Page:LewisRevision.djvu/3

To anyone unfamiliar with the prevailing theories of light, knowing only that light moves with a certain velocity and that in a beam of light momentum and energy are being carried with this same velocity, the natural assumption would be that in such a beam something possessing mass moves with the velocity of light and therefore has momentum and energy. Notwithstanding its apparent divergence from the commonly accepted light theories, I propose to adopt this view and see whither it leads.

Postulating the validity of the fundamental conservation laws mentioned above, we shall need in the following development only this one cardinal assumption, that a beam of radiation possesses not only momentum and energy, but also mass, travelling with the velocity of light, and that a body absorbing radiation is acquiring this mass as it also acquires the momentum and the energy of the radiation. Therefore a body which absorbs radiant energy increases in mass.

The amount of this increase is readily found. If in general we write momentum as the product of mass and velocity, then the momentum of any part of a beam of radiation having the mass m will be given by the equation :

$\mathrm {M} =m\mathrm {V}$.

(5)

The increase dM in the momentum of the body absorbing the radiation will therefore equal the increase dm in its mass, multiplied by the velocity of light,

$d\mathrm {M} =\mathrm {V} dm$.

(6)

Combining this equation with (3) we find

$d\mathrm {m} ={\frac {d\mathrm {E} }{\mathrm {V} ^{2}}}$,

(7)

or if we write $\mathrm {V} =3\times 10^{10}$ centimetres per second,

$dm=1.111\times 10^{-21}d\mathrm {E}$.

Thus a body receiving or emitting radiant energy gains or loses mass in proportion and by the amount $1.111\times 10^{-21}$ grams for every erg. This is a small quantity, indeed, but one which is not to be neglected.

Assuming the fundamental conservation law, we must regard mass as a real property of a body which depends upon its state, and not upon its history. Hence it is obvious that if in any other way than by radiation the body gains or loses energy it must still gain or lose mass in just the above proportion. In other words, any change in a body's content of energy is accompanied by a definite change in its mass,