THE MECHANICAL EQUIVALENT OP HEAT. 477 
estimated by a comj)arison of the columns headed “ mean ” and “ from curve ” in 
Table XL. 
None of these experiments call for special comment, with the exception of No. 34. 
This was performed with the object of testing the accuracy of the correction given by 
the formula §Tl = aC® (Section VII., Table IX.), and we did not anticipate from it 
results of much value. The irregularities in ranges 8, 9, 10, of Group D, Column 21, 
Table XL., are clearly an example of the eccentric behaviour of the thermometer 
when rising at this rapid rate; their mean however is excellent. 
Section XIV.— The Calculation of the Results. 
The method which we have adopted in our calculations can be put into a general 
form, thus :— 
Suppose a to be the rate of production of heat in the calorimeter at some standard 
temperature 6, whilst a denotes the value of a at any other temperature 0-^ ; 
p the change in temperature per one second due to radiation, &c., when the differ¬ 
ence between the external and internal temperature is 1“ C ; 
M the capacity for heat of the calorimeter and its contents at the standard 
temperature d, M' its value at 9-^ ; 
Then if 6i is the temperature of the calorimeter at any time t, the rate (a') of 
production of heat is 
M' + M> (0, - 0 ,}, 
where 6q is the temperature of the surrounding envelope. 
Thus the equation of condition is 
M''I'= «'- MV (^1 - «„).(1), 
Now, by Joule’s law, 
JM'^ = C®R.(2), 
therefore 
“• = “W = T-=je. (3), 
where a, is the rate of production of heat due to the electrical supply, and E is 
the E.M.F. of a Clark cell, and n is the number of cells used. 
But since the rate of production of heat is dependent on the resistance of a platinum 
wire, and E is kept constant, this rate will diminish as the temperature rises, or, 
tt’j — cc^ {1 — k 6^ — 9 -j- /8} .(4), 
* We have changed the notation adopted in Section I. to one more suited for arithmetical operations, 
