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calorimeter all signs of polarization disappeared, and the insulation of the coil was very perfect.
I will now describe the method of conducting an experiment. The tank was first brought to the desired temperature, and the experiment was not proceeded with until the tank-temperature had had time to become steady. Freshly distilled ether was then introduced into the silver flask, and dried air passed through it (the stirrer in the surrounding aniline being continually at work) until the whole of the ether was evaporated. The taps connected with the silver flask were then closed, the key inserted in the storage-circuit, the connexion with the Clark cells made, and the rheochord adjusted until the potential difference at the ends of the coil was shown by the highresistance galvanometer to be equal to that of the Clark cells used. Three or four of these cells were placed in parallel arc, and the files thus formed in series: therefore, when using an electromotive force of 4 Clark cells, we had really in use 12 or 16.
Throughout an experiment the attention of my assistant * was directed to keeping the potential balance as even as possible. I meanwhile had to observe and mark the time of transit across the graduations of the bridge-wire. A reversingkey was maintained at a constant period of oscillation (about twice per second), and as the temperature rose the oscillations of a dead-beat galvanometer mirror (which were viewed through a telescope fitted with a micrometer-scale) steadily diminished, and the moment when they ceased could, to my surprise, be determined with great accuracy. By pressing a key, the time was recorded on the chronograph tape.
The mercury-thermometer inserted in the walls of the steel chamber was observed at regular intervals, any alteration. noted, and a correction afterwards applied to the bridge-wire reading the value of each division of the bridge-wire in terms of a millimetre of the thermometer-scale being known. The time of each 1000 revolutions of the stirrer was automatically recorded on the tape, thus the only notes that had to be taken during an experiment were of the changes of the mercury-thermometer. The chronograph was one of somewhat novel construction, for which I am indebted to Mr. E. A. Pochin. It was worked by a water motor, had a triple set of recording hammers, and was controlled by an electric clock which was compared at regular intervals with a "rated"
*I take this opportunity of returning my thanks to Mr. C. Green, Scholar of Sydney College, Cambridge, for his able assistance during these experiments.
Dent's chronometer, but as the greatest gain in rate observed was less than 1 in 12,000, no correction was necessary.
I find it impossible to give a detailed record of the observations, as it would fill a volume. I therefore propose to give an example in full of one of the experiments by drawing at random one of the leaves from the mass of records.
Aniline Exp. No. 26: 4 cells. July 28th.
Cooled to reading 36 cm. b.w.
Temp. of b.w. 67°5 F.
Temp. Clark Cells 15°-27 C. throughout.
Reduction of the Results.
Let Oo be the temperature of the surrounding envelope and 1 that of the calorimeter at any time t. Let the change in temperature per second due to the work done by the stirrer be, and let p equal the gain in temperature per second due to the combined effects of convection, conduction, and radiation when the difference in temperature between the calorimeter and the surrounding envelope is unity.
Let a wire whose resistance is R at 0, and R1 at 0, be immersed in a liquid contained in the calorimeter, and let the mass of the contained liquid be M and its specific heat S, when the temperature is 1.
Let the capacity for heat of the calorimeter be w1 when the temperature is 0.
Thus the thermal capacity of the calorimeter and contents at any temperature 0, is S1M+w1.
If the ends of the wire be kept at a constant potentialdifference of E, then we get (paper J, p. 367) :—
σ Since is small and we can make 0, 0, of any magnitude we please, it is always possible to obtain a value of 0, such that o-p(0-0)=0, and in that case
the suffix denoting the nature of the supply.
This temperature (viz. that value of 0, which causes o-p(0-0) to vanish) I shall denote throughout this paper by the term "null point," by which I mean that value of 0, at which the observed rate of rise is due to the electrical supply only, and I shall use ON to indicate that temperature.
Two or three methods of finding ON suggest themselves. If the stirrer be set working when there is no electrical supply, then 1 will gradually approximate to ON, and a few observations as to the rate of change in 0, will supply sufficient information to enable the observer to set the value near to ON, and the calorimeter can then be left to gradually assume the true value. I have given this method a fair trial, for the apparatus has been left working for twenty-four hours at a time, and the value of ON ascertained with precision.
For example, at the rate of 9-10 revolutions per second it was found that the value of 0x-06 (expressed in terms of the
- mean bridge-wire centimetre) was about 9.2 (i. e. 0°-85 C. approximately), and that when the rate was 5.00 the value was about 27 (=0.25 C. approximately); and it is noticeable that the ratio 9-2: 27 is nearly that of (9.1)2: (5.0)2, thus indicating that the heat developed by the stirrer varied approximately as r2, where r is the rate of revolution.
A modification of this method renders it possible to determine the thermal value of the stirring work. After obtaining ON as above, find what value of 0, will cause the temperature to remain steady when the heating effect is that due to the stirring and a potential-difference of one Clark cell. Call this temperature One; we have thus two equations,
Whatever method is adopted the experiments involve much labour and time, for a redetermination of ex must be made. for each change in Oo, as it is probable that owing to changes in the viscosity and surface-friction of the contained liquid, ON would be some function of 0, when the rate of revolution of the stirrer is constant; and a complete determination of the value of ON for each value of 0 would have doubled or trebled the length of the investigation.
It has always appeared to me to be possible that the value of ρ is a function of the rate of change in the temperature of the calorimeter. The temperature-gradient from the calorimeter to the surrounding walls must alter slightly with the rate of change in 1, and the rate of loss or gain in temperature of the calorimeter must as a consequence be affected; or, in other words, I think it probable that the value of ON is a do,
function of hence the value of ON obtained by experiments dt
such as those described above, where the temperature of the calorimeter is constant, may differ appreciably from the value of ON when the temperature is rising.
The method I finally adopted must diminish, although it does not entirely eliminate, any error due to this change in ON.
Let several experiments be performed similar in all respects except that the potential-difference is changed in each case.
Let the potential-difference of a Clark cell be e, and let n be the number of cells used.
Let us assume for the time that ON is independent of n, then, when 1=ON, we get
where n1, ng, n3 &c. are the number of cells used in each
If, therefore, we plot the curves (which in this case are straight lines since the variables, viz., p(0,-0) and R1, S1, and w1 may for small changes of temperature be considered as linear functions of 01, see paper J, pp. 442-448), which de1 1
we obtain by taking X as ordinate, and 1 as abscissa, dt 712
they will intersect where the abscissa is ON, and there only, d01 and since the value of dt
can be experimentally determined
for different values of 0, the observations themselves can be made to give the value of N, and we can thus find the rise due to the electrical supply alone.
J.R1 (S,M+1) A small deviation from the true value of ON is of little consequence, for the resulting value of X will only
p is small as compared with the other magnitudes, 01-0N must be considerable before the error becomes appreciable. As this is an important point, I will select one of the threecell experiments (No. 37) in order to show the relative magnitude of the various quantities, and the probable limit of error arising from the assumption that ON is independent of n. The differences in temperature are expressed in terms of the