200 Sir J. J. Thomson on Conduction 



the temperature, but will reach a minimum value whose 

 tangent is D/M.L If this slope is greater .than that of the 

 tangent to the curve at the origin, whose tangent is NMF'(O), 

 there will be no critical temperature, hence the condition for 

 a critical temperature is 



_D less than NMF'(O), 

 ill A; 



or D less than w where u> =NM 2 /cF'(0), this is equivalent 

 to L less than PF'(0). The value of w at the critical tempe- 

 rature is now iv — D. 



When the slope of the line is considerable, we have from 

 equations (3) and (5) 



1 



k io + D— w ' 



1 w v 



- , ... . ^ A o> 



(„, + D - It , ), 



w epa 



and a the specific resistance is equal to 



h (w + T)—w ) _. 



I'/nl iv 



Unless the temperature is very low we may put w = l\0, and 

 we have 



^_ h /Rfl + D-ttyA 



~<?pa w y 



If <r is the resistance at 0° C, and a the temperature 

 coefficient of the resistance 



<r = cr (l + <*£), 



where t is the centigrade temperature; comparing this with 

 the previous expression we see that 



1 

 g "~273 + D~w ' 

 K 



The condition for the existence of a critical temperature is 

 D < ?('o, i. e. that the temperature coefficient of the resistance 

 when the temperature is not very low should be greater 

 than L/273. 



When D is considerable the line (5) will be steep, so that 

 at all temperatures the intersection of the curve and the line 

 will be quite close to the origin ; we may, therefore, use 



