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 principal data regarding the analyses 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 analyses are recorded in the lower left-hand
corner: first the weight of the water absorbed from 10 liters of air
passing 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 assumption 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.
----- | ------
(b) 19706 = 1.57 l. CO_{2} | " O + N = 691.56 l.
| " N = 552.96 l.
| ------
| " O = 186.57 l.
|
ABBREVIATED METHOD OF COMPUTATION OF OXYGEN ADMITTED TO THE CHAMBER FOR
USE DURING SHORT EXPERIMENTS.
Desiring to make the apparatus as practicable and the calculations as
simple as possible, a scheme of calculation has been devised whereby the
computations may be very much abbreviated and at the same time there is
not too great a sacrifice in accuracy. The loss in weight of the oxygen
cylinder has, in the more complicated method of computation, been
considered as due to oxygen and about 3 per cent of nitrogen. The amount
of nitrogen thus admitted has been carefully computed and its volume
taken into consideration in calculating the residual oxygen. If it is
considered for a moment that the admission of gas out of the steel
cylinder is made at just such a rate as to compensate for the decrease
in volume of the air in the system due to the absorption of oxygen by
the subject, it can be seen that if the exact volume of the gas leaving
the cylinder were known it would be immaterial whether this gas were
pure oxygen, oxygen with some nitrogen, or oxygen with any other inert
gas not dangerous to respiration or not absorbed by sulphuric acid or
potash-lime. If 10 liters of oxygen had been absorbed by the man in the
course of an hour, to bring the system back to constant apparent volume
it would be necessary to admit 10 liters of such a gas or mixture of
gases, assuming that during the hour there had been no change in the
temperature, the barometric pressure, or the residual amounts of carbon
dioxide or water-vapor.
Under these assumed conditions, then, it would only be necessary to
measure the amount of gas admitted in order to have a true measure of
the amount of oxygen absorbed. The measure of the volume of the gas
admitted may be used for a measure of the oxygen absorbed, even when it
is necessary to make allowances for the variations in the amount of
carbon dioxide or water-vapor in the chamber, the temperature, and
barometric pressure. From the loss in weight of the oxygen cylinder, if
the cylinder contained pure oxygen, it would be known that 10 liters
would be admitted for every 14.3 grams loss in weight.
From the difference in weight of 1 liter of oxygen and 1 liter of
nitrogen, a loss in weight of a gas containing a mixture of oxygen with
a small per cent of nitrogen would actually represent a somewhat larger
volume of gas than if pure oxygen were admitted. The differences in
weight of the two gases, however, and the amount of nitrogen present are
so small that one might almost wholly neglect the error thus arising
from this admixture of nitrogen and compute the volume of oxygen
directly from the loss in weight of the cylinder.
As a matter of fact, it has been found that by increasing the loss in
weight of the cylinder of oxygen containing 3 per cent nitrogen by 0.4
per cent and then converting this weight to volume by multiplying by
0.7, the volume of gas admitted is known with great accuracy. This
method of calculation has been used with success in connection with the
large chamber and particularly for experiments of short duration. It has
also been introduced with great success in a portable type of apparatus
described elsewhere.[27] Under these conditions, therefore, it is
unnecessary to make any correction on the residual volume of nitrogen as
calculated at the beginning of the experiment. When a direct comparison
of the calculated residual amount of oxygen present is to be made upon
determinations made with a gas-analysis apparatus the earlier and much
more complicated method of calculation must be employed.