Middle of the Nineteenth Century. 233 



act in the direction thus determined, its magnitude being 

 unaltered by the planet's motion. This amounts to supposing 

 that gravity is subject to an aberrational effect similar to that 

 observed in the case of light. It is easily seen that the modi- 

 fication thus introduced into Newton's law may be represented 

 by an additional perturbing force, directed along the tangent 

 to the orbit in the opposite sense to the motion, and pro- 

 portional to the planet's velocity and to the inverse square of 

 the distance from the sun. By considering the influence of 

 this force on the secular equation of the moon's motion, Laplace 

 found that the velocity of the gravific fluid must be at least a 

 hundred million times greater than that of light. 



The assumptions made by Laplace are evidently in the 

 highest degree questionable; but the generation immediately 

 succeeding, overawed by his fame, seems to have found no way 

 of improving on them. Under the influence of Weber's ideas, 

 however, astronomers began to think of modifying Newton's 

 law by^ adding a term involving the velocities of the bodies. 

 Tisserand* in 1872 discussed the motion of the planets round 

 the sun on the supposition that the law of gravitation is the 

 same as Weber's law of electrodynamic action, so that the 

 force is 



jp = / _^r n . -?.r J 



* . i x nv^* i i r ^i 



where / denotes the constant of gravitation, ra the mass of 

 the planet, // the mass of the sun, r the distance of the planet 

 from the sun, and h the velocity of propagation of gravitation. 

 The equations of motion may be rigorously integrated by 

 the aid of elliptic functions!; but the simplest procedure is 

 to write 



* Comptes Rendus, Ixxv (1872), p. 760. Of. also Comptes Rendus, ex (1890), 

 p. 313, and Holzmiiller, Zeitschrif t f iir Math. u. Phys., 1870, p. 69. 



t This had been done in an inaugural dissertation by Seegers, Gottingen, 1864. 



