Septemder 30, IDIOJ 



SCIENCE 



4:37 



enclosed, and the temperature controlled so 

 that the air within the condenser is altogether 

 stagnant. The droplet, once inside the con- 

 denser, is illuminated through a small window 

 by a beam from an arc light, so that it appears 

 in the field of view of the observing cathe- 

 tometer telescope like a bright star on a black 

 background. This star, of course, falls under 

 the action of gravity toward the lower plate, 

 but before it reaches it, an electrical field of 

 strength between 3,000 volts and 8,000 volts 

 per centimeter is thrown on between the 

 plates, and, if the droplet had received a 

 charge of the proper sign and strength as it 

 was blown out through the atomizer, it is 

 pulled up by this field against gravity, toward 

 the upper plate. Before it strikes this plate 

 the field is thrown off, the plates short-cir- 

 cuited, and the time required by the drop to 

 fall under gravity the distance corresponding 

 to the space between the cross hairs of the ob- 

 serving telescope is accurately determined. 

 Then the rate at which the droplet moves up 

 under the influence of the field is measured 

 by timing it through the same distance when 

 the field is on. This operation is repeated and 

 the speeds checked an indefinite number of 

 times, or until the droplet catches an ion from 

 among those which exist normally in air, or 

 which have been produced in the space be- 

 tween the plates by any of the usual ionizing 

 agents like radium or X-rays. The fact that 

 an ion has been caught, and the exact instant 

 at which the event happened are signaled to 

 the observer by the change in the speed of the 

 droplet under the influence of the field. From 

 the sign and magnitude of this change in 

 speed, taken in connection with the constant 

 speed under gravity, the sign and the exact 

 value of the charge carried by the captuTed 

 ion are determined. The error in a single ob- 

 servation need not exceed one third of one 

 per cent. Furthermore, it is from the values 

 of the speeds observed that all of the conclu- 

 sions above mentioned are directly and simply 

 deduced. 



§3. The Deduction of the Relative Values 

 of the Charges Carried hij a Given Droplet. — 

 The relations between the mass m of a drop. 



the charge e„, which it carries, its speed r, 

 under gravity, and its speed v^ under the in- 

 fluence of an electrical field of strength F, are 

 given by the simple equation 



r,^rn^_ ^^ e„ = f (v. + t,). (1) 



This equation involves no assumption what- 

 ever save that the speed of the drop is propor- 

 tional to the force acting upon it, an assump- 

 tion which is fully and accurately tested ex- 

 perimentally in the following work. Further- 

 more, equation (1) is suificient not only for 

 the correct determination of the relative values 

 of all of the charges which a given drop may 

 have after 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, and for the estab- 

 lishment of 4 no other exact relationship is 

 needed. However, for the sake of obtaining a 

 provisional estimate of the value of m in equa- 

 tion (1), and therefore of making a provi- 

 sional determination 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 assumption. 



This law states that if yu, 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 = 6Tr/iav. 



(2) 



The substitution in this equation of the 

 resulting gravitational force acting on a 

 spherical drop of density o- in a medium of 

 density p gives the usual expression for the 

 rate of fall, according to Stokes, of a drop 

 under gravity, viz.. 





(3) 



The elimination of m from (1) by means of 

 (">). and the further relation 



