Unstriafed Discharge and in tlie Arc. 279 



velocities, and there are negative ions formed by the union 

 of electrons with molecules which are of" molecular size and 

 move with small velocities. The two kinds of ions have the 

 same charges, and are equivalent to each other as far as 

 neutralizing the electrostatic effect of the positive ions is 

 concerned, but are very different in their velocities and 

 consequently in their power to carry current. 



As a result of this the two kinds of negative ions must be 

 considered separately when an equation is formed for the 

 current. This can be done by writing the equation as 

 follows : 



i = €(mu + n 1 Vi + n 2 v 2 ), (1) 



where m is the number of the positive ions per c.c, n x the 

 number of negative ions of electronic size and n 2 the number 

 of negative ions of molecular size ; u is the average velocity 

 of the positive ions, v x the average velocity of the electrons, 

 and v 2 that of molecular negative ions. 



But i\ is very much greater than u or v 2 . With discharge 

 in hydrogen the mass of a molecule is 1700 times that of an 

 electron, and i\ is correspondingly greater than u or i\. 

 With discharge in mercury the mass of the molecule is 

 170,000 times greater than that of the electron. Conse- 

 quently it would be a close approximation to write the 

 equation as follows : 



i = en 1 v 1 , (2) 



providing that ?? : is not excessively small when compared 

 with m or n 2 , and it will be shown shortly that such an 

 assumption leads to an entirely satisfactory explanation of 

 the observed phenomena. 



That n x is not appreciably smaller than m or n 2 is shown 

 by the high average velocity of the negative ions in the 

 mercury arc. Stark, Retschinsky, and Schaposnikoff * found 

 that the average velocity of the negative ions was much 

 greater than that of the positive. Sehenkel f , from a study 

 of the Hall effect in the mercury arc, concluded that the 

 velocity of negative ions was 1*42 x 10 7 cm. per sec. per 

 volt more than that of the positive ions when the pressure of 

 the gas was 1 mm. 



These measurements give the average velocity of the 

 negative ions, and if this is greater than the velocity of the 

 positive ions, it must be that the average mass of the negative 

 ions is much smaller than that of the positive ions. The 

 mass of the positive ions is that of molecules, and hence the 



* Ann. d. Phys. xviii. p. 230 (190-5). 



t Mitt. d. Phys. Ges. Zurich, p. 13 (1900). 



