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namely, the law of conservation of energy, the law of conservation of mass, and the law of conservation of momentum. To these we may add, if we will, the law of conservation of electricity.

The Relation of Mass to Energy.

When a black body^[1] is placed in a beam of light it is subject to a pressure or force which tends to move it in the direction in which the light is moving. If ${\frac {d\mathrm {E} }{dt}}$ denotes the time-rate at which the body receives energy, f the force, and V the velocity of light, we have in rational units the formula

$f={\frac {1}{\mathrm {V} }}{\frac {d\mathrm {E} }{dt}}$.

(1)

This important equation, which was obtained by Maxwell as a consequence of his electromagnetic theory, and by Boltzmann through the direct application of the laws of thermodynamics, has recently been verified with remarkable precision in the beautiful experiments of Nichols and Hull.^[2]

A body subjected to the pressure of radiation will acquire momentum, and if we are to accept the law of conservation of momentum, we must conclude that some other system is losing in the same direction an equivalent momentum. We are thus led inevitably, as Poynting has shown, to the idea that the beam of radiation carries not only energy but momentum as well.

The body subject to the constant force of radiation f, will obviously acquire momentum at the rate

${\frac {d\mathrm {M} }{dt}}=f$.

(2)

Combining equations (1) and (2) gives

${\frac {d\mathrm {E} }{d\mathrm {M} }}=\mathrm {V}$.

(3)

The ratio of the acquired energy to the acquired momentum is equal to the velocity of light. The beam of radiation must, therefore, possess energy and momentum in the same ratio. Hence for the beam itself, or any part of it,

${\frac {\mathrm {E} }{\mathrm {M} }}=\mathrm {V}$.

(4)

1. In place of a black body we might consider a partially reflecting one. The equations thus obtained are more complicated but lead also to the simple equation (7).
2. Phys. Review, xvii. pp. 26 and 91 (1903).