﻿Electricity in Flames containing Metallic Vapour*. 871 



The variation of the velocity of a carrier of molecular size 

 in a gas with the temperature can be deduced from a 



formula given by Lenard * 



3 eF 



2W2 D* a W 



where e is charge, F the potential gradient, D the density of 

 the gas, s the sum of the radii of carrier and gas molecule, 

 and W the mean molecular velocity of the gas. Thus, 

 assuming that the charge remains constant, we can find the 

 ratio of the velocity in the hot air to that in the flame. 



The upward velocity of the hot air will be less than that 

 of the flame gases. The greater intensity of the field and 

 the smaller upward velocity of the gases, together with the 

 fact that the path in air is much shorter than that in the 

 flame, tend to make the vertical rise of the carriers during 

 their passage through the air-gap much smaller than that in 

 the flame. Against this we have in the air a diminished 

 horizontal velocity in unit electric field, owing to the lower 

 temperature : this tends to increase the vertical rise in the 

 air. Measurements were made to find the relative magni- 

 tudes of these effects. The strength of the field in the air- 

 gap was estimated by measuring the field in the flame, and 

 the potential difference between the electrodes ; the difference 

 between the latter and the total fall in the flame gives the 

 fall in the air-gaps. The temperature at different places in 

 the air-gap was measured with a thermo-couple, and the 

 upward velocity of the air at the same places compared with 

 that of the flame by a method worked out by Becker f. It 

 was found that, with the distances of our experiment, i. e. 

 path in flame = 1*2 cm., path in hot air 0*8 cm., the vertical 

 rise of a carrier in the air-path would be only ^ of the total 

 rise, on the above assumptions. This is chiefly due to the 

 field being seven times as strong in the air, and the average 

 upward velocity of the gases less than half that of the flame. 

 (Later, we shall assume that the measured velocity is less 

 than that given by the formula of Lenard's already quoted, 

 because the positive carriers are not charged all the time, 

 but are during a certain fraction of their journey neutralized 

 by electrons present in the flame. Now there are far fewer 

 electrons in the hot air than in the flame ; consequently the 

 ratio of the horizontal velocity in the hot air to that in the 

 flame will probably be greater than that assumed in the 



* P. Lenard, Ann. der Physik [4] iii. p. 313 (1000). The original 

 formula is more general. 



t A. Becker, Ann, der Physik. [4] xxiv. p. 823 (1007 



