Page:Philosophical magazine 23 series 4.djvu/38

24 Prof. Maxwell on the Theory of Molecular Vortices

Prop. XVI.— To find the rate of propagation of transverse vibrations through the elastic medium of which the cells are composed, on the supposition that its elasticity is due entirely to forces acting between pairs of particles.

By the ordinary method of investigation we know that

$V={\sqrt {{\frac {m}{\rho }},}}$

(132)

where $m$ is the coefficient of transverse elasticity, and $\rho$ is the density. By referring to the equations of Part I., it will be seen that if $\rho$ is the density of the matter of the vortices, and $\mu$ is the "coefficient of magnetic induction,"

$\mu =\pi \rho ;\,$

(133)

whence

$\pi m=V^{2}\mu ;\,$

(134)

and by (108),

$E=V{\sqrt {\mu }}.$

(135)

In air or vacuum $\mu$=1, and therefore

$\left.{\begin{array}{ll}V&=E,\\&=310,740,000,000\ \mathrm {millimetres\ per\ second} ,\\&=193,088\ \mathrm {miles\ per\ second} .\end{array}}\right\}$

(136)

The velocity of light in air, as determined by M. Fizeau^[1], is 70,843 lenses per second (25 leagues to a degree) which gives

${\begin{array}{ll}V&=314,858,000,000\ \mathrm {millimetres} ,\\&=195,647\ \mathrm {miles\ per\ second} .\end{array}}$

(137)

The velocity of transverse undulations in our hypothetical medium, calculated from the electro-magnetic experiments of MM. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.

Prop. XVII.— To find the electric capacity of a Leyden jar composed of any given dielectric placed between two conducting surfaces.

Let the electric tensions or potentials of the two surfaces be $\Psi _{1}$ and $\Psi _{2}$. Let S be the area of each surface, and $\theta$ the distance between them, and let $e$ and $-e$ be the quantities of electricity

1. Comptes Rendus, vol. xxix. (1849), p. 90. In Galbraith and Haughton's 'Manual of Astronomy,' M. Fizeau's result is stated at 169,944 geographical miles of 1000 fathoms, which gives 193,118 statute miles; the value deduced from aberration is 192.000 miles.