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( 831 )
in the state of rest, and by U -j- XJ' the energy in the slate of motion, we have by the formulae of this paper, up to the terms of the second order,
an expression, agreeing in order of magnitude with the value used by Trouton for estimating the effect.
The intensity of the sudden jerk 01* impulse will therefore be —.
Now, supposing the apparatus to be initially at rest, we may compare the deflexion «, produced by this impulse, to the deflexion a' 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 and a similar effect (>” 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 I the distance from the condenser to the thread of the torsion-balance. Then it is easily found that
According to Trouton’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. Gr. S.-units. If we substitute this value for K and lake into account that the velocity of the Earth’s motion is 3 X 10" c.M. per sec., we immediately see that (39) must have been a very small fraction.