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PAUL S. EPSTEIN
to the same result because the effect is of the first order. The explanation why no effect exists lies in the fact that it is not the condenser alone which moves, but also the indicating needle. This gives
Moreover, Tomaschek tried the experiment with a metal cover around his needle. By this arrangement, cutting out all the magnetic actions between I and //, he eliminated any effect which might have existed without shielding. So it is not surprising that he did not obtain a positive effect. He might indeed have saved his efforts by not trying the experiment at all.
Tomaschek, and independently Mr. Chase in our laboratory, repeated the old experiment of Trouton and Noble, as they think, in a much more precise way. The underlying idea is the following:
Suppose I (Fig. 17) to be a charged condenser, suspended in such a way that it can rotate. For a condenser at rest there exists only a force of attraction between the two plates due to the charges of opposite sign. Now the apparatus being in motion with the velocity v (Fig. 18) means that the positive charge is moving in a magnetic field originated by the moving negative charge, and vice versa. Hence two additional forces are exerted on the condenser which would manifest themselves as a torque, so that a rotation of the condenser should be expected. It is easy to calculate this torque, M, which is
where Z7 equals the energy content of condenser, e the dielectric constant of material filling the condenser, and v the azimuth
rise to a second torsional moment which just balances the first one.
x
i
+++++++
N S
Fig. 17
Fig. i8
characterizing the projection of v on the plane of the condenser in relation to the suspension.
CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 387
The foregoing formula is derived on the assumption that the dielectric substance may be regarded as a continuum. The structure of e has not been taken into account; but the difference would not be appreciable. Both Tomaschek and Chase used not a single condenser, but a great number of plates in order to obtain a large capacity and thus have a large value for the electric energy.
The torque is practically the same for both the classical theory and the theory of relativity, the difference arising only in some terms of the fourth order, which are of no practical importance. In spite of the existence of a torque, relativity contends that no effect can be observed at all. This follows because the torque is compensated in some way. The explanation of this peculiar fact is to be found in the tensor character of the mass in relativity. In this theory mass has a different value for accelerations in direction of the motion (mi) and at right angles (mtr) to it. The ratio of the masses is given by the expression
mi _ i
mtr i — (v/c)2 '
In order to analyze the effect of the torque found above, we must divide the acting forces into two components, one in direction of the motion and one at right angles to it. The first component acts against the heavier mass mi and causes a relatively smaller acceleration than the second component. It thus happens that the two accelerations (as vectors) point to the center of gravity of the system (condenser) although the two forces do not. In this way the torque appears to be compensated in the end effect. Thus we see that the tensor character of mass is responsible for the lack of an effect. The Lorentz contraction has not to be taken into account at all. Even in case there were no Lorentz contraction, we should not obtain an effect on our condenser. If, however, an effect should really be observed it would be a contradiction of relativity, because the ratio mi/mtr is a direct consequence of this theory. Tomaschek and Chase both claim to be able to detect an uncompensated torque corresponding to a velocity of the earth of 4 km/sec. For lower velocities no deflection could be observed with their apparatus. This limit of precision is obtained by assuming the whole torque to be in action.