1893.] 



the Mechanical Equivalent of Heat, §c. 



15 



M 1 = w(i+fe l -e)+w x (i+gv l -e) ; 



hence ^{10(1 +f 6,-0) + w x (l + gb~^e)} = T ...... (4). 



By repeating observations with different weights of water, w x and w 2 , 

 and observing T x and T 3 , the' corresponding times, we obtain by sub- 

 traction 



^ i (w. i -w 1 )H+fO^0) = T 1 -T 2 (5). 



Hence when 61 = 6 (i.e., at the standard temperature) we can 

 find J without first ascertaining the values of /, g, or the water 

 equivalent of the calorimeter, and by repeating the observations 

 over different ranges we can find / without previously obtaining 

 J ; or, having obtained /, we can find w x and g, and then by 

 equation (4) deduce the value of J from a single experiment. We 

 have adopted both methods as a check upon the calculations, which 

 involve much arithmetic. The latter method is the more convenient, 

 as it enables us to ascertain the results of separate experiments, but 

 it cannot be applied until the values of /, g, and w x have previously 

 beeu obtained by observations on two different weights at two different 

 temperatures. 



The following table shows a few of the results given in Table XL 

 of our paper. We have divided our experiments into Series I 

 and II, and we have given reasons why more weight should be at- 

 tached to the latter series. We here give a summary of the values 

 of T deduced from Series II. By "group" we denote all experiments 

 conducted with the same weight of water, and in every case a group 

 contains experiments performed with different values of n (where 

 n is the number of Clark cells which determine the potential differ- 

 ence). As n was in some cases changed from 2 to 6, the rate of 

 production of heat was increased 9 times. The agreement amongst 

 the results of experiments performed with different values of n is not 

 shown in the portion of the table here given, but it is very close, and 

 affords a satisfactory proof of the accuracy of the values assigned to 

 a and p, and the validity of the method employed to ascertain the 

 actual temperature of the coil. 



The number of experiments performed in each group is shown by 

 the figure under the heading " mean." The extent of our experi- 

 mental irregularities is clearly indicated by this table. 



The " smooth curve " was in each case so drawn that the sum of 

 the positive and negative areas included between it and the slightly 

 irregular experimental curve (given by the numbers in the columns 

 headed "mean ") was zero. 



