The electron, its isolation and measurement and the determination of some of its properties

John Stuart Mill · en
[Pg 106]
and then plot the observed values of  as ordinates and the
corresponding values of  as abscissae we should get a
straight line, provided our corrected form of Stokes’s Law (15) (p. 101)
is adequate for the correct representation of the phenomena of
fall of the droplets within the range of values of  in
which the experiments lie. If no such linear relation is found, then
an equation of the form of (15) is not adequate for the description of
the phenomena within this range. As a matter of fact, a linear relation
was found to exist for a much wider range of values of 
than was anticipated would be the case.



[Pg 107]






Fig. 5





[Pg 108]






Fig. 6





The intercept of this line on the axis of ordinates, that is, the
value of  when  is seen from (20) to be
 and we have but to raise this to the ³⁄₂ power to
obtain the absolute value of . Again,  is seen from (20)
to be merely the slope of this line divided by the intercept on the
 axis.



In order to carry this work out experimentally it is necessary to vary
 and find the corresponding values of . This
can be done in two ways. First, we may hold the pressure constant
and choose smaller and smaller drops with which to work, or we may
work with drops of much the same size but vary the pressure of the
gas in which our drops are suspended, for the mean free path  is
evidently inversely proportional to the pressure.



[Pg 109]



Both procedures were adopted, and it was found that a given value of
 always corresponded to a given value of ,
no matter whether  was kept constant and  reduced to,
say, one-tenth of its first value, or  kept about the same
and  multiplied tenfold. The result of one somewhat elaborate
series of observations which was first presented before the Deutsche
physikalische Gesellschaft in June, 1912, and again before the British
Association at Dundee in September, 1912,[53] is shown in Figs. 5
and 6. The numerical data from which these curves are plotted are
given fairly fully in Table X. It will be seen that this series of
observations embraces a study of 58 drops. These drops represent all of
those studied for 60 consecutive days, no single one being omitted.




TABLE X




   
      No.
      Tem. °C
      P.D.

      (Volts)
       (Sec.)


      cm./Sec.
      
      
       cm.


   
   
      1
      23.00
      5,168
      4.363
      .2357
      .003293
      77-102
      58.56


      2
      23.80
      5,120
      8.492
      .1202
      .004670
      27-36
      32.64


      3
      23.46
      5,100
      9.905
      .1032
      .004996
      22-27
      30.29


      4
      22.85
      5,163
      10.758
      .09489
      .005211
      18-36
      28.94


      5
      23.08
      5,072
      10.663
      .09575
      .005176
      20-30
      29.14


      6
      22.82
      5,085
      11.880
      .08584
      .005497
      17-24
      27.54


      7
      23.79
      5,090
      11.950
      .08368
      .005480
      19-22
      27.57