Page:Electromagnetic phenomena.djvu/23

 in the state of rest, and by U+U'  the energy in the state of motion, we have by the formulae of this paper, up to the terms of the second order,

$$U'=\frac{2w^{2}}{c^{2}}U$$,

an expression, agreeing in order of magnitude with the value used by for estimating the effect.

The intensity of the sudden jerk or impulse will therefore be $$\frac{U'}{w}$$.

Now, supposing the apparatus to be initially at rest, we may compare the deflexion α, produced by this impulse, to the deflexion α'  which may be given to the torsion-balance by means of a constant couple K, acting during half the vibration time. We may also consider the case in which a swinging motion has already been set up: then the impulse, applied at the moment in which the apparatus passes through the position of equilibrium, will alter the amplitude by a certain amount β and a similar effect β'  may be caused by letting the couple K act during the swing from one extreme position to the other. Let T be the period of swinging and l the distance from the condenser to the thread of the torsion-balance. Then it is easily found that

According to 's statements U' amounted to one or two ergs, and the smallest couple by which a sensible deflexion could be produced was estimated at 7,5 C. G. S.-units. If we substitute this value for K and take into account that the velocity of the Earth's motion is 3 × 106 c.M. per sec., we immediately see that (39) must have been a very small fraction.