114 DISSERTATION SECOND. [tart u. 



produce a tide of lO.i 1 French feet, which agrees not ill 

 with what is observed in the open sea, at a distance from 

 land. 



The calculus of Newton stopped not here. From the 

 force that the moon exerts on the waters of the ocean, he 

 found the quantity of matter in the moon to that in the 

 earth as 1 to 39.78, or, in round numbers, as 1 to 40. He 

 also found the density of the moon to the density of the 

 earth as 1 1 to 9. 



Subsequent investigations, as we shall have occasion to re- 

 mark, have shown that much was yet wanting to a complete 

 theory of the tides ; and that even after Maclaurin, Ber- 

 noulli, and Euler had added their efforts to those of Newton, 

 there remained enough to give full employment to the calcu- 

 lus of Laplace. As an original deduction, and as a first ap- 

 proximation, that of which I have now given an account, will 

 be for ever memorable. 



The motion of Comets yet remained to be discussed. 

 They had only lately been acknowledged to belong to the 

 heavens, and to be placed beyond the region of the earth's 

 atmosphere ; but with regard to their motion, astronomers 

 were not agreed. Kepler believed them to move in straight 

 lines ; Cassini thought they moved in the planes of great cir- 

 cles, but with little curvature. Hevelius had come much 

 nearer the truth ; he had shown the curvature of their paths 

 to be different in different parts, and to be greatest when 

 they were nearest the sun ; and a parabola having its vertex 

 in that point seemed to him to be the line in which the comet 

 moved. Newton, convinced of the universality of the prin- 

 ciple of gravitation, had no doubt that the orbit of the comet 



1 Neivtoni, Prin. Lib. HI. Prop. 36 ad 37. 



3 See the solutions of these three mathematicians in the Com' 

 menlary of Le Seur and Jacquier on the Third Book of the 

 Prmcipia. 



