278 Mr. C. D. Child on Ionization in the 



negative ions per unit volume, u and v the velocities of the 

 positive and negative ions respectively, N the number of 

 recombinations o£ ioas per sec. per unit volume, and a some 

 constant depending on the kind, pressure, and temperature 

 of the gas. 



In both the unstriated discharge and in the arc the electric 

 force is approximately independent of the current, and 

 therefore u and v may also be considered as independent 

 of the current, and e is a constant under all conditions. 

 Therefore n is proportional to i. But N, the rate at which 

 ions recombine, varies as the square of n, and therefore as 

 the square of the current. The following considerations 

 show that this is highly improbable. 



The work which has been done in recent years on the 

 light produced by electrical discharge indicates that part of 

 the light, if not all, is produced by the recombination of the 

 positive and negative ions. From this we should expect the 

 intensity of at least part of the light to be proportional to 

 the number of ions recombining, and if we accept the state- 

 ment that the rate of recombination of the ions varies as the 

 square of the current, we should conclude that the amount of 

 light should vary as the square of the current. In reality 

 the light varies approximately as the first power of the 

 current and not as the square *. 



A consideration of the energy used to produce the ions 

 leads us to the same result. Since the field is uniform for 

 some distance in this form of discharge, as many ions are 

 brought into a given region by the field as are drawn out, 

 and hence with a constant current the number of ions formed 

 per sec. in each c.c. must equal the number recombining. 

 Therefore, this number must also be proportional to the 

 square of the current, if the preceding equations are correct. 

 It requires a certain amount of energy to produce an ion, 

 and therefore the energy required to produce the total 

 number of ions formed each second must also be proportional 

 to the square of the current. However, since the electric 

 force is constant, the total energy given to the discharge 

 varies as the first power of the current. This brings us to 

 the improbable conclusion that the part of the current used 

 to ionize increases as the square of the current, while the 

 total energy increases as the first power of this quantity. 



These difficulties may be explained if we remember that 



there are in reality two kinds of negative ions. There are 



negative ions called electrons which are but small parts of 



molecules, having but small masses and moving with high 



* Cutting, 'Bulletin of Bureau of Standards/ iv. p. 517 (1007). 



