Page:Philosophical magazine 23 series 4.djvu/34

18 Prof. Maxwell on the Theory Molecular Vortices whose density is $$\rho$$, and having its normal inclined to the axes of $$z$$; then the tangential force upon it will be

T beings as before, the tangential force on each side of the surface. Putting $$\rho=\tfrac{1}{2\pi}$$ as in equation (34), we find

The displacement of electricity due to the distortion of the sphere is

and if $$h$$ is the electric displacement per unit of volume, we shall have

or

so that

or we may write

provided we assume

Finding $$e$$ and $$f$$ from (87) and (90), we get

The ratio of $$m$$ to $$\mu$$ varies in different substances; but in a medium whose elasticity depends entirely upon forces acting between pairs of particles, this ratio is that of 6 to 5, and in this case

When the resistance to compression is infinitely greater than the resistance to distortion, as in a liquid rendered slightly elastic by gum or jelly,

The value of $$E^2$$ must lie between these limits. It is probable that the substance of our cells is of the former kind, and that we must use the first value of $$E^2$$, which is that belonging to