484 Dr. W. F. Gr. Swann on the Electrical 



from A by multiplying all the ordinates of the latter by a factor 



proportional to V/ -9 • — ^7 •> which as a whole is propor- 

 tional to 6 *. In virtue of the comparatively slow variation 

 of this factor with 0, and of the very rapid variation of Si 

 with 6 in those regions where s 1 has a value appreciably 

 greater than its minimum value unity, it will be obvious that 

 the minimum in B cannot occur in a vertical line with any 

 point in A which is far up the steep part of the curve. Our 

 theory in its present form thus predicts that the value of the 

 specific resistance for which a temperature coefficient re- 

 versal is obtained, cannot be a value which is much greater 

 than the normal value. This does not prevent a film of 

 which the resistance is far above the normal at any given 

 temperature showing a reversal at some other temperature,, 

 in fact it must do so. The point is, however, that this would 

 have to be a temperature which was so high that the resistance 

 was little above the normal for that temperature. 



A little consideration will show that a modification of our 

 conditions in the direction of assuming either a smaller 

 value of X/l or a diminution of X/l with the temperature will 

 only enhance the above difficulty. An assumption of a larger 

 value of X/l than the value y 1 ^ would make matters better,, 

 but not appreciably so. X/l must of course never be greater 

 than unity, and even when it approaches this value our 

 calculation of (10) would require modification. 



The fact is that our theory requires too sharp a variation 

 of $i with 6 for small values of 0, and, indeed, apart from 

 the above considerations, though variation of the resistance 

 of the very thin films with temperature is very great, it is not 

 as great as our theory in its present form would require. 

 The difficulties in these respects can be surmounted if we 

 imagine that u 2 is a function of the temperature of such a 

 kind as to insure that 6/iv 2 varies according to a smaller 

 power of the temperature than the first f. Suppose, for 

 example, that u 2 were proportional to # 3 ' 4 , so that 0/ir was 

 proportional to # 1/4 . si would then vary very much less 

 rapidly with temperature, while at constant temperature it 

 would vary as rapidly with u 2 as before. The curve B would 

 now represent s 1 plotted against a quantity proportional to 

 # 1/4 . If we now multiply the ordinates by a quantity pro- 

 portional to 6 to obtain relative values of s, we obtain the 



* It must he remembered that n is a function of 9. 

 t There are many ways in which such a state of affairs can be 

 imagined. 



