THE KINETIC THEdRY OF MATTER 437 



for, while . seeing the oil drops dance may satisfy the average man, it 

 will not satisfy the scientist, for he is never content until he has two 

 parallel columns headed, respectively, " calculated " and " observed " 

 values. How shall we set about obtaining such parallel columns ? The 

 way was blazed by Einstein in 1905. He showed that if a body like 

 one of our minute oil drops is dancing about in a resisting medium 

 subjected to no forces but those arising from its own energy of agita- 

 tion, that is, from the bombardment of the surrounding molecules, the 

 mean distance which it will drift in a given time, say ten seconds, from 

 its position at the beginning of this time, can be computed in terms of 

 three factors: (1) its energy of agitation, (3) a resistance factor of 

 the medium, and (3) the length of the time interval through which the 

 drift is observed. 2 But this same quantity can also be easily and di- 

 rectly observed in our experiment by simply balancing the force of 

 gravity upon the drop by the force of an electrical field in the manner 

 already described, and then noting over how large a distance on the 

 average it wiggles in a given time by virtue of its energy of agitation. 

 In the actual experiments we took, in the case of each drop, the mean of 

 several hundred observations on the distance moved in ten seconds in 

 a vertical direction over a set of horizontal scale divisions placed in the 

 eye-piece of the observing telescope ; for Einstein's theory was developed 

 in such a way that the movements to right and left did not need to be 

 considered. The computed and the observed values of this average dis- 

 placement were in every case in so perfect agreement as to satisfy the 

 most skeptical of scientists that the kinetic theory can successfully 

 meet a rigorous and exacting kind of quantitative test. 



But in order to show how free from uncertainties of any sort are 

 the results of this comparison it will be necessary to say just a word 

 more about the theory, for the question is at once raised " how, in 

 computing the theoretical value of the average displacement of the 

 drop, do you obtain the first two of the factors in terms of which this 

 displacement is given, namely, the kinetic energy of agitation of the 

 drop and the resistance factor of the medium ? " We obtain a partial 

 answer to this question when we remember that one of the fundamental 

 assumptions of the kinetic theory is that the energy of agitation of a 

 molecule is determined by temperature alone, and is independent of 



^Einstein's actual equation is D-^4/3 ■ E/K ■ t, in which D- is a quantity 

 obtained by squaring each individual displacement and then taking the mean of 

 these squares, E is the mean kinetic energy of agitation of the drop, K is a 

 resistance factor depending upon both the medium and the drop, and t is the 

 length of the time interval used. If the average displacement B is used instead 

 of the average square of the displacements D^ the correct form of the equation is 





