512 Dr. O. J. Lodge on the Variation of 



assumed in the former paper, I shall now assume as the law 

 of the variation of thermal conductivity. 



fc=6*(l+i «)=*(&+<), 



where b is positive for metals whose conductivity increases 

 with temperature, but both b and k are negative for those 

 whose conductivity diminishes with temperature, like iron. 



It will be necessary to reckon temperature, as before, from 

 the temperature of the enclosure (r — 274 = £ ) as zero; so 

 instead of b + t we write m + 0, where >?i = £ + 6. 



Similarly, for the law of variation of specific heat and den- 

 sity, we may assume (see § 8), 



cp = /3a(l+^?} = a({3 + t) = a(n + 0), 



where n = t + /3 and is always positive, because the specific 

 heat of all metals except mercury appears to increase with 

 temperature. 



§§ 10-15 remain unaltered: but I shall only attempt the 

 case of a rod in vacuo, as in air the integration appears imprac- 

 ticable. §§ 25-29 also remain practically unaltered. 



31. We start, then, with the following equations to the va- 

 riables, of which the numbering agrees with that of the cor- 

 responding equations in the preceding paper, whether they are 

 the same or different; but the numbers are put into square 

 brackets when for any reason the equation is modified, lum- 

 bers above 32 characterize those equations which did not 

 appear in the former paper. 



k=/c(m+ 0), [4] 



•'• M =K= f = ^n~+r > ( 33 ) 



cp = *(n + d), ' (34) 



H=^0, (2) 



0=Pa«*(a*-l)=R(a*-l). . . . (5') 

 And the fundamental equation is 



dkq-^ = Kpd.e; [1] 



or, neglecting the expansion by heat of the cross section y, 

 d ,d0 Ep a 



