or Centrifugal Theory of Elasticity. 413 



In the double integralj let A,= loggV be put for k<^, G for a, 

 and H for the single integral, as in equation (9). Then the 

 double integral becomes 



1 /*^i 1 dYi. 



p- / Y{d\= ~c"~jff ^y equation (10) 



_ fc rfHj 

 Also because pjMV = ^p-* by equation (9), and tts = —{t—k), 



Jul I rCjjx K 



the second part of the integral (23) is found to be 



Hence, adding together (33 A) and (23 B), we find for the 

 total variation of latent heat, 



SQ'=-|(x-.)|Sr.-^^ + SV. (_ + -^^>j j. (24) 



To express this in tenns of qua'.itities which may be known 

 directly by experiment, we have by equations (10) and (9), 



-R.dX^ H, ^' 

 that is to saVj 



6?log„Hi_^^ T M _ jr_ 



dY ~W^ KY~hi>,P~ kY' 

 and therefore 



M 



/(r) is easily found to be = — logg t for a perfect gas, and being 

 independent of the density, is the same for all substances in all 

 conditions ; hence we find (the integrals being so taken that for 

 a perfect gas they shall =0), 



dr U \lnidr «V / t 



^M0geH, _M rd^.yr\ 



drr^ ~hnJ dr^ ^ r^ 



M /* T 



loge Hj = T- ijjdN loge V +/(t) + coustaut. 



^_Udp 1_ 



dTd\ ~hildT kY' 



* This coefficient corresponds to — — in the notation of my previous 



K 



paper on the Mechanical Action of Ileut. 



