156 BRIDGMAN. 



is a linear function of the rate of heat input up to rates which are near 

 the burning out point. When this point is approached there is a break 

 in the curve, and the temperature rise increases more rapidly than the 

 heat input. The probable explanation is that the lines of flow of the 

 cooling water are changed, it not being unlikely that there are localities 

 where the water is even vaporized. The general magnitude of the 

 temperature rise observed is consistent with this idea. 



In the second place, the steady temperature rise shows no corre- 

 lation whatever with the thickness of the sample or its material, but 

 the rise for the thickest and the thinnest gold or for the silver is 

 approximately the same for the same breadth of sample. This estab- 

 lishes the correctness of the assumption that the dissipation takes 

 place in the layer of water in contact with the specimen, and does not 

 depend at all on the properties of the metal, always provided of course, 

 that the metal is sufficiently thin. The rise of temperature for speci- 

 mens of different breadths is less at the same input per cm^ of surface 

 for the wider specimens. The total variation was by a factor of 2, the 

 rise of temperature of the narrowest specimen per unit heat input per 

 cm^ being about twice that of the widest. The breadths varied from 

 0.007 to 0.022 cm. At the same time it was a matter of experiment 

 that it was possible to reach higher current densities in the narrow 

 samples without burning out than in the wider ones. The reason for 

 this is that the break in the curve at which the linear relation between 

 temperature rise and heat input ceases is reached much sooner for the 

 wide than for the narrow samples. 



Effect of Breadth of Saviple on Heating. In order to test more 

 exactly the precise dependence of rise of temperature on breadth, a 

 series of runs was made on the same piece of gold, cutting down the 

 breadth after each run so as to make it successively narrower. The 

 sample was initially 1.18 mm. broad and 1.33 mm. long. End effects 

 are important at these dimensions, and agreement with the results of 

 the dimensional analysis is to be expected only for the narrower 

 samples. Readings were made at six breadths. In the first place, 

 as the breadth became less the heating effect became continually 

 greater for the same current. Now if p is the two dimensional resist- 

 ance of the thin metal film, and b its breadth, its resistance per unit 

 length is p/b, and the heat input Q per unit length is Pp/b. Our 

 dimensional analysis shows that 



T = 



P p /cgh 

 k'b'^ \k 



,2^ 



