356 Dr. J. R. Ashworth on the Calculation of 



1 

 t 



magnetic problem, and put it equal to RT-, where R is the 



gas constant and t is the time. 

 Hence ., 



RTi = STtf, (12) 



and if v is written for - we obtain 

 i 



m 



to = \/ 15 



vi'- ( 13 > 



Thus the maximum current density can be calculated from 

 a knowledge of the constants R and S, which can easily be 

 obtained for most of the pure metals, and from a know- 

 ledge of v the velocity of the electron as it passes along 

 a conductor. 



For the sake of estimating a limiting value to the current 

 density the velocity of the electron will be taken to be of the 

 same order as that of the cathode ray, namely, 10 9 cm. per 

 second. 



The following, then, are some examples of the calculation of 

 i , the maximum current density, according to equation (13), 

 expressed as amperes per sq. cm., the other quantities in the 

 table being in c.g.s. units. 



Metal. Atomic Density. E. S. io. 



weight. per cb. cm. 



Silver 107*9 10-5 809x10° 5-7 3-8 XlO* 



Copper 63-57 8-93 11-66x10° 5'5 4-5x10* 



Aluminium ... 27-1 2-65 6"60xl0° 10-1 2-5x10* 



Tin 119-1 7-29 5-08x10° 38-8 1-2x10* 



Lead 207'1 11-37 4-56x10° 71"4 0*8x10* 



The calculation is made on the supposition that the 

 molecule contains one atom ; if it contains n atoms R must 

 be divided by n and i G by \/n. 



Nernst (' Theory of the Solid State,' p. 81) states that 

 silver, copper, aluminium, and lead are probably monatomic 

 in the solid state, and, if so, i for these metals must be 

 of the order 10 8 amperes per sq. cm. 



These examples include good and bad conductors of elec- 

 tricity, metals of high and low atomic weight, of high and 

 low valency, and of high and low density. The temperature 



