122 
Lord Kelvin on 
from the junction J and the surfaces II, CC, to prevent rise of 
temperature (§ 5 above), is 
QVtf-f), or -QV«'-£). 
Hence if e(£, t) denote the energy of the apparatus in the condition 
(£, t), we have 
^3--(jy2+jQY) . . . (l) 
Considering now change of temperature with £ constant, we have 
= ... ( 2 ) 
where K(£, t ) denotes the thermal capacity of the apparatus with £ 
constant. When we consider the possible or probable quasi-Peltier 
productions of heat at II and CC, and the probability that these 
are different for the two metals, and the Peltier effect at J, we 
must regard N as probably varying with £ We must therefore 
regard it as a function of £ and t. 
§ 9. Consider now the motivity * of our apparatus, which we 
shall denote by ra(£, t ), being, as is the energy, a function of 
£ and t. 
When the slab CC is drawn out so as to diminish the capacity 
from £ to the heat QV(£-£), which, to prevent temperature 
from rising, must be given to external matter at temperature t , 
contributes to the recipient an amount of motivity equal to 
where T denotes the lowest temperature of neighbouring matter, 
available for receiving heat. Hence we have 
^--(i y+^Qv) . - (3) 
And if we raise the temperature of the whole apparatus infinitesi- 
mally from t - \dt to t + ^di, we add to its motivity an amount 
*-Ans T (f, t) dt . 
L 
* Proc. Poy. Soc. Edin., 1876 ; Phil. Mag., May 1879 ; Math, and Phys. 
Papers, vol. i. Art. I.; Proc. Roy. Soc. Edin., March 21, 1898. 
