 9370 9376 9382 9388 9394 9357 9363 9369 9375 9381 9345 9351 9357 9363 9369 9331 9337 9343 9349 9355 9318 9324 9330 9336 9342 9304 9310 9316 9322 9328 9291 9297 9303 9309 '9315 766 767 768 769 9717 9723 9729 S735 9707 9713 9719 9725 9697 9703 9709 9714 9686 9692 9698 9703 9676 9682 9688 9694 9665 9671 9677 9683 9655 9660 9666 9672 9644 9650 9655 9661 9633 9639 9645 9650 9623 9628 9634 9640 9612 9618 9623 9629 9600 9606 9612 9618 9589 9595 9601 9607 9578 9584 9590 9596 9568 9573 9579 9584 9556 9562 9568 9574 9544 9550 9556 9562 9533 9539 9545 9551 9521 9527 9533 9539 9509 9515 9521 9527 770 9740 9731 9720 9709 9699 9688 9677 9667 9656 9645 9635 9623 9613 9602 9590 9579 9567 9556 9545 9533 9498 9504 9509 9515 9521 9486 9492 9497 9503 9509 9474 9480 9485 9491 9497 9462 9468 9473 9479 9485 9450 9456 94,62 9467 9473 9438 9444 9450 9455 9461 9425 9431 9436 9442 9448 9412 9418 9424 9430 9436 9400 9406 9411 9417 9423 9387 9393 9399 9405 9411 9375 9380- 9386 9392 9398 9361 9367 9373 9379 9385 9348 9354 9360 9366 9372 9334 9340 9346 9352 9358 9321 9327 9333 9339 9345 APPENDIX 103 Table II (Con't.) Log Factor for Reducing Volume of Gases to Standard Temperature and Pressure, Dry; Including Reduction of Barometric Height to Standard Temperature (brass scale). Barometer in Millimeters, Temp. C 770 771 772 773 774 775 15.0 1.9740 9746 9752 9758 9763 9769 15.5 9731 9736 9742 9748 9753 9759 16.0 9720 9726 9732 9737 9743 9749 16.5 9709 9715 9721 9726 9732 9738 17.0 9699 9705 9711 9717 9722 9728 17.5 9688 9694 9700 9706 9711 9717 18.0 9677 9683 9689 9695 9700 9706 18*5 9667 9673 9679 9684 9690 9696 19.0 9656 9662 9668 9674 9679 9685 19.5 9645 9651 9657 9663 9668 9674 20.0 9635 9641 9646 9652 9658 9664 20.5 9623 9629 9635 9641 9647 9652 21.0 9613 9618 96.24 9630 9636 9641 21.5 9602 9608 9613 9619 9625 9631 22.0 9590 9596 9602 9608 9613 9619 22.5 9579 9585 9591 9597 9603 9608 23.0 9567 9573 9579 9585 9591 9596 23.5 9556 9562 9568 9573 9579 9585 24.0 9545 9550 9556 9562 9568 9574 24.5 9533 9538 9544 9550 9556 9562 25.0 9521 9527 9533 9539 9545 9550 25.5 9509 9515 9521 9527 9533 9538 26.0 9497 9503 9509 9515 9521 9526 26.5 9485 9491 9497 9503 9509 9514 27.0 9473 9479 9485 9491 9497 9503 27.5 9461 9467 9472 9478 9484 9490 28.0 9448 9454 9460 9466 9472 9478 28.5 9436 9442 9448 9453 9459 9465 29.0 9423 9429 9435 9441 9446 9452 29.5 9411 9417 9423 9428 9434 9440 30.0 9398 9404 9409 9415 9421 9427 30.5 9385 9391 9397 9402 9409 9414 31.0 9372 9378 9384 9390 9396 9401 31.5 9358 9364 9370 9376 9382 9387 32.0 9345 9351 9357 9363 9369 9374 776 777 778 779 780 9775 9780 9786 9792 9798 9764 9770 9776 9781 9787 9755 9760 9766 9772 9777 9744 9749 9755 9761 9766 9734 9740 9745 9750 9756 9723 9729 9735 9740 9746 9712 9718 9723 9729 9735 9702 9707 9713 9719 9724 9691 9696 9702 9708 9714 9680 9686 9691 9697 9703 9670 9675 9681 9687 9692 9658 9664 9670 9675 9681 9647 9652 9658 9664 9670 9636 9642 9648 9654 9659 9625 9631 9636 9642 9648 9614 9620 9625 9631 9637 9602 9608 9614 9619 9625 9591 9596 9602 9608 9614 9579 9585 9591 9597 9602 9567 9573 9579 9585 9591 9556 9561 9567 9573 9579 9544 9550 9556 9562 9567 9532 9538 9544 9550 9555 9520 9526 9531 9537 6543 9508 9514 9520 9526 9532 9496 9502 9508 9513 9519 9483 9489 9495 9501 9506 9471 9477 9483 9488 9494 9458 9464 9470 9475 9481 9446 9452 9458 9464 9469 9433 9439 9445 9451 9456 9420 9426 9432 9438 9443 9407 9413 9419 9425 9430 9393 9399 9405 9411 9416 9380 9386 9392 9397 9403 Table III. The oxygen percentages of the inspired air are cor- rected to the basis of the expired volume as explained on page 84. The corrected oxygen percentage is equal to 20.93 X =^, where x is the percentage of nitrogen of the expired air which is equal to 104 BASAL METABOLIC RATE 100 per cent, minus (CO2 + Oz) per cent, of the expired air. In- stead of tabulating the various nitrogen percentages we use the sum of the carbon dioxid and oxygen percentages of the expired air, sav- ing the step of deriving the nitrogen values. In case room air is used the values for the correction of the inspired oxygen percentage given in this table can be utilized by subtracting from them the dif- ference between the percentage of oxygen in outdoor air (20.93) and the percentage of oxygen in the inspired room air. Table III. Correct ion Inspired Oxygen Percentage to Basis of Expired Volume. .00 .01 .02 .03 .04 .05 ,06 .07 .08 >09 19.5 21.32 21.32 21.31 21.31 21.31 21.31 21.30 21.30 21.30 21.30 19.6 21.29 21.29 21.29 21.28 21.28 21.28 21.28 21.27 21.27 21.27 19.7 21.27 21.26 21.26 21.26 21.26 21.25 21.25 21.25 21.25 21.24 19.8 21.24 21.24 21.24 21.23 21.23 21.23 21.22 21.22 21.22 21.22 19.9 21.21 21.21 21.21 21.21 21.20 21.20 21.20 21.20 21.19 21.19 20.0 21.19 21.18 21.18 21.18 21.18 21.17 21.17 21.17 21.17 21.16 20.1 21.16 21.16 21.16 21.15 21.15 21.15 21.15 21.14 21.14 21.14 20.2 21.13 21.13 21.13 21.13 21.12 21.12 21.12 21.12 21.11 21.11 20*5 21.11 21.10 21.10 21.10 21.10 21.09 21.09 21.09 21.09 21.08 20.4 21.08 21.08 21.08 21.07 21.07 21.07 21.07 21.06 21.06 21.06 20.5 21.05 '21.05 21.05 21.05 21,04 21.04 21.04 21.04 21.03 21.03 20.6 21.03 21.03 21.02 21.02 21.02 21.02 21.01 21.01 21.01 21.00 20.7 21.00 21.00 21.00 20.99 20.99 .20.99 20.99 20.98 20.98 20.98 20.8 20.98 20.97 20.97 20.97 20.96 20.96 20.96 20.96 20.95 20.95 20.9 20.95 20.95 20.94 20.94 20.94 20.94 20.93 20.93 20.93 20.93 21.0 20.92 20.92 20.92 20.91 20.91 20.91 20.91 20,90 20.90 20.90 21.1 20.90 20.89 20.89 20.89 20.89 20.88 20.88 20.88 20.87 20.87 21.2 20.87 20.87 20.-86 20.86 20.86 20.86 20.85 20.85 20.85 20.85 Table IV. The logarithms of the calorific values of 1 liter of oxygen are given for various respiratory quotients, plus the log of sixty minutes. We have taken Zuntz and Schumburg's calorie tables and to the log of the various factors given by them have added the log of 60 in order to change in this single process the time period from one minute to one hour. For example, for a non- protein respiratory quotient of 0.85, the calorific value of 1 liter of APPENDIX 105 oxygen is 4.863, the log of which is 0.68690, and to this is added the log of 60 minutes: Log 4.863 = 0.68690 Log 60 = 1.77815 2.46505 = 0.4651 + 2 Table IV. Calorific Value of One Liter of Oxygen for Various (Non-Protein) Respiratory Quotients together with the Log of the Calorific Value to which is Added the Log of 60 Minutes* R.Q. 0.707 71 .72 .73 .74 .75 .76 .77 .78 .79 .80 .81 .82 .85 84 85 .86 .87 .90 .91 .92 .93 .94 .95 96 .97 .98 .99 Calories for 1 Liter of Oxygen 4.686 4.690 4.702 4.714 4.727 4.739 4.752 4.764 4.776 4.789 4.801 4.813 4.825 4.838 4.850 4.863 4.875 4.887 4.900 4912 4.924 4.936 4.948 4.960 4.973 4.985 4.997 5.010 5.022 5.034 Log Calories P'lus Log 60 2-.4490 4494 4505 4517 4528 4539 4551 4562 4573 4584 4596 4607 4618 4629 4640 4651 4662 4673 4684 4695 4705 4716 4727 4738 4748 4759 4770 4781 4791 4802 1.00 5.047 4813 106 BASAL METABOLIC RATE Table V Du Bois "height-weight chart." 34 APPENDIX I0 7 Table VI. The normal standards for comparison, published by Aub and Du Bois. Table VI. Standards of Normal Metabolism Average Calories Per Hour Per Square Meter of Body Surface (Du Bois). Age (Years) 16-18 18-20 20-30 30-40 40-50 50-60 60-70 70-80 Males Cals. 46.0 43.0 41.0 39.5 39.5 38.5 37.5 36.5 35.5 Log Cals, 1.6628 6335 6128 5966 5966 5855 5740 5623 5502 Females Cals. 43.0 40.0 38.0 37.0 36.5 36.0 35.0 34.0 33.0 Log Cals, 1.6335 6021 5798 5682 5623 5563 5441 5315 5185 Table VII. Four place logarithms. Table VII. Four Place Logarithms. 3456 10 1.00 0.0000 0004 0009 0013 0017 0022 0026 0030 0035 0039 0043 1.01 0043 0048 0052 0056 0060 0065 0069 0073 0077 0082 0086 1.02 0086 0090 0095 0099 0103 0107 0111 0116 0120 0124 0128 1.03 0128 0133 0137 0141 0145 0149 0154 0158 0162 0166 0170 1.04 0170 0175 0179 0183 0187 0191 0195 0199 0204 0208 0212 1.05 0212 0216 0220 0224 0228 0233 0237 0241 0245 0249 0253 1.06 0253 0257 0261 0265 0269 0273 0278 0282 0286 0290 0294 1;07 0294 0298 0302 0306 0310 0314 0318 0322 0326 0330 0334 1.08 0334 0338 0342 0346 0350 0354 0358 0363 0366 0370 0374 1.09 0374 0378 0382 0386 0390 0394 0398 0402 0406 0410 0414 1.10 0.0414 0418 0422 0426 0430 0434 0438 0441 0445 0449 0453 1.11 0453 0457 0461 0465 0469 0473 0477 0481 0484 0488 0492 1.12 0492 0496 0500 0504 0508 0512 0515 0519 0523 0527 0531 1.13 0531 0535 0538 0542 0546 0550 0554 0558 0561 0565 0569 1.14 0569 0573 0577 0580 0584 0588 0592 0596 0599 0603 0607 ,1.15 0607 0611 0615 0618 0622 0626 0630 0633 0637 0641 0645 1.16 0645 0648 0652 0656 0660 0663 0667 0671 0674 0678 0682 1.17 0682 0686 0689 0693 0697 0700 0704 0708 0711 0715 0719 1.18 0719 0722 0726 0730 0734 0737 0741 0745 0748 0752 0755 1.19 0755 0759 0763 0766 0770 0774 0777 0781 0785 0788 0792 1.20 0.0792 0795 0799 0803 0806 0810 0813 0817 0821 0824 0828 1.21 0828 0831 0835 0839 0842 0846 0849 0853 0856 0860 0864 1.22 0864 0867 0871 0874 0878 0881 0885 0888 0892 0896 0899 1.23 0899 0903 0906 0910 0913 0917 0920 0924 0927 0931 0934 1.24 0934 0938 0941 0945 0948 0952 0955 0959 0962 0966 0969 1.25 0969 0973 0976 0980 0983 0986 0990 0993 0997 1000 1004 1.26 1004 1007 1011 1014 1017 102 1 1024 1038 1031 1035 1038 1.27 1038 1041 1045 1048 1052 1055 1059 1062 1065 1069 1072 1.28 1072 1075 1079 1082 , 1086 1089 1092 1096 1099 1103 1106 1.29 1106 1109 1113 1116 1119 1123 1126 1129 1133 1136 1139 1.30 0.1139 1143 1146 1149 1153 1156 1159 1163 1166 1169 1173 1.31 1173 1176 1179 1183 1186 1189 1193 1196 1199 1202 1206 1.32 1206 1209 1212 1216 1219 1222 1225 1229 1232 1235 1239 1.33 1239 1242 1245 1248 1252 1255 1258 1261 1265 1268 1371 1.34 1271 1274 1278 1281 1284 1287 1290 1294 1297 1300 1303 1.35 1303 1307 1310 1313 1316 1319 1323 1326 1329 1332 1335 1.36 1335 1339 1342 1345 1348 1351 1355 1358 1361 1364 1367 1.37 1367 1370 1374 1377 1380 1383 1386 1389 1392 1396 1399 1.38 1399 1402 1405 1408 1411 1414 1418 1431 1424 1427 1430 1.39 1430 1433 1436 1440 1443 1446 1449 1452 1455 1458 1461 1.40 0.1461 1464 1467 1471 1474 1477 1480 1483 1486 1489 1493 1.41 1492 1495 1498 1501 1504 1508 1511 1514 1517 1520 1523 1.42 1523 1526 1529 1532 1535 1538 1541 1544 1547 1550 1553 1.43 1553 1556 1559 1562 1565 1569 1572 1575 1578 1581 1584 1.44 1584 1587 1590 1593 1596 1599 1602 1605 1608 1611 1614 1.45 1614 1617 1620 1623 1626 1629 1632 1635 1638 1641 1644 1.46 1644 1647 1649 1652 1655 1658 1661 1664 1667 1670 1673 1.47 1673 1676 1679 1682 1685 1688 1691 1694 1697 1700 1703 1.48 1703 1706 1708 1711 1714 1717 1720 1723 1726 1729 1732 1.49 1732 1735 1738 1741 1744 1746 1749 1752 1765 1758 1761 108 Table VII. (Con't.) Four Place Logarithms, 3456 10 1.50 0.1761 1764 1767 1770 1772 1775 1778 1781 1784 1787 1790 1.51 1790 1793 1796 1798 1801 1804 1807 1810 1813 1816 1813 1.52 1818 1821 1824 1827 1830 1833 1836 1838 1841 1844 1847 1.53 1847 1850 1853 1855 1858 1861 1864 1867 1870 1872 1875 1.54 1875 1878 1881 1884 1886 1889 1892 1895 1898 1901 1903 1.55 1903 1906 1909 1912 1915 1917 1920 1923 1926 1928 1931 1.56 1931 1934 1937 1940 1942 1945 1948 1951 1953 1956 1959 1.57 1959 1962 1965 1967 1970 1973 1976 1978 1981 1984 1987 1.58 1987 1989 1992 1995 1998 2000 2003 2006 2009 2011 2014 1.59 2014 2017 2019 2022 2025 2028 2030 2033 2036 2038 2041 1.60 0.2041 2044 2047 2049 2052 2055 2057 2060 2063 2066 2068 1.61 2068 2071 2074 2076 2079 2082 2084 2087 2090 2092 2095 1.62 2095 2098 2101 2103 2106 2109 2111 2114 2117 2119 2122 1.63 2122 2125 2127 2130 2133 2135 2138 2140 2143 2146 2148 1.64 2148 2151 2154 2156 2159 2162 2164 2167 2170 2172 2175 1.65 2175 2177 2180 2183 2185 2188 2191 2193 2196 2198 2201 1.66 2201 2204 2206 2209 2212 2214 2217 2219 2222 2225 2227 1.67 2227 2230 2232 2235 2238 2240 2243 2245 2248 2251 2253 1.68 2253 2256 2258 2261 2263 2266 2269 2271 2274 2276 2279 1.69 2279 2281 2284 2287 2289 2292 2294 2297 2299 2302 2304 1.70 0.2304 2307 2310 2312 2315 2317 2320 2322 2325 2327 2330 1.71 2330 2333 2335 2338 2340 2343 2345 2348 2350 2353 2355 1.72 2355 2358 2360 2363 2365 2368 2370 2373 2375 2378 2380 1.73 2380 2383 2385 2388 2390 2393 2395 2398 2400 2403 2405 1.74 2405 2408 2410 2413 2415 2418 2420 2423 2425 2428 2430 1.75 2430 2433 2435 2438 2440 2443 2445 2448 2450 2453 2455 1.76 2455 2458 2460 2463 2465 2467 2470 2472 2475 2477 2480 1.77 2480 2482 2485 2487 2490 2492 2494 2497 2499 2502 2504 1.78 2504 2507 2509 2512 2514 2516 2519 2521 2524 2526 2529 1.79 2529 2531 2533 2536 2538 2541 2543 2545 2548 2550 2553 1.80 0.2553 2555 2558 2560 2562 2565 2567 2570 2572 2574 2577 1.81 2577 2579 2582 2584 2586 2589 2591 2594 2596 2598 2601 1.82 2601 2603 2605 2608 2610 2613 2615 2617 2620 2622 2625 1.83 2625 2627 2629 2632 2634 2636 2639 2641 2643 2646 2648 1.84 2648 2651 2653 2655 2658 2660 2662 2665 2667 2669 2672 1.85 2672 2674 2676 2679 2681 2683 2686 2688 2690 2693 2695 1.86 2695 2697 2700 2702 2704 2707 2709 2711 2714 2716 2718 1.87 2718 2721 2723 2725 2728 2730 2732 2735 2737 2739 2742 1.88 2742 2744 2746 2749 2751 2753 2755 2758 2760 2762 2765 1.89 2765 2767 2769 2772 2774 2776 2778 2781 2783 2785 2788 1.90 0.2788 2790 2792 2794 2797 2799 2801 2804 2806 2803 2810 1.91 2810 2813 2815 2817 2819 2822 2824 2826 2828 2831 2833. 1.92 2833 2835 2838 2840 2842 2844 2847 2849 2851 2853. 2856 1.93 2856 2858 2860 2862 2865 2867 2869 2871 2874 2876 2878 1.94 2878 2880 2882 2885 2887 2889 2891 2894 2896 E898 2900 1.95 2900 2903 2905 2907 2909 2911 2914 2916 2918 2920 2923 1.96 2923 2925 2927 2929 2931 2934 2936 2938 2940 2942 2945 1.97 2945 2947 2949 2951 2953 2956 2958 2960 2962 2964 2967 1.98 2967 2969 2971 2973 2975 2978 2980 2982 2984 2986 2989 1.99 2989 2991 2993 2995 2997 2999 3002 3004 3006 3008 3010 109 no BASAL METABOLIC RATE Table VII. (Con't.) Four Place Logarithms, Interpolation* 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 2.0 0.3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 3222 2 4 6 8 11 2.1 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 3424 2 4 6 8 10 2.2 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 3617 2 4 6 8 10 2.3 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 3802 2 4 5 7 9 2.4 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 3979 2 4 5 7 9 2.5 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 4150 2 3 5 7 9 2.6 4150 4166 4183 4200 4216 4232 4249 4265 4281 42.98 4314 2 3 5 7 8 2.7 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 4472 2 3 5 6 8 2.8 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 4624 2 3 5 6 8 2.9 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 4771 1 3 4 6 7 3.0 0.4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 4914 1 3 4 6 7 3.1 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 5051 1 3 4 6 7 3.2 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 5185 1 3 4 5 7 3.3 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 5315 1 3 4 5 6 3.4 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 5441 1 3 4 5 6 5.5 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 5563 1 2 4 5 6 3.6 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 5682 1 2 4 5 6 3.7 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 5798 1 2 3 5 6 3.8 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 5911 1 2 3 5 6 3.9 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 6021 1 2 3 4 6 4.0 0.6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 6128 1 2 3 4 5 4.1 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 6232 1 2 3 4 5 4.2 6232 6243 6253 6263 6274 6284 6294 -6304 6314 6325 6335 1 2 3 4 5 4.3 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 6435 1 2 3 4 5 4.4 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 6532 1 2 3 4 5 4.5 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 6628 1 2 3 4 5 4.6 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 6721 1 2 3 4 5 4.7 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 6812 1 2 3 4 5 4.8 6812 6821 6830 68J39 6848 6857 6866 6875 6884 6893 6902 1 2 3 4 4 4.9 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 6990 1 2 9 4 4 5.0 0.6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 7076 1 2 3 3 4 5.1 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 7160 1 2 3 3 4 5.2 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 7243 1 2 2 3 4 5.3 7245 7251 7259 7267 7275 7284 7292 7300 7308 7316 7324 1 2 2 3 4 5.4 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 7404 1 2 2 3 4 5.5 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 7482 1 2 2 3 4 5.6 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 7559 1 2 2 3 -4 5.7 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 7634 1 2 2 3 4 5.8 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 7709 1 1 2 3 4 5.9 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 7782 1 1 2 3 4 APPENDIX III Table VII. (Con't.) Four Place Logarithms. Interpolations 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6.0 0.7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 7853 1 1 2 3 4 6.1 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 7924 1 1 2 3 4 6.2 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 7993 1 1 2 3 3 6.3 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 8062 1 1 2 3 3 6.4 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 8129 1 1 2 3 3 6.5 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 8195 1 1 2 3 3 6.6 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 8261 1 1 2 3 3 6.7 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 8325 1 1 2 3 3 6.8 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 8388 1 1 2 3 3 6.9 8388 8395 8401 8407 8414 8420 8426 8452 8439 8445 8451 1 1 2 3 3 7.0 0.8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 8513 1 1 2 2 3 7.1 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 8573 1 1 2 2 3 7.2 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 8633 1 1 2 2 3 7.3 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 8692 1 1 2 2 3 7.4 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 8751 1 1 2 2 3 7.5 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 8808 1 1 2 2 3 7.6 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 8865 1 1 2 2 3 7.7 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 8921 1 1 2 2 3 7.8 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 8976 1 1 2 2 3 7.9 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 9031 1 1 2 2 3 8.0 0.9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 9085 1 1 2 2 3 8.1 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 9138 1 1 2 2 3 8.2 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 9191 1 1 2 2 3 8.3 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 9243 1 1 2 2 3 8.4 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 9294 1 1 2 2 3 8.5 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 9345 1 1 2 2 3 8.6 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 9395 1 1 2 Z 3 8.7 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 9445 1 1 2 2 8.8 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 9494 1 1 2 2 8.9 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 9542 1 1 2 2 9.0 0.9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 9590 1 1 2 2 9.1 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 9638 1 1 2 2 9.2 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 9685 1 1 2 2 9.3 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 9731 1 1 2 2 9.4 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 9777 1 1 2 2 9.b 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 9823 1 1 2 2 9.6 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 9868 1 1 2 2 9.7 9868 9872 9871 9881 9886 9890 9894 9899 9903 9908 9912 1 1 2 2 9.8 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 9956 1 1 2 2 8.9 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 1 1 2 2 INDEX ABSORPTION, carbon dioxid, potash solu- Basal metabolic rate, calculation of, tion for, 81 Air, expired, collection of, in gasometer, 50 outdoor, 41 analysis, Form 4, facing page 112 analysis of, with Haldane gas an- alysis apparatus, 79 room, 41 stratification of, in gasometer, 53 Allen and Du Bois, 88, 89 Analysis, outdoor air, Form 4, facing p. 112 Appendix, 94 Atwater, 12 At water and Benedict, 12, 20, 89 Atwater and Rosa, 12, 89 Aub and Du Bois, 89, 107 Aub and Means, 92 BAROMETER, 49, 95 Barr and Du Bois, 29, 89 Barr, Olmstead, and Du Bois, 92 Barr, Soderstrom, and Du Bois, 24, 93 Basal metabolic rate, body position, 31 calculation of, 82 calories per square meter per hour, 86 carbon dioxid production, 84 checking calculations, 86 correction for water vapor, 83 of barometer to C., 83 in diabetes, 88 non-protein respiratory quo- tient, 87 oxygen absorption, 84 reduction to standard pressure, 83 temperature, 83 respiratory- quotient, 30, 85 8 113 ventilation rate, 84 volume of expired air, 82 character of respiration, 30 definition, 11 effect of body temperature, 29 of sleep, 30 gasometer, 42 and accessory apparatus, 35 general discussion, 11 Haldane gas analysis apparatus, 56 influence of food on, 24 laboratory errors, detection of, 34, 86 muscular activity, 24 normal standards, 14, 107 observer's chart, 32 Form 1, facing p. 112 postabsorptive condition, 24 prediction of, from unit of sur- face area, 14 preliminary rest period, 25 repetition of test, 34 technic, details of, 24 Bell, gasometer, 47, 49 Benedict, 13, 14, 16, 17, 21, 24, 78, 79, 89, 90 Benedict and Atwater, 12, 20, 89 Benedict and Carpenter, 24, 25, 30, 90 Benedict and Cathcart. 90 Benedict and Emmes, 90 Benedict and Harris, 15, 91 on prediction of basal metabolic rate, 15 Benedict and Joslin, 31, 90 Benedict and Murschhausen, 90 Benedict and Roth, 90 Benedict and Smith, 90 Benedict and Talbot, 90 Benedict and Tompkins, 21, 91 114 INDEX Benedict, Emmes, Roth, and Smith, 90 Benedict, Miles, Roth, and Smith, 90 Benedict's unit apparatus for indirect calorimetry, 20 portable, 21 Bibliography, 89-93 Black rubber grease, 81 Body position, 31 temperature, effect of, 29 Boothby, 14, 29, 30, 91 Boothby and Sandiford, 17 Bornstein, Landolt, and Roth, 92, 95 Boyle's law, 83 Buret, Haldane, calibration of, 60 CALCULATION of basal metabolic rate, 82 calories per square meter per hour, 86 carbon dioxid production, 84 checking calculations, 86 correction for water vapor, 83 of barometer to C., 83 non-protein respiratory quo- tient, 87 of diabetic, 88 oxygen absorption, 84 reduction to standard pressure, 83 temperature, 83 respiratory quotient, 85 sheet, Form 2, facing p. 112 ventilation rate, 84 volume of expired air, 82 Calibration of gasometer, 49 of Haldane buret, 60 Calorimeter, respiration, 18 definition of, 18 Calorimetry, clinical, 17 direct, 18 and indirect, agreement between, 20 indirect, 18, 20 and direct, agreement between, 20 closed-circuit type of apparatus, 20 gasometer method, 22 portable unit apparatus, 21 Tissot's gasometer method, 22 Calorimetry, indirect, unit apparatus, 20 Carbon dioxid absorption, potash solu- tion for, 81 of expired air, effect on, from standing in gasometer, 55 Card, summary, Form 3, facing p. 112 Carnegie Institute, 12, 13 Carnegie Nutrition Laboratory, 13 Carpenter, 20, 21, 37, 38, 42, 53, 91 Carpenter and Benedict, 24, 25, 30, 90 Carpenter, Hendry, and Emmes, 35, 91 Cathcart and Benedict, 90 Charles' law, 83 Chart, Du Bois height-weight, 10*6 observer's, 32 Form 1, facing p. 112 Chauveau, 42 Cleaning mercury, 81 solution, 81 Clinical calorimetry, 17 Coleman and Du Bois, 29, 91 Connections, 42 Control tube of Haldane gas analysis apparatus, 68 Gushing, 17 Czerny, 93 DAPPER, 93 Denis and Means, 91 Dennis, 91 Diabetes, calculation of basal metabolic rate in, 88 Douglas and Haldane, 30, 91 Douglas valves, 38 Du Bois, 13, 14, 15, 17, 25, 86, 91, 106, 107 Du Bois and Allen, 88, 89 Du Bois and Aub, 89 Du Bois and Barr, 29, 89 Du Bois and Coleman, 29, 91 Du Bois and Du Bois, 14, 16, 91 Du Bois and Du Bois' formula for de- termination of surface area, 14, 106 Du Bois and Gephart, 20, 91 Du Bois and Lusk, 13, 20 Du Bois height-weight chart, 106 Du Bois, Meyer, and Soderstrom, 31, 93 INDEX Du Bois, Olmstead, and Barr, 92 Du Bois, Sawyer, and Stone, 93 Du Bois, Soderstrom, and Barr, 24, 93 Du Bois, Soderstrom, and Meyer, 31 EDSALL, 17 Electric glass cutter, 66 Emmes and Benedict, 90 Emmesand Riche, 31, 91 Emmes, Benedict, Roth, and Smith, 90 Emmes, Hendry, and Carpenter, 35, 91 Expired air, collection of, in gasometer, 50 Explanation of tables, 94 FILLING Haldane gas analysis appa- ratus, 77 Food, influence of, on basal metabolic rate, 24 Formula, Du Bois and Du Bois', for determination of surface area, 14 Meeh's, for determination of surface area, 14 GEPHART and Du Bois, 20, 91 Gas analysis apparatus, Haldane, 56 analysis of outdoor air, 78 of room air, 41 assembling, 65 care, 73 control tube, 68 description of, 56 filling, 77 management, 69 analysis, 72 preliminary, 69 sampling, 70 shaker, 79 Gasometer, 42 and accessory apparatus, 35 bell, 47 calibration of, 49 collection of expired air in, 50 construction of, 47 cross-section of, 43 Gasometer, effect on carbon dioxid of expired air from standing in, 55 on oxygen content of expired air from standing in, 55 method of indirect calorimetry, 22 movable, 46 room, 45 stationary, 44 stratification of air in, 53 Glass cutter, electric, 66 Grease, black rubber, 81 HALDANE, 56, 63, 65, 74, 78, 80, 91 Haldane and Douglas, 30, 91 Haldane buret, calibration of, 60 gas analysis apparatus, 56 analysis of outdoor air, 78 assembling, 65 care, 73 control tube, 68 description, 56 filling, 77 management, 69 analysis, 72 preliminary, 69 sampling, 70 shaker, 79 potassium pyrogallate solution, 80 Harris and Benedict, 15, 91 on prediction of basal metabolic rate, 15 Height-weight chart, Du Bois, 106 Hendry, Carpenter, and Emmes, 35, 91 Higgins and Means, 91 Howland, 20, 91 Huntington, 92 INTAKE pipe, 41 JOHANSSON, 31, 92 Joslin and Benedict, 31, 90 KRAUS, 93 Krogh, 20, 92 Krogh and Lindhard, 52, 92 n6 INDEX LABORATORY errors, detection of, 34, 86 Landolt, Bornstein, and Roth, 92, 95 Laplace and Lavoisier, 92 Lavoisier, 11, 24 on physiologic importance of oxygen, 11 Lavoisier and Laplace, 92 Lavoisier and Seguin, 92 Law, Boyle's, 83 Charles', 83 Lindhard and Krogh, 52, 92 Little, 45 Loewi, 93 Lusk, 13, 20, 24, 29, 89, 92 Lusk and Du Bois, 13, 20 Lusk and Williams, 13 Lusk, Williams, and Riche, 93 MAGNUS-LEVY, 87, 92, 93 Mask, 35 Matthes, 93 Means, 14, 17, 92 Means and Aub, 92 Means and Denis, 91 Means and Higgins, 91 Meeh, 14, 92 Meeh's formula for determination of surface area, 14 Mercury, cleaning, 81 Metabolic rate, basal, 11. See also Basal metabolic rate. Meyer, Du Bois, and Soderstrom, 31 Meyer, Soderstrom, and Du Bois, 93 Miles, Benedict, Roth, and Smith, 90 Mohr, 93 Movable gasometer, 46 Murschhausen and Benedict, 90 Muscular activity, 24 NEUBERG, 93 OBSERVER'S chart, 32 Form 1, facing p. 112 Olmstead, Barr, and Du Bois, 92 Outdoor air, 41 Outdoor air analysis, Form 4, facing p. 112 Oxygen content of expired air, effect on, from standing in gasometer, 55 PETTENKOFER, 12, 92 Pettenkofer and Voit, 12, 92 Pipe, intake, 41 Plummer, 18 Position, body, 31 Postabsorptive condition, 24 Potash solution for carbon dioxid ab- sorption, 81 Potassium pyrogallate solution, 80 REGNAULT and Reiset, 11, 92 Reiset and Regnault, 11, 92 Repetition of test, 34 Respiration calorimeter, 18 definition, 18 character of, 30 Respiratory exchange, Tissot's gasom- eter method of determining, 42 Rest period, preliminary, 25 Riche and Emmes, 91 Riche and Soderstrom, 93 Riche, Williams, and Lusk, 93 Rinsing connections, 69 Room air, 41 gasometer, 45 Rosa and At water, 12, 89 Roth and Benedict, 90 Roth, Benedict, Emmes and Smith, 90 Roth, Benedict, Miles and Smith, 90 Roth, Landolt, a^nd Bornstein, 92, 95 Rubber flutter valve, 39 Rubner, 12, 14, 20, 93 Russell and Williamson, 68, 93 Russell Sage Institute of Pathology, 13 SALOMON, 93 Sampling tubes, 52 Sandiford and Boothby, 17 Sawyer, Stone, and Du Bois, 93 Schmidt, 93 INDEX 117 Schumburg and Zuntz, 93, 104 Seguin and Lavoisier, 92 Shaker, 79 Sheet, calculation, Form 2, facing p. 112 Sleep, effect of, 30 Smith and Benedict, 90 Smith, Benedict, Emmes, and Roth, 90 Smith, Benedict, Miles and Roth, 90 Soderstrom and Riche, 93 Soderstrom, Barr, and Du Bois, 24, 93 Soderstrom, Meyer, and Du Bois, 31, 93 Solution, cleaning, 81 potash, for carbon dioxid absorption, 81 potassium pyrogallate (Haldane), 80 Solutions, 80 Standards, normal, 14, 107 Steinitz, 93 Stone, Sawyer, and Du Bois, 93 Stratification of air in gasometer, 53 Strauss, 93 Summary card, Form 3, facing p. 112 TABLE I, explanation of, 94 Table II, explanation of, 94-103 Table III, explanation of, 103, 104 Table IV, explanation of, 104, 105 Table V, explanation of, 106 Table VI, explanation of, 107 Table VII, explanation of, 107-111 Tables, explanation of, 94 Talbot and Benedict, 90 Temperature, body, effect of, 29 Test, repetition of, 34 Tissot, 17, 22, 42, 93 Tissot's gasometer method of deter- mining respiratory change, 42 of indirect calorimetry, 22 Tompkins and Benedict, 21, 91 Tube, control, of Haldane gas analysis apparatus, 68 Tubes, sampling, 52 UNIT apparatus for indirect calorim- etry, 20 portable, for indirect calorimetry, 21 VALVE, rubber flutter, 39 Valves, 37 Douglas, 38 Voit, 12 Voit and Pettenkofer, 12, 92 Von Noorden, 93 WASHING connections, 69 Weintraud, 93 Williams, 93 Williams and Lusk, 13 Williams, Riche, and Lusk, 93 Williamson and Russell, 68, 93 ZUNTZ and Schumburg, 93, 104 UNIVERSITY OF CALIFORNIA Medical Center Library THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW Books not returned on time are subject to fines according to the Library Lending Code. 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