THE MECHANICAL EQUIVALENT OF HEAT. 
369 
by subtraction we obtain 
J - tcg) (1 +/6'i - 6») = .(10). 
Hence, when 9^ = 9, the value of J can be found without ascertaining the value 
of the water equivalent or the temperature coefficient of the specific heat of water. 
As J is a constant quantity we can, by repeating the observations at different 
temperatures, obtain from equation (10) the value of f. 
Or we can obtain f without finding J, for repeating the observations at tempera¬ 
tures 9-^ and 9^ 
J - iv^) (1 -f / 9^-9) = Bi,i - B^,! 
and 
J {w^ - ?c,) (L -1-/6»3 - 9) = Bi,3 - B2,2 
the second suffix of B denoting the temperatures. 
Hence, by division, we obtain 
1 + f9\ — 9 _ 
I +/03 - 0 “ ]h,2 - B2,2. ^ 
An alternative method of finding J is to first find /^by equation (11), and then to 
find the value of iv^. and g* The value of J can then be deduced from a single 
experiment by means of equations (8) or (9), and as this method enables us more 
easily to compare the results of individual experiments we have, as a ride, adopted it 
in our reductions. 
In the remainder of this section we briefly indicate the manner in which we have 
determined the various quantities grouped together and denoted in the above equa¬ 
tions by B. 
The calorimeter was suspended by means of glass tubes in an air-tight chamber 
whose walls were kept at a constant temperature. The pressure of the dry air in 
this chamber was reduced to under ’5 millim. The water in the calorimeter was 
stirred at a very rapid rate throughout the experiments, and the value of [cWjdt) 
ascertained at all parts of the range 14° to 26° C. ; firstly, when the work was done 
by the stirrer only, secondly, when the rise was due to both the electrical and the 
mechanical supply of heat. 
The masses of water used during the experiments varied in the ratio of about 
1 to 3, and the difference of potential at the ends of the coil was so altered that the 
heat developed by the current was changed in the proportion of 1 to 9. 
As shown by equation (10) supra, there was no necessity to ascertain the water 
equivalent of the calorimeter, although it was found convenient, as a check upon the 
* These values can be obtained from the preceding equations without first determining J. The 
process is fully explained in Section XIV. 
MLCCCXCIII.—A. 3 B 
