Conductivity of Metals with Temperature. 207 



experimental investigations of Mr. Crookes ; for if the en- 

 closure containing the cooling hody be gradually exhausted 

 of air, so that -sr progressively diminishes, a discontinuity, 

 in the direction of a sudden increase in the rate of cooling, 

 would probably arise at the instant when the average free 

 path of the molecules was long enough to reach from the 

 surface of the cooling body to that of the enclosure. And it 

 is probable that for exhaustions higher than this the law of 

 cooling is different, and in all probability simpler than it was 

 when the heat had to be conveyed between the surfaces by 

 the unsystematic and irregular agency of convection-currents, 

 a process of true gaseous conduction then setting in. This is 

 a point which should be attended to in subsequent investiga- 

 tions ; and it would be an important though somewhat difficult 

 research to discover experimentally the law of cooling and its 

 alteration with pressure when the distance between the cooling 

 body and enclosure is less than the free path of the molecules: 

 probably it could be more readily deduced from theory. It is 

 not likeiy, however, that any of the investigators on the law of 

 cooling hitherto have attained an exhaustion any thing like so 

 perfect as this. 



12. These objections, however, only apply to the convection 

 part of the formula (5); and I will assume that the radiation 

 part 



= Pa»°O*-l) (50 



is practically true as it stands. Since this, however, is not a 

 very simple function for a second differential coefficient like 

 (3), it will be well to see with what amount of accuracy we 

 may expand it into a series and neglect higher terms. The 

 expansion is 



6 = Fa°°(0loga+l(dlogay+ g(01oga) 3 + i(«oga)« + ...) (6) 



which may be conveniently written 



or, putting in the numerical value of a, viz. 1*0077 (that is, 

 putting log e a = *0076), 



0=C<9(266-6 + <9 + -0025 2 + -000005 6 3 + ...), 

 or 



Eemember that is to be ultimately the excess of the tempe- 



