88 r roceedings of the Roij(d Irish Academy. 



mass of air, from which all the large ions have been removed by an electric 

 field, but which contains a certain number of liquid nuclei. Large ions will 

 be gradually produced in the air. Suppose N.^ is the number of uncharged 

 nuclei at any time, and X the number of large ions of either sign. An 

 increase in ^Y will be due to fiu-ther diffasiou of the small ions to the neutral 

 nuclei, and the rate of this increase will be proportional to the product of 

 LA^^ and the number of small ions of either sign which we shall call n. 

 Opposed to this iaerease will be the loss due to recombination of the large 

 ions of one sign with the small ions of the opposite sign, the rate of which 

 will be proportional to the product Nn, and also the loss due to recombinatioir 

 of the large ions of one sign with those of the opposite sign, the rate of 

 which will be proportional to K-. Henee we have 



dX 3 „ 1- ^ T. 



^= P^i'i -y^'i -i^-, 



where /3, y, o are constants. Theoretical considerations show tliat (5 and y 

 are each of the same order as «, the ordinary coefficient of recombination of 

 small ions, though somewhat less than this quantity, while 8 is very much 

 smaller. The eqiiation shows that X will increase to a maximum when 



jiX.n = yX,< + BX\ 



after which it will diminish gradually. If the. air be strongly ionised, n 



will be great compai'ed with X, so that SX' will be small compared 



with the other terms. In this case when X is maximum the fraction 



X y 



—. will approach the value ■^. If, however, the air be exposed to the weak 



natural sources of ionisation, then 



Consequently, when X is maximum, a less fraction of the nuclei then present 

 will be large ions.- 



The Small Ions. 



The number of small ions in the atmosphere at any time is of great 

 importance ; and for the past ten year's much work has been done in 

 measuring it under very vaiied concUtions. The number usually found per c.c. 

 varies considerably, but generally lies between 500 and several thousands, a 

 mean value being about 1.500. These results are usually deduced from 

 observations with Ebert's well-known apparatus. In sucli calculations, how- 

 ever, no account is taken of tlie large ions present in.the atmosphere ; and 



