Page:Electromagnetic phenomena.djvu/19

 published by in 1902. From each series he has deduced two quantities η and ζ, the "reduced" electric and magnetic deflexions, which are related as follows to the ratio $$\beta=\frac{w}{c}$$:

Here ψ(β) is such a function, that the transverse mass is given by

whereas k1 and k2 are constant in each series.

It appears from the second of the formulae (30) that my theory leads likewise to an equation of the form (35); only 's function ψ(β) must be replaced by

$$\frac{4}{3}k=\frac{4}{3}\left(1-\beta^{2}\right)^{-1/2}$$.

Hence, my theory requires that, if we substitute this value for ψ(β) in (34), these equations shall still hold. Of course, in seeking to obtain a good agreement, we shall be justified in giving to k1 and k2 other values than those of, and in taking for every measurement a proper value of the velocity w, or of the ratio β. Writing $$sk_{1},\ \frac{3}{4}k_{2}^{'}$$ and β'  for the new values, we may put (34) in the form

and

has tested his equations by choosing for k1 such a value that, calculating β and k2 by means of (34), he got values for this latter number that remained constant in each series as well as might be. This constancy was the proof of a sufficient agreement.

I have followed a similar method, using however some of the numbers calculated by. I have computed for each measurement the value of the expression

that may be got from (37) combined with the second of the equations (34). The values of ψ(β) and k2, have been taken from 's tables and for β' I have substituted the value he has found for β, multiplied by s, the latter coefficient being chosen with a view to