336 Mr H. Meikle m the Specific Heat 



d\os \ ~ I -^ l"» r = — ' — — = o. Hence, d m = o, 

 ° ( e\r/ } X m 



p & 



and, therefore, log- d r — d r = o ; or hyp-log - = 1, and 



r = ^^,^..^^ - I^is value of r is independent of x. When r 

 2.71828 ^ 



and X are given, m may in every case be found, from the above 



formulae, or from 



, w X r . r 



m lOff — = m ; — lOff -. 



^ e I + X ^ e 

 l^x = |, and r = ^ly^' then m = .903184 e. Every 

 value of m, but its minimum, answers to two different values of 

 r. For instance, r = - e should give the same value to m as 



rz= - e. If three-fourths of the air be extracted from a close 

 4 



vessel, and, after the temperature has settled, one-fourth be in- 

 stantly restored, no change of temperature should ensue. 



The law of temperature admits of a somewhat simpler inves- 

 tigation than was formerly given. Let t be the temperature, or 

 rather the indication on the common scale of an air-thermome- 

 ter, p the pressure, and ^ the density of the mass of air ; then 

 a and b being constants, we have, as before, from the law of 

 Boyle, p=z6g(l-fa^). Now, the specific heat under a con- 

 stant pressure being to that under a constant volume, in the in- 

 verse ratio of the variations of temperature produced in these 

 two different cases by equal variations in the quantities of heat, 

 the following expressions respectively contain all the variables 

 which enter into these specific heats, relatively to the ordinary 

 graduation. 



1 -__ JL ^g and— -— ^P 

 dt~ d^'l+af df dpi+ut 



which are obtained from the above equation, by making jo and ^ 



respectively to vary with t, whilst the other is constant. The 



variations of the quantities of heat being constant, and, as men- 



4 



