AND LIQUIDS AND THEIR VARIATION WITH TEMPERATURE. 403 



Hence we have, to a very close degree of approximation,* 





The total heat imparted to the discs and lost from their surfaces 

 = H = ^h % -f t> c -f ft** + t s v -^ 



Eliminating & between these equations we have 



and from the second equation we have 



H 



l + - *M + M + l + - *C + - + 



which will enable us to determine & and h from observations of H and the tempera- 

 tures of the discs. 



In the foregoing theory it has been assumed that the steady state of temperature 

 distribution had been attained. As, however, an infinite time is required before this 

 condition is satisfied, it remains to determine at what previous period observations 

 may be taken without the results deduced from these observations being in error by 

 say per cent. 



If the temperature of the " middle disc " is increasing at a rate dv^/dt, the expres- 

 sion for the heat it receives becomes 



i M 

 -f- - - V M 



T I 



(It 



where m x is the mass, and C M the specific heat of the material, of the disc. 



Similarly, the expression for the heat received by the disc of substance, since we 

 may assume that the discs increase in temperature at the same rate dv/dt, becomes 



+ msCs ) . 



* It will be noticed that the heat flowing through the substance has been taken equal to the mean of 

 the heats flowing into and out of it respectively. The closeness of this approximation may be tested by 

 using the values of v in terms of x, obtained on the usual assumption of plane-isothermal surfaces, i.e., 



v = A cosh ax + B sinh cue. 

 3 F 2 



