438 THE POPULAR SCIENCE MONTHLY 



whether the molecule is large or small. Hence, the energy of agitation 

 of our oil drop ought to be exactly the same as that of one of the mole- 

 cules of the gas which surrounds it. But this is the quantity which we 

 have just determined experimentally, and which, furthermore, can be 

 computed with great precision from the kinetic theory.^ Hence, we 

 may consider that this quantity is known. The second factor, how- 

 ever, is not known with certainty, except under conditions which may 

 or may not be fulfilled in any experimental work, and herein lies the 

 uncertainty in all preceding attempts like those of Perrin to subject 

 the kinetic theory of Brownian movements to any rigorous experi- 

 mental test. Fortunately for the present work, however, this factor 

 does not need to he l-noivn at all. For obviously the resistance which 

 the medium offers to the motion at a given speed of this particular 

 drop though it must be the same whether it is an electrical force, a 

 gravitational force, or a force arising from molecular bombardments 

 which is causing the motion. Consequently all that was necessary for 

 us to do in order to eliminate this resistance factor entirely was first 

 to observe the successive displacements of the balanced drop as indi- 

 cated above and then to destroy the balance and measure how fast the 

 drop moved on the average, both under gravity and under an electrical 

 field of known strength, in precisely the way we had done when we 

 Avere determining the successive values of the charge carried by the 

 oil drops. From the results of the two experiments we could then 

 eliminate the resistance factor and obtain the average displacement in 

 terms of quantities every one of which was measurable with the great- 

 est precision.'* Indeed the experimental error in measuring the aver- 



^ The kinetic theory equation is -B = 3/2 . ST/N in ^Yhich E is the mean 

 energy of molecular agitation, E an accurately known gas constant, T the abso- 

 lute temperature, and N the number of molecules in 2 grams of hydrogen. 

 Although N is not accurately known save through experiments of this sort, it 

 fortunately does not need to be known, as will be shown in the next footnote, 

 for the quantitative test here sought. When the above value of E is substituted 

 in the equation of the last footnote it becomes 



* When the drop is moving down through the medium under the force of 

 gravity, mg, alone, its average velocity i\ is given by mg = Ki\. The substitu- 

 tion of this value of mg/%\ in the equation of the footnote on page — gives 

 e = K/F . (fi "1- t'O and the elimination of K between this equation and that 

 given in the preceding footnote gives 



A'tt F{Ne) 

 Since D was of course different for different drops instead of making the com- 

 parison between the observed and calculated values of D it was thought prefer- 

 able to make the comparison in every case between the value of Ne obtained 



