524 
MR. H. A. 5YILS0N ON THE ELECTRICAL CONDUCTIVITY 
Taking this source of error into account, it is still clear that the velocities in the 
flame are very much greater than those in the hot air. The average temperature of 
the flame may be taken as say 2000° C., whilst that of the hot air was nearly 
1000° C. ; consequently, if the size of an ion is supposed to be independent of the 
temperature, the velocity of the ions in the flame should have been about double that 
in the hot air. Actually the negative ions were found to move forty times quicker in 
the flame than in the hot air. 
The results obtained by McClelland"^ for the velocities of the ions in the hot 
gases coming from flames appear to bear on this point. He found that the velocity of 
the ions rapidly diminished as the distance from the flame was increased, and this 
pointed to “ a rapid condensation on the charged carrier of some uncharged body 
greatly increasing its mass.” 
The theoretical velocity of an ion supposed to be one atom, carrying the same 
charge that an ion does in solutions, can be calculated by means of the formula 
-n 
U — —7 D 
mk 
where u is the velocity of the ion, 
D the coefficient of interdiflusion of the ions and the gas, 
ni the mass of an ion, 
e the charge on it, 
X the electromotive intensity, 
h the quotient of pressure by density for the ions, t 
This gives for the velocity of an ion of molecular weight 32 in air at the ordinaiy 
temperature about 40 centims. per second. At a temperature of 2000° C., its velocity 
would be 300 centims. per second, and at 3000° C., about 400 centims. per second. 
The velocity of the negative ions in the flame, 1000 centims. per second, is, there¬ 
fore, of the same order of magnitude as the theoretical velocity of an ion consisting 
of one atom. 
All the other velocities are less than this, which indicates that the ions consist of 
clusters of atoms, that is, assuming that they carry the same charge as the ions in 
electrolysis of solutions. This result is in agreement with those of Rutherford on 
the velocities of the ions in Rontgen ray and uranium ray conductivity, and of 
McClelland on the velocities of the ions in the hot gases coming from flames. 
The size of this cluster appears to he much greater in the case of positively- 
charged ions than in the case of negatively-charged ions. Zeleny (‘ Phil. Mag.,’ 
July, 1898) has shown that the velocity of the negative ions produced in gases by 
* ‘Phil. Mag.,’ July, 1898. 
t See J. J. Thomson, ‘Brit. Assoc. Reijort,’ 1894, Art., “Diffusion,” ‘ Encyclopredia Britannica,’ and 
E. Rutherford, ‘Phil. Mag.,’ Nov., 1897. 
