Resistance of I hin Metallic Films. 485 



curve C. It will be seen that the minimum now occurs for 



a smaller value of - — „ , and it occurs in a vertical line with 

 'dmir 



the point P, i. e. a point in B which corresponds to a value 



s 1 = ll*8, i. e. to a case where the resistance of the film has 



.11*8 times the normal value. While it is not suggested that 



the variation of u 2 with is of any such simple nature as 



that which we have cited above, this method of looking at 



the matter is perhaps useful as indicating the kind of 



physical assumption which it is necessary to make in order to 



bring the present theory into a more strict agreement with 



the facts than it would show in its most elementary form. 



It will be noticed that the films for very large times of 

 deposit all show very small temperature coefficients from 

 0° C. to 100° 0. We might expect, for example, that since 

 film 4, Table III., which corresponds to a time of deposit of 

 130 sees., shows a positive temperature coefficient, film 10, 

 which corresponds to a time of deposit of 960 sees., would 

 show a temperature coefficient equal to that shown by the 

 metal in bulk ; we must remember, however, that the value 

 -of u for film 10 is probably not far different from that for 

 film 4. Once several layers of molecules have become 

 grouped one on top of the other, a further increase of the 

 quantity of deposit would have very little effect on u. It 

 seems probable that the continuation of the deposition only 

 diminishes u down to a certain limit, alter which some 

 totally different process becomes necessary to reduce it much 

 farther. Ln favour of this view we have the fact that the 

 specific resistances of the thickest films obtained by deposition 

 .are much greater than that for the metal in bulk. 



It is interesting to notice that the phenomena resulting 

 from the collection of the molecules into groups might be 

 expected to occur even in the metal in bulk if the metal 

 partakes at all of a crystalline structure, and the bounding 

 planes between the crystals would function as what we have 

 called the gaps. The normal high value of the temperature 

 coefficient for ordinary metals suggests that the values of u 

 and of / are such that these phenomena are not appreciable 

 at ordinary temperatures, but there should always be some 

 temperature sufficiently low at which the temperature co- 

 efficient does attain a zero value, below which value it would 

 of course be negative, and it is a significant fact in favour 

 of this view that experiments have shown that at low tempe- 

 ratures the temperature coefficient becomes abnormally small, 

 which seems like an approach to the zero value referred to 

 above. 



