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I have shown (p. 65) that the error introduced by this uncertainty is in any case small, more especially so as the results are deduced from differences in the ordinates. The most probable position appears to me to be about midway between the points of intersection of the 2-cell line with the other lines; but as it is improbable that the position of the point would vary capriciously as the temperature rose, I have selected points on the smoothed curve (called the "null-point curve") which passes most nearly through the various inter
It will be noticed that the null-point curve approaches more nearly to the outside temperature as the value of 0, increases *. This indicates either (1) that the work done by the stirrer had diminished (this would probably be due to diminished viscosity or surface friction); or (2) that the loss by convection, &c., had increased. The former is I think the more probable explanation.
When the depth of the liquid is increased, the stirrer has more work to do and the supply of heat is greater while the loss remains unchanged. The null point therefore is at a higher elevation when the mass is greater, and Pl. I. shows that ON-06 is nearly proportional to the depth, i. e. to the mass, of the contained liquid.
In order to illustrate the method of applying the various corrections, and also to indicate their comparative magnitude, 1 give in full (Table III.) the working out of experiment 26, of which the details were given in Table II. The numbers in Roman numerals indicate the sections on the preceding pages, in which the particulars of the correction are given. The greatest correction is that given by the calibration of the bridge-wire, and this can be applied with great certainty.
I do not consider it necessary to crowd this paper with similar details regarding the remaining experiments. Table IV. (pp. 71, 72) is a summary in which I have given the numbers necessary for the remaining calculations.
* This curvature is more marked than would at first sight appear from an inspection of Plate I. Owing to the difference in the temperature coefficient of the two differential thermometers, the true bridge null point is given by the expression 59.84+0003 01, where 6, is the temperature of the thermometers. The position of the bridge null point is shown by the vertical lines on the left,
Showing the Corrections necesssary for the Reduction of
Since the points thus found should lie on a straight line, the best result is arrived at by treating the results so as to obtain 2 points only. If we mean A and B, and again B and C, we attach undue value to B. The true mean is obtained by
We thus get::
plotting) the values of
Mean value of
We can thus obtain (either
at B.W. readings
arithmetically or by
Now the value of R, near found to be 8.46093 true ohms. due to a potential-difference of hence correction to R-8.5000 is Hence
de at B.W. readings
the null point" (about 62.5 b.w.) was
The value of having been ascertained as above indi
cated, the capacity for heat of calorimeter and contents is easily deduced.
The operations are shown in Table V.
Col. I. gives the temperature of the null point in degrees C. of the air-thermometer (from Table IV.). II. the rate of rise at the null point as deduced from the group of experiments at that temperature (from Table IV.).
III. the value of the mean centimetre of the bridgewire at the temperature of the null point, denoted by Co.
IV. gives the rate of rise when R=1 true ohm and the potential-difference 1 volt (e=1.4342, e2=2·0570), expressed in degrees C. of the air-thermometer. The value of R' used in this reduction is 8.4966 instead of the 8.5 ohms which was selected as a convenient arbitrary value of R' in the reductions in Table IV. The two wires connecting the roof of the calorimeter with the steel lid had a total resistance of 0068 ohm. We may assume that half the heat generated in these wires passed into the steel lid, and half into the calorimeter. We may therefore consider their resistance as 0034 ohm=r. Now the points which were kept at a constant P.D. were at the lid of the calorimeter and between these wires and the coil. The equa
tion is J.H.= R(1+1); hence the effective
V. gives the reciprocals of the numbers in Col. IV. VI. The value of J is assumed as 4-198 *. The numbers in this column give the capacity for heat of calorimeter and contents expressed in terms of "a thermal unit at 15° C." The results when plotted as ordinates, with 1 as abscissa, are shown in Plate II (a).