Liters.

Volume of the chair calorimeter chamber (without fixtures) 1360.0 Permanent fixtures (5); chair and supports (8) 13.0 ------ Apparent volume of air inside chamber 1347.0 Air in pipes, blower, and valves to surface of acid in first acid vessel 4.5 ------ Apparent volume of air containing water-vapor 1351.5 Air above surface of acid in first sulphuric-acid vessel and potash-lime can 16.0 ------ Apparent volume of air containing carbon dioxide 1367.5 Air in potash-lime can, second sulphuric-acid vessel and connections, sodium-bicarbonate cans, and pipes to calorimeter chamber 23.5 ------ Apparent volume of air containing carbon dioxide, water, oxygen, and nitrogen 1391.0

These volumes represent conditions existing inside the chamber without the subject, _i. e._, conditions under which an alcohol check-test would be conducted. In an experiment with man it would be necessary to deduct the volume of the man, books, urine bottles, and all supplemental apparatus and accessories. Under these circ.u.mstances the apparent volume of the air in the chamber may at times be diminished by nearly 90 to 100 liters. At the beginning of each experiment the apparent volume of air is calculated.

RESIDUAL a.n.a.lYSES.

CALCULATION FROM RESIDUAL a.n.a.lYSES.

The increment in weight of the absorbers for water and carbon dioxide and the loss in weight of the oxygen cylinder give only an approximate idea of the amounts of carbon dioxide and water-vapor produced and oxygen absorbed during the period, and it is necessary to make correction for change in the composition of the air as shown by the residual a.n.a.lyses and for fluctuations in the actual volume. In order to compute from the a.n.a.lyses the total carbon-dioxide content of the residual air, it is necessary to know the relation of the air used for the sample to the total volume, and thus we must know accurately the volume of air pa.s.sing through the gas-meter.

In the earlier apparatus 10-liter samples were used, and the volume of the respiration chamber was so large that it was necessary to multiply the values found in the residual sample by a very large factor, 500.

Hence, the utmost caution was taken to procure an accurate measurement of the sample, the exact amounts of carbon dioxide absorbed, and water-vapor absorbed. To this end a large number of corrections were made, which are not necessary with the present type of apparatus with a volume of residual air of but about 1,300 liters, and accordingly the manipulation and calculations have been very greatly simplified.

While formerly pains were taken to obtain the exact temperature of the air leaving the gas-meter, with this apparatus it is unnecessary. When the earlier type of apparatus was in use there were marked changes in the temperature of the calorimeter laboratory and in the water in the meter which were naturally prejudicial to the accurate measurement of the volume of samples, but with the present control of temperature in this laboratory it has been found by repeated tests that the temperature of the water in the meter does not vary a sufficient amount to justify this painstaking measurement and calculation. Obviously, this observation also pertains to the corrections for the tension of aqueous vapor. It has been found possible to a.s.sume an average laboratory temperature and reduce the volume as read on the meter by means of a constant factor.

The quant.i.ty of air pa.s.sing through the meter is so adjusted that exactly 10 liters as measured on the dial pa.s.s through it for one a.n.a.lysis. The air as measured in the meter is, however, under markedly different conditions from the air inside the respiration chamber. While there is the same temperature, there is a material difference in the water-vapor present, and hence the moisture content as expressed in terms of tension of aqueous vapor must be considered. This obviously tends to diminish the true volume of air in the meter.

Formerly we made accurate correction for the tension of aqueous vapor based upon the barometer and the temperature of the meter at the end of the period, but it has now been found that the reduction of the meter readings to conditions inside of the chamber can be made with a sufficient degree of accuracy by multiplying the volume of air pa.s.sing through the meter by a fraction, _(h-t)/h_, in which _h_ represents the barometer and _t_ the tension of aqueous vapor at the temperature of the laboratory, 20 C. Since the tension of aqueous vapor at the laboratory temperature is not far from 15 mm., a simple calculation will show that there may be considerable variations in the value of _h_ without affecting the fraction materially, and we have accordingly a.s.sumed a value of _h_ as normally 760 mm., and the correction thus obtained is (760 - 15)/760 = 0.98, and all readings on the meter should be multiplied by this fraction.

On the one hand, then, there is the correction on the meter itself, which correction is +1.4 per cent (see page 75); and on the other hand the correction on the sample for the tension of aqueous vapor, which is -2.0 per cent, and consequently the resultant correction is -0.6 per cent. From the conditions under which the experiments are made, however, it is rarely possible to read the meter closer than 0.05 liter, as the graduations on the meter correspond to 50 cubic centimeters. It will be seen, then, that this final correction is really inside the limit of error of the instrument, and consequently with this particular meter now in use no correction whatever is necessary for the reduction of the volume. The matter of temperature corrections has been taken up in great detail in an earlier publication, and where there are noticeable differences in temperature between the meter and the calorimeter chamber the calculation is very much more complicated.

For practical purposes, therefore, we may a.s.sume that the quant.i.ty of air pa.s.sed through the meter, as now in use, represents exactly 10 liters measured under the conditions obtaining inside of the respiration chamber, and in order to find the total amount of water-vapor present in the chamber it is necessary only to multiply the weight of water found in the 10-liter sample by one-tenth of the total volume of air containing water-vapor.

The total volume of air which contains water-vapor is not far from 1,360 liters; consequently multiplying the weight of water in the sample by 136 gives the total amount of water in the chamber and the piping. The volume of air containing carbon dioxide is that contained in the chamber and piping to the first sulphuric-acid vessel plus 16 liters of air above the sulphuric acid and connections in the first porcelain vessel, and in order to obtain the amount of carbon dioxide from the sample it is only necessary to multiply the weight of carbon dioxide in the sample by 137.6.

Since in the calculation of the total amount of residual oxygen volumes rather than weights of gases are used, it is our custom to convert the weights of carbon dioxide and water-vapor in the chamber to volumes by multiplying by the well-known factors. The determination of oxygen depends upon the knowledge of the true rather than the apparent volume of air in the system, and consequently the apparent volume must be reduced to standard conditions of temperature and pressure each time the calculation is made. To this end, the total volume of air in the inclosed circuit (including that in the tension-equalizer, amounting to 1,400 liters in all) is reduced to 0 and 760 millimeters by the usual methods of computation. The total volume of air (which may be designated as _V_) includes the volumes of carbon dioxide, water-vapor, oxygen, and nitrogen. From the calculations mentioned above, the volumes of water-vapor and carbon dioxide have been computed, and deducting the sum of these from the reduced volume of air gives the volume of oxygen plus nitrogen. If the volume of nitrogen is known, obviously the volume of oxygen can be found.

At the beginning of the experiment, it is a.s.sumed that the chamber is filled with ordinary air. By calculating the amount of nitrogen in the chamber at the start as four-fifths of the total amount, no great error is introduced. In many experiments actual a.n.a.lyses of the air have been made at the moment of the beginning of the experiment. The important thing to bear in mind is that having once sealed the chamber and closed it tightly, no nitrogen can enter other than that admitted with the oxygen, and hence the residual amount of nitrogen remains unaltered save for this single exception. If care is taken to keep an accurate record of the amount of nitrogen admitted with the oxygen, the nitrogen residual in the chamber at any given time is readily computed. While from an absolute mathematical standpoint the accuracy of this computation can be questioned, here again we are seeking an accurate record of differences rather than an absolute amount, and whether we a.s.sume the volume of the air in the chamber to contain 20.4 per cent of oxygen or 21.6 per cent is a matter of indifference. It is of importance only to note the increases in the amount of nitrogen, since these increases represent decrease in the residual oxygen and it is with the changes in the residual oxygen that we particularly have to do.

INFLUENCE OF FLUCTUATIONS IN TEMPERATURE AND PRESSURE ON THE APPARENT VOLUME OF AIR IN THE SYSTEM.

The air, being confined in a s.p.a.ce with semi-rigid walls, is subjected naturally to variations in true volume, depending upon the temperature and barometric pressure. If the air inside of the chamber becomes considerably warmer there is naturally an expansion, and were it not for the tension-equalizer there would be pressure in the system. Also, if the barometer falls, there is an expansion of air which, again, in the absence of the tension-equalizer, would produce pressure in the system.

It is necessary, therefore, in calculating the true volume of air, to take into account not only the apparent volume, which, as is shown above, is always a constant amount at the end of each period, but the changes in temperature and barometric pressure must also be noted. Since there is a volume of about 1,400 liters, a simple calculation will show that for each degree centigrade change in temperature there will be a change in volume of approximately 4.8 liters. In actual practice, however, this rarely occurs, as the temperature control is usually inside of 0.1 C. and for the most part within a few hundredths. A variation in barometric pressure of 1 millimeter will affect 1,400 liters by 1.8 liters.

In actual practice, therefore, it is seen that if the barometer falls there will be an expansion of air in the system. This will tend to increase the volume by raising the rubber diaphragm on the tension-equalizer, the ultimate result of which is that at the final filling with oxygen at the end of the period less is used than would be the case had there been no change in the barometer. In other words, for each liter expansion of air inside of the system, there is 1 liter less oxygen required to bring the apparent volume the same at the end of the period. Similarly, if there is an increase in temperature of the air, there is expansion, and a smaller amount of oxygen is required than would be the case had there been no change; and conversely, if the barometer rises or the temperature falls, more oxygen would be supplied than is needed for consumption. It is thus seen that the temperature and barometer changes affect the quant.i.ty of oxygen admitted to the chamber.

INFLUENCE OF FLUCTUATIONS IN THE AMOUNTS OF CARBON DIOXIDE AND WATER-VAPOR UPON RESIDUAL OXYGEN.

Any variations in the residual amount of carbon dioxide or water-vapor likewise affect the oxygen. Thus, if there is an increase of 1 gram in the amount of residual carbon dioxide, this corresponds to 0.51 liter, and consequently an equal volume of oxygen is not admitted to the chamber during the period, since its place has been taken by the increased volume of carbon dioxide. A similar reasoning will show that increase in the water-vapor content will have a similar effect, for each gram of water-vapor corresponds to 1.25 liters and therefore influences markedly the introduction of oxygen. All four of the factors, therefore (barometric pressure, temperature, residual carbon dioxide, and residual water-vapor), affect noticeably the oxygen determination.

CONTROL OF RESIDUAL a.n.a.lYSES.

Of the three factors to be determined in the residual air, the oxygen (which is most important from the standpoint of the relative weight to be placed upon the a.n.a.lysis) unfortunately can not be directly determined without great difficulty. Furthermore, any errors in the a.n.a.lysis may be very greatly multiplied by the known errors involved in the determination of the true volume of the air in the chamber as a result of the difficulties in obtaining the average temperature of the air. Believing that the method of a.n.a.lysis as outlined above should be controlled as far as possible by other independent methods, we were able to compare the carbon dioxide as determined by the soda-lime method with that obtained by the extremely accurate method used by Sonden and Pettersson. An apparatus for the determination of carbon dioxide and oxygen on the Pettersson principle has been devised by Sonden and constructed for us by Grave, of Stockholm.

In the control experiments, the air leaving the mercury valve D (fig.

30, page 66) was caused to pa.s.s through a T-tube, one arm of which connected directly with the sampling pipette of the Sonden gas-a.n.a.lysis apparatus, the other arm connecting with the U-tubes for residual a.n.a.lyses. By lowering and raising the mercury reservoir on the gas-a.n.a.lysis apparatus, a sample of air could be drawn into the apparatus for a.n.a.lysis. The results of the a.n.a.lysis were expressed on the basis of moist air in volume per cents rather than by weight, as is done with the soda-lime method. Hence in comparison it was necessary to convert the weights to volume, and during this process the errors due to not correcting for temperature and barometer are made manifest. However, the important point to be noted is that whatever fluctuations in composition of the residual air were noted by the soda-lime method, similar fluctuations of a corresponding size were recorded by the volumetric a.n.a.lysis with the Sonden apparatus. Under these conditions, therefore, we believe that the gravimetric method outlined above is sufficiently satisfactory, so far as the carbon-dioxide content is concerned, for ordinary work where there are no wide variations in the composition of the air from period to period.

NITROGEN ADMITTED WITH THE OXYGEN.

It is impossible to obtain in the market absolutely chemically pure oxygen. All the oxygen that we have thus far been able to purchase contains nitrogen and, in some instances, measurable amounts of water-vapor and carbon dioxide. The better grade of oxygen, that prepared from liquid air, is practically free from carbon dioxide and water-vapor, but it still contains nitrogen, and hence with every liter of oxygen admitted there is a slight amount of nitrogen added. This amount can readily be found from the gasometric a.n.a.lysis of the oxygen and from the well-known relation between the weight and the volume of nitrogen the weight can be accurately found. This addition of nitrogen played a very important role in the calculation of the oxygen consumption as formerly employed. As is seen later, a much abbreviated form of calculation is now in use in which the nitrogen admitted with the oxygen does not influence the calculation of the residual oxygen.

REJECTION OF AIR.

In long-continued experiments, where there is a possibility of a noticeable diminution in the percentage of oxygen in the chamber--a diminution caused either by a marked fall in barometer, which expands the air inside of the chamber and permits admission of less oxygen than would otherwise be required, or by the use of oxygen containing a high percentage of nitrogen, thus continually increasing the amount of nitrogen present in the system--it is highly probable that there may be such an acc.u.mulation of nitrogen as to render it advisable to provide for the admission of a large amount of oxygen to restore the air to approximately normal conditions. In rest experiments of short duration this is never necessary. The procedure by which such a restoration of oxygen percentage is accomplished has already been discussed elsewhere.[25] It involves the rejection of a definite amount of air by allowing it to pa.s.s into the room through the gas-meter and then making proper corrections for the composition of this air, deducting the volume of oxygen in it from the excess volume of oxygen introduced and correcting the nitrogen residual in order to determine the oxygen absorption during the period in which the air has been rejected.

INTERCHANGE OF AIR IN THE FOOD-APERTURE.

The volume of air in the food-aperture between the two gla.s.s doors is approximately 5.3 liters. When the door on the inside is opened and the material placed in the food-aperture and the outer door is subsequently opened, there is by diffusion a pa.s.sage outward of air of the composition of the air inside of the chamber, and the food-aperture is now filled with room air. When the inner door is again opened this room air enters the chamber and is replaced by air of the same composition as that in the chamber. It is seen, then, that there may theoretically be an interchange of air here which may have an influence on the results.

In severe work experiments, where the amount of carbon dioxide in the air is enormously increased, such interchange doubtless does take place in measurable amounts and correction should undoubtedly be made. In ordinary rest experiments, where the composition of the air in the chamber is much more nearly normal, this correction is without special significance. Furthermore, in the two forms of calorimeter now in use, the experiments being of but short duration, provision is made to render it unnecessary to open the food-aperture during the experiment proper.

Consequently at present no correction for interchange of air in the food-aperture is made, and for the same reason the slight alteration in volume resulting from the removal or addition of material has also not been considered here.

USE OF THE RESIDUAL BLANK IN THE CALCULATIONS.

To facilitate the calculations and for the sake of uniformity in expressing the results, a special form of blank is used which permits the recording of the princ.i.p.al data regarding the a.n.a.lyses of air in the chamber at the end of each period. Thus at the head of the sheet are recorded the time, the number of the period, kind of experiment, the name or initials of the subject, and the statement as to which calorimeter is used. The barometer recorded in millimeters is indicated in the column at the left and immediately below the heading, together with the temperature of the calorimeter as expressed in degrees centigrade. The temperature of the calorimeter as recorded by the physical observer is usually expressed in the arbitrary scale of the Wheatstone bridge and must be transposed into the centigrade scale by means of a calibration table.

The apparent air-volumes in the subsections of the ventilating system are recorded under the headings I, which represents the volume of air containing water-vapor and therefore is the air in the chamber plus the air in the piping to the surface of the acid in the first sulphuric-acid absorber; I-II, which represents the air containing carbonic acid and includes volume I plus the volume of the air in the first sulphuric-acid vessel and the volume of air in the potash-lime absorber; I-III, which includes the total confined volume of the whole system, since this air contains both oxygen and nitrogen. These volumes change somewhat, depending upon the size of the body of the subject, the volume of the materials taken into the chamber, and the type of calorimeter.

The data for the residual a.n.a.lyses are recorded in the lower left-hand corner: first the weight of the water absorbed from 10 liters of air pa.s.sing through the meter; to the logarithm of this is added the logarithm of volume I; the result is the logarithm of the total weight of water-vapor in the ventilating air-current. To convert this into liters the logarithmic factor 09462[26] is added to the logarithm of the weight of water and (_a_) is the logarithm of water expressed in liters.

A similar treatment is accorded the weight of carbon dioxide absorbed from the air-sample, (_b_) being ultimately the logarithm of the volume of carbon dioxide.

In order to determine the total volume of air in the chamber under standard conditions of temperature and pressure, to the logarithm of volume I-III is added, first, a logarithmic factor for the temperature recorded for the calorimeter to correct the volume of air to standard temperature. As the temperature fluctuations are all within 1 degree, a table has been prepared giving the standard fluctuation represented by the formula

1 ----- 1 + _at_

in which _t_ is the temperature of the calorimeter. The correction for pressure has also been worked out in a series of tables and the logarithmic factor here corresponds to the ratio _p_/760, in which _p_ is the observed barometer. The logarithm of the total volume is recorded as a result of the addition of these three logarithms enumerated, and from this logarithm is expressed the total volume of air in liters.

Deducting the sum of the values (_a_) and (_b_) from the total volume leaves the volume of oxygen plus nitrogen.

The calculation of the residual volume of nitrogen and the record of the additions thereto was formerly carried out with a refinement that to-day seems wholly unwarranted when other factors influencing this value are taken into consideration. For the majority of experiments the residual volume of nitrogen may be considered as constant in spite of the fact that some nitrogen is regularly admitted with the oxygen. The significance of this a.s.sumption is best seen after a consideration of the method of calculating the amount of oxygen admitted to the chamber.

RESIDUAL SHEET No. 1.

Calculation of residual amounts of nitrogen, oxygen, carbon dioxide and water-vapor remaining in chamber at 8.10 A. M., June 24, 1909.

Residual at end of Prelim. period. Exp.: Parturition. No.........

Subject: Mrs. Whelan. Calorimeter: Bed.

-------------------------------------------+------------------------------- Barometer, 756.95 mm.

Miscellaneous Calculations Temp. cal., 20.08 C

875 48.65 -------------------------------------------+ 164.55 25.9

------ 90.

Apparent Volume of Air

710.46 ------

4.6 164.55 I containing H_{2}O 715. liters

------ I-II " CO_{2} 781. "

715.0 I I-III " O+N 755. "

14 -------------------------------------------+ ------ Log. wt. H_{2}O to residual

781.0 I-II .0815 = 91116

24 Log. I = 85431

------ -----

755.0 I-III 76547 = 5.88 gms. H_{2}O +----------------------------- Gms. to liters, 09462

(a) 7.26 l.

-----

(b) 1.57 l.

(a) 86909 = 7.25 l. H_{2}O

-----

8.82 = l. CO_{2} + H_{2}O

Log. wt. CO_{2} in residual

Log. I-III = 87796 .0438 = 62634

" temp. = 96912 Log. I-II = 84392

" pressure = 99856 -----

------ 49026 = 3.09 gms. CO_{2}

Total volume 84588 = 700.37 l.

Gms. to liters, 70680

Volume CO_{2} + H_{2}O = 8.82 l.