space, that there would in fact be optical dispersion in the free aether if such second-order terms existed. The amount of such dispersion that would be at all allowable is known to be excessively minute, from the circumstance that celestial bodies on emerging from eclipse or occupation show no changes of colour: the smallness of the amount that would be required may be estimated by comparing the electric force between two ions with their gravitational attraction. Unless the effects of such terms of higher order, in the equations of aethereal activity, increased enormously in importance at molecular distances, relatively to the main linear terms, the proposition that the interactions of molecules are mainly of electric quality would remain valid: now such increase of importance does not seem likely as regards the mechanism of gravitation, for gravity and electric force both obey the same law of the inverse square of the distance, a law which in fact belongs, of mathematical necessity, to the steady permanent interactions between any kinds of molecular nuclei of elastic or motional disturbance in an extended medium, which are of the type of simple poles.
A question of some interest arises, as to whether the assumption that the linear equations of free aether are a first approximation, obtained by the omission of non-linear terms, would imply a virtual recognition of structure in that medium. A presumption of this kind would be useless except for purposes of vivid illustration after the manner of mechanical models, so long as there is absolutely no means of experimenting on the properties of free aether: and this practically comes to the same thing as taking such structure to be non-existent.
121. There is thus little to be urged in favour of leaving this loophole for the explanation of gravitation. On the other side moreover there appears to be the fatal objection that any action accounted for in this way would have relations with radiation, including a velocity of transmission of the same order as that of light. The knowledge that the speed of transmission of gravitation, if finite at all, enormously transcends that of radiation, shows that it forms no objection to a theory of electric and radiant phenomena that gravitation is not found
