316 Mr Camphell, Discontinuities in Light Emission. 



X — X', with those of X or of X', by simply putting one of the 

 two beams investigated out of action. If the two beams are 

 independent the ratio of the fluctuations in the first case to those 

 in the second should be 1, if they are dependent it should be 



2^ . .... . . 



-^=. Here again a distinction will be possible only if rf for 



ft)^ + rf 



the dependent beams is small compared to eo^. The objection 

 to this method is that, as will be seen, it is not easy to exclude 

 sources of fluctuation which affect the single cell, but do not affect 

 the balanced cells. 



rT 

 % 10. Let us now investigate briefly the quantity f^(t)dt. 



Jo 

 It can be shown by mere algebra that, if the form oif{t) given 

 in equation (2) of the previous paper is correct, involving the 

 constancy of the capacity of the system and the proportionality 

 of/(i) to the charge communicated to the instrument, we have 



r fHt)dt-~ oc^ip + ct + 0) 



O' ' 4ap(p + a' + b') 



according as a and /3 are real or imaginary*. Here e is the 

 charge on an electron, C the capacity of the system, R the re- 

 sistance between the quadrants of the electrometer, p = l/MG the 

 logarithmic constant of decay of the charge, a and /3, or a and b, 

 time constants determined by the period and damping of the 

 electrometer, and s the sensitiveness of that instrument, i.e. the 

 ratio of the deflection to the steady p.d. between the quadrants. 



The following deductions from (11) and (11') are important, if 

 it is desired to make d^'^ as large as possible : 



(1) It is desirable to decrease G as far as possible : but, taking 

 into account the fact that p is a function of C and (4) below, C 

 practically enters only as the first power and not as the square. 



(2) s should be made as large as possible. Since s enters as 

 its square its value is far more important than that of G. 



(3) R should be made as large as possible. It will be seen 

 that there are practical limits to the value of R. 



(4) So long as p is small compared with a and j3, or a and h, 

 which are of the same order of magnitude in all ordinary instru- 



* It should be remarked that the previous paper is deficient in its algebra. It 

 ■was not noticed that equation (20) can be reduced to the form given here and, con- 

 sequently, the conclusions of paragraph 10 as to the most desirable values of the 

 instrumental constants are worthless. The conclusions given here are believed to 

 be correct, subject to further considerations given below in paragraph 15. 



