Prof. Tait on Thermal Conductivity. 149 



In the method devised and carried out by Forbes, the 

 change of specific heat must be attended to during the calcu- 

 lations. Thus we cannot, without going over again the whole 

 numerical work connected with what he called the Statical 

 Curve of Cooling, estimate accurately what will be the effect 

 of this element upon the values of the conductivity. But we 



can easily show that its influence upon Angstrom's results is 

 to be calculated, at least approximately, by the simple process 

 above. 



To avoid the error introduced by supposing rate of surface- 

 loss to be proportional to v } we take (instead of a bar) a 

 plane slab heated and cooled periodically over one surface. 



The equation for the consequent distribution of temperature 

 is 



If we assume 



dv _ d /, dv \ 



dt ~~ dx\ doc ) 



c = c (l + au), 



where u and $ are small positive constants, and put 



k 



Co 



v = u + co, 



where co depends upon first powers of ct and /3 only, higher 

 powers being neglected, the equation splits into two as fol- 

 lows: — 



du _ d 2 u n . 



dt- K oTx» W 



do* d 2 co . m <Pu ( du \ 2 /n\ 



For our present purpose it is sufficient to take 



u = — B# + Qe~ mx cos 2fcm 2 t — mx, 



which satisfies (1), and shows the ultimate effect of a persist- 

 ent simple harmonic application of heat to one side of the slab, 

 whose temperature is taken as our temporary zero ; the other 

 side being kept at the temperature — Bs, where s is the thick- 

 ness of the slab. Here s must be supposed so large that 

 Q e -ms j fl insensible • e lse the- value oft* would be so complicated 

 that (2) would become unmanageable. 



Substituting the above value of u in (2) and integrating, 

 we obtain the value of a>. It consists of three parts. 



