Now until the • last few years this rather striking conclusion was of academic interest only and it had no practical bearing because we could not produce any such prodigious speeds, in electrified bodies, as were necessary in order to give rise to any sensible increase in their apparent mass. When, however, it was discovered that the negative corpuscles in high vacuum tubes are moving with speeds compara ble with (though always materially less than) the speed of light, the conclusions summarized above began to have an important practical bearing and physicists asked themselves whether any increase in the apparent mass of these cor puscles could be detected, that could be assigned to the causes indicated — that is, whether any experimental evidence could be adduced, to show that the apparent mass of a swiftly-mov ing electrified particle increases with the speed with which the particle is traveling. The ques tion became far more interesting and import ant when it was shown that the so-called Meta rays* emitted by radium are identical with the negatively electrified corpuscles observed in vacuum tubes, because the speed of these beta particles has been found to be as high as from 95 to 97 per cent. of that of light in some cases, and hence they should show a marked increase of apparent mass, if the previous theoretical conclusions about the effect of speed upon mass were sound.
Partly with the object of testing this point, and partly with the broader idea of gaining a general insight into the nature of mass and in ertia and into the constitution of the negative corpuscle, W. Kaufmann, of Calittingen, under took to determine the ratio of charge to mass for these rapidly-moving particles, at various speeds. An interesting semi-popular account of his best-known experiments will be found in Sir Oliver Lodge's 'Electrons.' (For the origi nal papers, see Comptes rendus, 13 Oct. 1902; Physikalische Zeitsrhrift, 4, 1902-03, p. 55; Annalen der Physik, Vol. XIX, 1906). The method employed by Kaufmann was a modifi cation of the one outlined above for determin ing the speed of cathode-ray corpuscles by sub)ecting the particles simultaneously to mag netic and electrostatic fields of force, except that Kaufmann made use of a stream cf beta particles, emitted by radium, and arranged his apparatus so that the magnetic field tended to deflect each corpuscle toward (say) the north, while the electric instead of being dis posed so as to neutralize this effect, was ar ranged so that it tended to deflect the corpuscle (say) toward the east. The stream of beta particles impinged against a photographic plate in such a way that a small, round, single spot was registered upon it when neither field was active. When the magnetic field alone was ex cited, the spot would have been merely dis placed toward the north if the beta particles all had the same speed; but inasmuch as they had a great variety of speeds, it was drawn out into a straight line, extending in a north-and south direction. Similarly, the electric field,
Olen acting alone, caused it to be drawn out nto a straight line extending in an east-and s, cst direction. In the actual experiment, with both fields acting at once, the line that was ob served was a curve; and from a study of the ,hape and position of this curve it was found zo be possible to determine, separately, the ye ocity, u, of the particleS impinging upon auy ;iven part of it, and the ratio for these ame particles. If it is assumed (in accordance with all the other evidence that we have) that i• remains invariable, the data thus obtained show the relation between the mass, m, of a negative particle and the speed, it, with which the particle is moving.
The relation between speed and mass, as re vealed by these experiments, was very marked. For example, at the highest speed observed (which was about 97 per cent. of that of light) the apparent mass of a corpuscle was found to be about three times as great as the mass of the same corpuscle when at rest.
Kaufmann's experiments provide us with means of testing, to a certain extent, theories of the constitution of the negative corpuscle, .nasmuch as for every theory concerning the general nature of the corpuscle there will be a corresponding law of variation of mass with speed. This was recognized immediately, and was, in fact, largely what led to the making of the experiments to which we have just re ferred. A curious fact that has to be reckoned v ith, in applying tests of this kind to the ob servational data, is, that every negative-corpuscle theory yet proposed indicates that the mass of a body moving at high speed is a vector quantity — that is, that the mass of the body, as meas ured in the direction of the motion (i.e., the so-called longitudinal mass) is different from the mass of the same body as measured at right angles to the direction of the motion (i.e., dif ferent from the so-called transversal mass). It is the transversal mass, as Abraham pointed out in 1902, with which we have to deal in dis cussing experiments such as Kaufmann's.
If R is the ratio that the speed of a given negative corpuscle bears to the speed of light when the electrical part of the transversal mass of the corpuscle is m, and if mo is the electrical part of the mass of this same corpuscle when it is at rest, then for m ino we have the fol lowing values for the respective theories of negative-corpuscle structure mentioned above: 4 3 i 1 (I R) • log —11. for the Abraham RI 2R theory; T/1 for the Lorentz theory; and —R 1 for the Bucherer-Langevin theory.