450 Prof. Challis on the Force of Gravity. 



that the hypotheses on which the reasoning rests cannot be con- 

 sidered as established, unless the laws of the other physical 

 forces are deducible from them in a similar manner. 



It may be urged against this theory, that if such be the 

 modus operandi of gravity, some distinct indication of it might 

 be expected to be given by phsenoniena. With reference to this 

 point I remark that, if the rate of propagation of large waves 

 through the interior of the earth be in a very small degree less 

 than in free space, the form of the large inequalities of the 

 earth's surface will have an influence on the direction of gravity. 

 The normals to the fronts of the waves will be made to incline 

 towards high ground; and, in particular, the normals about a 

 small island in the midst of a large ocean will incline towards its 

 centre, and there produce an abnormal excess of gravity. And 

 even if there be no difference between the exterior and interior 

 rates of propagation, the waves must undergo a sudden diminu- 

 tion of condensation and rarefaction on emergence from the 

 surface of the earth, in consequence of the space in the interior 

 being partly occupied by the matter of the atoms ; the efl'ect of 

 which change on the directions of the normals, as affected by 

 the form of the surface, will be the same as that just described. 

 It is certainly remarkable that the local irregularities of gravity 

 which have chiefly attracted notice are precisely of this kind. 

 The excess of gravity in insular oceanic positions was long since 

 a matter of observation ; and recently Archdeacon Pratt has shown 

 that the plumb-line in India inclines from the zenith towards 

 the Himalaya i*ange, after the effect of the attraction of the 

 elevated regions has been allowed for. 



Again, the mathematical theory seems to indicate that, if the 

 approximation were carried further, the law of gravity would be 



found to be expressed by such a function as -^ -I- ^, /a being 



excessively small. This second term, if at all sensible, would 

 be most likely to be detected in the action of the Sun on Mer- 

 cury. In fact, M. Le Verrier has recently shown that the mo- 

 tion of the perihelion of this planet is not wholly accounted for 

 by the attraction of known bodies. The proper course in this 

 case is no doubt that which M. Le Verrier has recommended, 

 viz. to endeavour to ascertain whether there are small bodies 

 circulating between the Sun and Mercury, to which the residual 

 motion of Mercury's perihelion may be ascribed. But should 

 this explanation fail, it might, I think, be reasonably questioned 

 whether the law of gravity is so absolutely that of the inverse 

 square as has been generally assumed. Bode's law of the 

 distances of the planets, which is considered to have I'eceived 

 confirmation by the discovery of the small planets between Mars 



