FAILURE OF OHM's LAW AT HIGH CURRENT DENSITIES. 145 



with gold and silver leaf that I made the measurements. I was afraid 

 to try films deposited by cathode spattering because it did not seem 

 to me that the condition of the metal was sufficiently like that of 

 ordinary metals, whereas the leaf may be supposed to be more like 

 the massive aggregates of metal of ordinary dimensions. However, 

 a few experiments at the end with spattered films of gold gave the 

 same results as beaten leaf of the same thickness, and my fears are 

 probably ill founded. The next work that suggests itself in this 

 connection is an extension of the results found here for silver and gold 

 to other metals, using spattered films. 



The thickness of the gold and silver leaf was determined by weighing 

 a known area, assuming in the calculation that the density is the same 

 as that of ordinary metal. The thickness of the silver leaf was 2.0 X 

 10-5 cm. Three thicknesses of gold were used, 8 X 10-«, 1.67 X lO'S 

 and 5 X 10-^. 



It was with some difficulty that I obtained the intermediate thick- 

 ness of gold. Gold is beaten out in comparatively large quantities 

 at a time in books of gold beaters skin, a great many thicknesses 

 together. The last stage of the beating reduces the thickness by a 

 factor of 6, from 5 X 10"^ to 8 X 10"^, and only these thicknesses can 

 be obtained commercially. I am indebted to Mr. Drew of Province 

 Court, Boston, for his kindness in interrupting the last stage of the 

 beating, and at some trouble removing a few of the partially beaten 

 leaves from a large book. The sheets so obtained from the partially 

 completed process were not nearly as perfect as those from the nor- 

 mally completed beating. 



The state of the metal in a thin film differs in some unknown 

 respects from that in larger masses. It has long been known that the 

 specific resistance of spattered films is several times higher than that 

 of the massive metal. ^ The specific resistance of gold films has been 

 shown to be very high for very small thicknesses, to decrease rapidly 

 as the thickness increases up to a certain point where the resistance 

 is about five times normal, from here on to remain nearly constant 

 over a range of thickness of about 20 fold, and beyond this point to 

 decrease to the normal value. The temperature coefficient of resist- 

 ance of spattered films has been frequently observed to be negative. 

 The films of leaf metal used in this work did not show such great 

 abnormalities as the usual spattered films, but nevertheless the 

 resistance was very different from that of the massive metal. The 

 temperature coefficient of my gold leaf was about 0.0015 between 0° 

 and 30°, and was the same for the two thicknesses with which most of 



