Page:On the light thrown by recent investigations on Electricity on the relation between Matter and Ether.djvu/13

 principle of the Conservation of Energy hold with both these estimates of the kinetic energy, or does it depend upon the particular system of axes we use to measure the velocity of the bodies? Well we can easily show that if the principle of the equality of action and reaction is true the Conservation of Energy holds whatever axes we use to measure our velocities, but that if action and reaction are not equal and opposite this principle will only hold when the velocities are measured with reference to a particular set of axes.

The principle of action and reaction is thus one of the foundations of Mechanics and a system in which this principle did not hold would be one whose behaviour could not be imitated by any mechanical model. The study of electricity however makes us acquainted with cases where the action is apparently not equal to the reaction. Take for example the case of two electrified bodies A and B in rapid motion, we can, from the laws of electricity, calculate the forces which they exert on each other, and we find that, except in the case when they are moving with the same speed and in the same direction, the force which A exerts on B is not equal and opposite to that which B exerts on A, so that the momentum of the system formed by B and A does not remain constant. Are we to conclude from this result that bodies when electrified are not subject to the Third Law, and that therefore any mechanical explanation of the forces due to such bodies is impossible, this would mean giving up the hope of regarding electrical phenomena as arising from the properties of Matter in Motion. Fortunately, however, it is not necessary. We can follow a famous precedent and call into existence a new world to supply the deficiencies of the old. We may suppose that connected with A and B there is another system, which though invisible possesses mass and is therefore able to store up momentum, so that when the momentum of the system A, B alters, the momentum which has been lost by A and has not gone to B has been stored up in