Mr Oamphell, The study of discontinuous phenomena. 127 



be equivalent to -j- observations. But it might appear at first 



sight that this method was unjustifiable because all the periods 

 T would not be independent. But the only dependence between 

 them is expressed by 



K4:'"' '^P (^o) /(^«) = ^r=; <^Po+.„ {r)f(r) (22), 



a relation which affects in no way the argument that the probable 

 value of <f)^(ro) is independent of Vq: it is independent of everything 

 except Nt and, as was shown in § 3, Nr is independent of the 

 way T is selected. Or, if that proof seems inconclusive, we may 

 remember that the average value of d'^j> for successive independent 

 periods T must be the same at whatever moment (distant by an 

 amount greater than T from the moment of insulation) the first 

 period is dated. The proposed method consists of nothing more 

 than averaging the averages of the same number of independent 

 periods starting from different moments. 



Again, it may be argued that this method adds nothing in 

 accuracy since the same observations are used over and over 

 again. It is quite true that the method does nothing to diminish 

 errors due to faulty observations of ^'y^but it does diminish errors 

 due to the application of a theory in which we have assumed 

 z/ = 00 to experiments in which v is finite. 



We may note also that photography adds to the accuracy 

 in the observation of the position of a moving object. The only 

 objection to the method is that greater weight is assigned to 

 observations in the middle of a series than to those at the ends, 

 but this objection does not seem to be serious; if observations are 

 really of equal weight no harm is done by attributing a greater 

 weight to a selection taken at random. 



§ 10. Let us now consider the instruments which it will be 

 desirable to use. 



Firstly, we must be able to determine their constants with 

 accuracy. The determination will doubtless be carried out by 

 raising the electrode system (including the resistance) to a known 

 potential v and watching the return of the needle to zero. (See 

 I 16, below.) The equation of motion of the needle in this 

 experiment will be 



= A'e-'^' + B'e-^' + P'e-P^ (23), 



where a, ^, p are as before and 



p.^ KV ^^^_ P(^-p)-V^ 



{Ip"" - fip + k)' a - /3 



P(a-p)-Va 

 a-y8 



