162 STATIC ELECTRICITY 



Taking x and as the independent variables, put 

 dm = cdx + hdO 

 d$ = adx + bdO 



and it follows, as in the investigation on p. 159, that h = 



Let us apply the formulae to the case of a tourmaline 1 sq. mi. 



cross-section and thickness t. 

 According to Riecke (p. 150) 



(dm\ 



h = (de)x = 8 * 



If is constant, i.e. if we allow no heat to pass in or out, 



fdO\ a _ h 



l~ I 



-=27 is the heat capacity, which we may put as pvt, where p is tin 



ttC7 



density, cr the specific heat in work measure. 



Then (^\ = l* 



\dx'<j> pert 



Integrating from x = to # = #, the rise of temperature is 



where E is the electric intensity. In practice this is Mn.-ill. If, 

 for instance, E is 100, is 300, and pa- is of the order 10 7 , S> 

 of the order 0-005 C. 



Let us now apply the formulae to find the temperature change 

 on charging an ordinary condenser. 



We are to find -*- when <j> is constant. 



d0 h 



We have 



where h = and b = 



Now 



rp, 



neglecting the change in t 



