Velocity of the Ions of Alkali- Salt Vapours in Flames. 711 



no longer constant, is the width of the lamina in the direction 

 of motion at level z, we have 



¥ = 2p{i>/7r)*Y^h*th (52) 



It will be seen that the result is not expressible in terms of 

 the area of the lamina. In (49) c is not constant, unless the 

 lamina remains always similar in shape. 



The fundamental condition as to the smallness of v would 

 seem to be realised in numerous practical cases ; but anyone 

 who has looked over the side of a steamer will know that the 

 motion is not usually of the kind supposed in the theory. It 

 would appear that the theoretical motion is subject to in- 

 stabilities which prevent the motion from maintaining its 

 simply stratified character. The resistance is then doubtless 

 more nearly as the square of the velocity and independent of 

 the value of v. 



When in the case of bodies moving through air or water 

 we express V, a, and v in a consistent system of units, we 

 find that in all ordinary cases vjYa is so very small a quantity 

 that it is reasonable to identify f(v/Ya) with /(0). The in- 

 fluence of linear scale upon the character of the motion then 

 disappears. This seems to be the explanation of a difficulty 

 raised by Mr. Lanchester (loc. cit. § 56). 



t = 



--~ — 



LXXXIII. The Velocity of the Ions of Alkali Salt Vapours 

 in Flames. By Prof. H. A. Wilson, F.E.S., F.R.S.C., 



McGill University, Montreal*. 



IT was shown by the writer in 1899 t that, in flames, all 

 the alkali metals give positive ions which have equal 

 velocities due to an electric Held. This result has been con- 

 firmed by Marx and Moreau. The value of the velocity is 

 about 70 cms. per sec. for one volt per cm. 



The fact that the maximum quantity of electricity which 

 can be carried by a definite amount of any alkali salt vapour 

 is equal to that required to electrolyse the same amount in a 

 solution f, shows that the product Ne has the same value in 

 salt vapours as in solutions. Here N is the number of 

 positive ions formed from one gram molecule of the salt 

 when completely ionized and e the charge carried by each 

 ion. Since in solutions each atom of the alkali metal forms 



* Communicated bv the Author. 



t Phil. Trans. A. ccxxxvii. (1899). 



$ II. A. Wilson, Phil. Trans. A. ccxcvi. (1001). 



