ISOLATION OF AN ION— MILLIKAN. 235 



This equation involves no assumption whatever save that the speed 

 of the drop is proportional to the force acting upon it, an assump- 

 tion which is fully and accurately tested experimentally in the fol- 

 lowing work. Furthermore, equation (1) is sufficient not only for 

 the correct determination of the relative values of all of the charges 

 which a given drop may have through the capture of a larger or 

 smaller number of ions, but it is also sufficient for the establishment 

 of all of the assertions made above, except 3, 4, and 6. However, for 

 the sake of obtaining a provisional estimate of the value of 7)% in 

 equation (1), and therefore of making at once a provisional deter- 

 mination of the absolute values of the charges carried by the drop, 

 Stokes's law will for the present be assumed to be correct, but it is 

 to be distinctly borne in mind that the conclusions just now under 

 consideration are not at all dependent upon the validity of this as- 

 sumption. 



This lavv- in its simplest form states that if ix is the coefficient of 

 viscosity of a medium, x the force acting upon a spherical drop of 

 radius a in that medium, and v the velocity with which the drop moves 

 under the influence of the force, then 



x = Q7ciJ.av. (2) 



The substitution in this equation of the resulting gravitational force 

 acting on a spherical drop of density <T in a medium of density/? gives 

 the usual expression for the rate of fall, according to Stokes, of a 

 drop under gravity, viz, 



The elimination of m from (1) by means of (3), and the further 

 relation in =-f ^a^Cc — p) gives the charge e„ in the form 



'- ^"U; \g{<y-o)) F • ^^^ 



It is from this equation that the values of e'„ in Tables I-XII are 

 obtained. 



rRELIMINARY OBSERVATIOXS UPON THE CATCHING OF IONS BY OIL DROPS. 



Table I presents the record of the observations taken upon a drop 

 which was watched through a period of four and one-half hours as it 

 Avas alternately moved up and down between the cross hairs of the 

 observing telescope under the influence of the field F and gi-avity G. 

 How completely the eiTors arising from evaporation, convection cur- 

 rents, or any sort of disturbances in the air are eliminated is shown 



