430 Mr. H. A. Wilson : Determination of the Charge 



The droplets of the cloud produced presumably each con- 

 tain one or more ions. Let a droplet containing one ion, and 

 consequently having a charge e, have a mass m which can be 

 determined by observing its rate o£ fall fa say) in air. If 

 now a vertical electrostatic field of strength X is applied to 

 this droplet, there will be a vertical force on the droplet equal 

 to Xe due to the field, so that the total force on the droplet 

 will be Xe -f mg, where g is the acceleration due to gravity, 

 and reckoning X<? positive when it is in the same direction 

 as the weight mg. Xow the rate of steady motion of a sphere 

 in a viscous fluid is proportional to the force acting on it, so 

 that the rate of fall of the droplet will be altered by the 

 electric field. Let it be now v 2 . Then we have 



mg + X^ v 2 ' 



The relation between m and v x is given by the equation 



?/z = 3-lxl0- 9 x^l* 

 so that 



0=3'lXlO- 9 |:(v 2 --tfl)t^, 



Thus if X is known measurements of v ± and v 2 are sufficient 

 to determine e absolutely. This is the method which I have 

 employed. 



It was found that, using strong Rontgen rays, some of the 

 droplets in the cloud had bigger charges than others. In 

 fact there sometimes appeared to be several sets of droplets 

 having charges nearly in the ratios 1:2:3. It appeared, 

 therefore, that some of the droplets contained one ion, some 

 two ions, and so on. This agrees with Prof. Thomson's ob- 

 servation that when the strength of the Rontgen rays was 

 increased beyond a certain amount, the number of droplets 

 in his clouds did not increase proportionally to the number 

 of ions present at the moment of expansion. Prof. Thomson 

 therefore used weak rays so that in his experiments each 

 droplet probably only contained one ion, which is a necessary 

 condition for the success of the method he employed. 



The principal advantages of my method are that it is not 

 necessary to estimate either the number of drops in the cloud, 

 or the number of ions present at the moment of its formation, 

 or to make the assumption that each droplet contains only 

 one ion. Both these estimations involve assumptions which 

 in practice can only be approximately true, and there is 



* J. J. Thomson, Phil. Mag. Dec. 1899, p. 561. 



