THE MECHANICAL EQUIVALENT OF HEAT. 
439 
example, the mean value of t7^ for the weight 194‘20 is 1600, the greatest departure 
from the mean is 1611 in Experiment 13. By assuming tr^ — 1600, we find the rise 
per 1 secojid at rate 30 = '001687 (expressed in millims. of E,„), whereas if we assume 
that tr^ = 1611 and correct Experiment 13 (rate 26'33) to rate 30, we get '001676.* 
Again, the mean value of tr^ for weight 285'37 is 2119, which gives the rise at rate 30 
as '001274. Experiment 22 (rate 26'60) is an extreme case; this would give '001265 
at rate 30. 
Experiment 7 (weight 104'02) shows a greater divergence from the mean value, 
since it would give a rise of '00242 per 1 second as against '00238, the value as given 
by the mean tr^. As, however, we discarded all J experiments where the weight of 
water was less than 130 grms., this extreme case did not afiect our results. 
During our J experiments our rate was always between 29 and 31 (generally 
between 29'8 and 30'2), hence the divergences in the cases, above selected, are far 
greater than any which occurred during our experiments. 
The value of tr^ appeared to increase very regularly as the quantity of wmter 
increased, and thus changes in its value caused by small changes in the mass could 
he deduced. Thus experiment 30 (239'27 grms.) gave a value of 1839. Hence we 
deduced that, if the weight of water was 239'73 (as in Nos. 17 to 19), the value of 
tr^ — 1843 as against 1842, the mean of the actual experiments with the latter 
weight. 
Had the work done by the stirrer been independent of the quantity of water, we 
could have deduced the water equivalent of the calorimeter from the values of for. 
if Kj, Kg, etc., are the values of when W^, Wg are the weights, we have —^ 
as the value of the water equivalent. Using the values of K deduced from 
Table XVHI., we get 
f 
w. 
K. 
Water equivalent. 
^ M/K. 
104-02 
1134 
1 
> , 115-5 
( 105-7 
. J 73-5 
•1418 
194-20 
1600 
J 
•1740 
239-73 
1843 
1 
•1769 
285-37 
2119 
J 
•1753 
We ultimately ascertained that the water equivalent was as nearly as possible 
86'0. Assuming this value and denoting by M the mass of contained water + water 
equivalent, then, if the work done by the stirrer was constant, M/K would be constant 
The numbers in the last column show that the quantity of heat developed increases 
rapidly at first and arrives at a maximum. 
This maximum, as well as we can estimate, occurs when the quantity of water is 
* We required but three significant figures when we applied a similar correction to our J experiments. 
