482 Dr. W. F. G. Swann on the Electrical 



tacts with regard to the temperature coefficient are contained 

 in the theory which L have put forward to account for the 

 behaviour of these films. If X/t 7 were independent of the 

 temperature, since s x would then be a function only of 

 ud/mu 2 , fig. 4 would be the shape of the curve S]_ plotted 

 against 0, u 2 being constant. It would of course correspond 

 to a rapid decrease of s x with the temperature for small 

 values of 0, and a slow decrease for large values. The only 

 effect of a diminution of X with increase of temperature, 

 such as is necessary to insure agreement with the Thomson 

 effect, would be to accentuate the decrease of s 1 with in- 

 crease of temperature. We know that the factor u9jne 2 \v 

 in 10 increases on the whole with the temperature, so that 

 £ will show a minimum for some temperature, and for that 

 temperature the temperature coefficient will be zero. Above 

 this temperature s will increase with rise in temperature owing 

 to the preponderance of the effect of the factor ad/ne 2 \v ; 

 below it s will decrease with rise in temperature. The greater 

 u 2 , the greater the value of 6 for which the reversal occurs. 



If we turn to Tables II. and III. we see that these are 

 just the phenomena which we find experimentally. Films 

 4-10, Table III. and films 6 and 7, Table II. are so thick 

 (i. e. u is so small) that over each of the ranges tested the 

 temperature coefficient is positive. A sufficiently low tem- 

 perature has not been reached in the case of these films to 

 enable them to show a decrease, or at any rate a net de- 

 crease, of resistance with rise of temperature over the ranges 

 tested. On the other hand, film 3, Table III. and film 5, 

 Table II. show a slight increase in resistance from 0° C to 

 100° 0., and a decrease iu resistance from —180° 0, to 14° C. 

 The value of OJu 2 for these particular films is thus such that 

 the reversal occurs over the range tested. Again, films 2, 

 Table III. and films 1-4, Table II., which correspond to very 

 small times of deposit (large values of u) show only negative 

 temperature coefficients. At sufficiently high temperatures 

 they would, however, according to the theory, show an 

 increase of resistance with temperature. 



At ordinary temperatures the exponential functions in (10) 

 result in s diminishing very rapidly with increase of 6 for 

 large values of u 2 (thin films), and this is just what is found 

 experimentally. The very thin films (films 1-4, Table II. 

 film 2, Table III.) show enormous negative temperature 

 coefficients. 



The present theory thus qualitatively accounts for the 

 facts concerned with the temperature coefficients of the films, 

 und it is to be noted that our arguments in this connexion 



