In the arithmetical examples of Chapter IX we reckon merely the force between two bodies; but the Newtonian tension mentioned in Chapter VIII does not signify that force, but rather a certain condition or state of the medium, to variations in which, from place to place, the force is due. This Newtonian tension is a much greater quantity than the force to which it gives rise; and, moreover, it exists at every point of space, instead of being integrated all through an attracted body.

It rises to a maximum value near the surface of any spherical mass; and if the radius be R and the gravitational intensity is g, the tension at the surface is T₀ = gR. At any distance r, further away, the tension is T = gR²/r.

This follows at once thus:—

Stating the law of gravitation as F = ?mm´ / r², the meaning here adopted for etherial tension at the surface of the earth is

T = ?_R⁸ ?E / r² dr = ?E / R;

so that the ordinary intensity of gravity is

g = -dT / dR = ?E / R² = 4 / 3p??R.

Accordingly, near the surface of a planet the tension is T₀ = gR, or for different planets is proportional to ?R².

The velocity of free fall from infinity to such a planet is v(2T₀); the velocity of free fall from circumference to centre, assuming uniform distribution of density, is v(T₀); and from infinity to centre it is v(3T₀).

Expanding all this into words:—

The etherial tension near the earth's surface, required to explain gravity by its rate of variation, is of the order 6 × 10¹¹ c.g.s. units. The tension near the sun is 2500 times as great (p. 103). With different spheres in general, it is proportional to the density and to the superficial area. Hence, near a bullet one inch in diameter, it is of the order 10^-6; and near an atom or an electron about 10^-21 c.g.s.

If ever the tension rose to equal the constitutional elasticity or intrinsic kinetic energy of the ether,—which we have seen is 10³³ dynes per square centimetre (or ergs per c.c.) or 10²² tons weight per square millimetre,—it seems likely that something would give way. But no known mass of matter is able to cause anything like such a tension.

A smaller aggregate of matter would be able to generate the velocity of light in bodies falling towards it from a great distance; and it may be doubted whether any mass so great as to be able to do even that can exist in one lump.

In order to set up a tension equal to what is here suspected of being a critical, or presumably disruptive, stress in the ether [10³³ c.g.s.], a globe of the density of the earth would have to have a radius of eight light years. In order to generate a velocity of free fall under gravity equal to the velocity of light, a globe of the earth's density would have to be equal in radius to the distance of the earth from the sun, or say 26,000 times the earth's radius. If the density were less, the superficial area would have to be increased in proportion, so as to keep ? R² constant.

The whole visible universe within a parallax of ¹/₁₀₀₀ second of arc, estimated by Lord Kelvin as the equivalent of 10⁹ suns, would be quite incompetent to raise etherial tension to the critical point 10³³ c.g.s. unless it were concentrated to an absurd degree; but it could generate the velocity of light with a density comparable to that of water, if mass were constant.

If the average density of the above visible universe (which may be taken as 1.6 × 10^-23 grammes per c.c.) continued without limit, a disruptive tension of the ether would be reached when the radius was comparable to 10¹³ light years; and the velocity of light would be generated by it when the radius was 10⁷ light years. But heterogeneity would enable these values to be reached more easily.

Gravitation is thus supposed to be the result of a mechanical tension inherently, and perhaps instantaneously, set up throughout space whenever the etherial structure called an electric charge comes into existence; the tension being directly proportional to the square of the charge and inversely as its linear dimensions. Cohesion is quite different, and is due to a residual electrical attraction between groups of neutral molecules across molecular distances: a variant or modification of chemical affinity.