256 Dr. 0. J. Lodge on the Variation of the Thermal 



Hence /jl is inversely proportional to the square root of the 

 conductivity ; and if the values of fx are known for any two 

 metals coated with the same varnish and otherwise under 

 precisely similar conditions, their thermometric conductivities 

 at zero Centigrade are inversely as /ul 2 ; so that 



jM-^-^T (22) 



k o c oPo P 

 Or, again, the conductivity of any one metal may be ex- 

 pressed in absolute measure as soon as we know fju and have 

 determined the radiation-constant P (or C) by direct experi- 

 ment on the rate of cooling of the rod in vacuo ; for 



h Pa uo lo* 



CoPo V? 



(23) 



The mode of calculating P is given in § 27 and equation (32). 

 On the other hand, the variation-coefficient m is involved in 

 the constant X ; so that, if one knows X, it can be easily calcu- 

 lated. For the meaning of X, refer to equations (16), (13), 

 and (7 ; ), which show that its value is 



1 log a © 

 3m 6 '^ 6000 



( l0 S a ~3 ; 



or, expressing m in terms of X ; 



2 - 7 _ 2000-© 



6X-«-«y~ 6OOOX-7-6--OO760' * K J 



and as soon as m is known, the law of variation of conducti- 

 vity with temperature can be expressed by the equation 



cp~m + 0~b+t? W 



where & = m + 274— v ; compare equations (9) and (4). 



Hence what we have to do is to determine the constants X 

 and /j, from observed values of the temperature down the rod, 

 on the hypothesis that this curve of temperature is correctly 

 represented by equation (18). 



Calculation of the Constants X and fju. 



23. Let the excess of temperature of the rod over the en- 

 closure be observed very accurately (by thermoelectric or other 

 means) at equal intervals all along the rod, say at successive 

 distances from the origin £, 2f, 3f, &c. Call any three con- 

 secutive values of these temperatures 1} 6 2 , and 6 3 ; then it is 

 easy to show from equation (18) that the quotient 



(h J+ h J Hb J ) 



