Page:A Dynamical Theory of the Electromagnetic Field.pdf/47

such gold-leaf. Much of this is transmitted through holes and cracks; there is enough, however, transmitted through the gold itself to give a strong green hue to the transmitted light. This result cannot be reconciled with the electromagnetic theory of light, unless we suppose that there is less loss of energy when the electromotive forces are reversed with the rapidity of the vibrations of light than when they act for sensible times, as in our experiments.

Absolute Values of the Electromotive and Magnetic Forces called into play in the Propagation of Light.

(108) If the equation of propagation of light is

$F=A\cos {\frac {2\pi }{\lambda }}(z-Vt)$

the electromotive force will be

$P=-A{\frac {2\pi }{\lambda }}V\sin {\frac {2\pi }{\lambda }}(z-Vt);$

and the energy per unit of volume will be

${\frac {P^{2}}{8\pi \mu V^{2}}}$

where P represents the greatest value of the electromotive force. Half of this consists of magnetic and half of electric energy.

The energy passing through a unit of area is

$W={\frac {P^{2}}{8\pi \mu V}}$

so that

$P={\sqrt {8\pi \mu VW}}$

where V is the velocity of light, and W is the energy communicated to unit of area by the light in a second.

According to Pouillet's data, as calculated by Professor W. Thomson^[1], the mechanical value of direct sunlight at the Earth is

83.4 foot-pounds per second per square foot.

This gives the maximum value of P in direct sunlight at the Earth's distance from the Sun,

P=60,000,000,

or about 600 Daniell's cells per metre.

At the Sun's surface the value of P would be about

13,000 Daniell's cells per metre.

At the Earth the maximum magnetic force would be .193^[2].

At the Sun it would be 4.13.

These electromotive and magnetic forces must be conceived to be reversed twice in every vibration of light; that is, more than a thousand million million times in a second.

1. Transactions of the Royal Society of Edinburgh, 1854 ("Mechanical Energies of the Solar System"),
2. The horizontal magnetic force at Kew is about 1.76 in metrical units.