156 RELATIVITY, THE SPECIAL THEORYincreased. ...' Thus he discovered the electromagnetic mass /i, though he did not
give it that name. The reader will enjoy repeating the calculation he made for the
H of the earth electrified to the highest potential possible without discharge.
Continuing his Columbia lecture, Lorentz remarked, 'If, in the case of the ball
moving in the perfect fluid, we were obliged to confine ourselves to experiments
in which we measure the external forces applied to the body and the accelerations
produced by them, we should be able to determine the effective mass [m 0 + fi],
but it would be impossible to find the values of m 0 and [p] separately. Now, it is
very important that in the experimental investigation of the motion of an electron,
we can go one step farther. This is due to the fact that the electromagnetic mass
is not a constant but increases with velocity' [L8].
Not long after Thomson made his calculations, it became clear that the energy
of the charged sphere has a much more complicated form than %mv^2 if effects
depending on v/c are included (see, e.g., [H3, S5, S6]). The charged hard-sphere
calculations to which Lorentz referred in his lectures Were those performed in
Goettingen by Max Abraham, whose results seemed to be confirmed by experi-
ments performed by his friend Walter Kaufmann, also in Goettingen.*
There is a tragic touch to the scientific career of both these men. In 1897, Kauf-
mann had done very good cathode-ray experiments which led him to conclude: 'If
one makes the plausible assumption that the moving particles are ions, then e/m
should have a different value for each substance and the deflection [in electric and
magnetic fields] should depend on the nature of the electrodes or on the nature of
the gas [in the cathode tube]. Neither is the case. Moreover, a simple calculation
shows that the explanation of the observed deflections demands that e/m should
be about 107 , while even for hydrogen [e/m] is only about 10"' [K2]. Had Kauf-
mann added one conjectural sentence to his paper, completed in April 1897, he
would have been remembered as an independent discoverer of the electron. On
the 30th of that same month, J. J. Thomson gave a lecture on cathode rays before
the Royal Institution in which he discussed his own very similar results obtained
by very similar methods but from which he drew a quite firm conclusion: 'These
numbers seem to favor the hypothesis that the carriers of the charges are smaller
than the atoms of hydrogen' [T3]. It seems to me that Kaufmann's paper deserves
to be remembered even though he lacked Thomson's audacity in making the final
jump toward the physics of new particles.
As for Abraham, he was a very gifted theoretical physicist (Einstein seriously
considered him as his successor when in 1914 he left the ETH for Berlin), but it
was his fate to be at scientific odds with Einstein, in regard both to the special
theory and the general theory of relativity—and to lose in both instances. We shall
encounter him again in Chapter 13.
I return to the electromagnetic mass problem. Kaufmann was the first to study
experimentally the energy-velocity relation of electrons. In 1901 he published a
paper on this subject, entitled 'The Magnetic and Electric Deflectability of Bec-
*For details about this episode, see [Gl].