228 ASTRONOMY. 



the attracting power would have never come in question ; 

 one law would have served as well as another ; an answer 

 to the scheme may be drawn from the consideration of these 

 same perturbing forces. The system retaining in other 

 respects its present constitution, though the planets had 

 been at first sent round in exact circular orbits, they could 

 not have kept them ; and if the law of attraction had not 

 been what it is, (or, at least, if the prevailing law had trans- 

 gressed the limits above assigned,) every evagation would 

 have been fatal ; the planet once drawn, as drawn it neces- 

 sarily must have been out of its course, would have wan- 

 dered in endless error. 



(*) V. What we have seen in the law of the centripetal 

 force, viz. a choice guided by views of utility, and a choice 

 of one law out of thousands which might equally have tak- 

 en place, we see no less in the figures of the planetary or- 

 bits. It was not enough to fix the law of the centripetal 

 force, though by the wisest choice ; for, even under that 

 law, it was still competent to the planets to have moved in 

 paths possessing so great a degree of eccentricity, as, in 

 the course of every revolution, to be brought very near to 

 the sun, and carried away to immense distances from him. 

 The comets actually move in orbits of this sort : and, had 

 the planets done so, instead of going round in orbits near- 

 ly circular, the change from one extremity of temperature 

 to another must, in ours at least, have destroyed every ani- 

 mal and plant upon its surface. Now, the distance from 

 the centre at which a planet sets off, and the absolute 

 force of attraction at that distance being fixed, the figure 

 of its orbit, its being a circle, or nearer to, or further off 

 from a circle, viz. a rounder or a longer oval, depends up- 

 on two things, the velocity with which, and the direction 

 in which the planet is projected. And these, in order to 

 produce a right result, must be both brought witiiin certain 

 narrow limits. One, and only one velocity, united with 

 one, and only one direction, will produce a perfect circle. 

 And the velocity must be near to this velocity, and the di- 

 rection also near to this direction to produce orbits, such 

 as the planetary orbits are, nearly circular ; that is, ellipses 

 with small eccentricities. The velocity and the direction 

 must both be right. If the velocity be wrong, no direction 

 will cure the error; if the direction be in any considerable 

 degree oblique, no velocity will produce the orbit required. 

 Take, for example, the attraction of gravity at the surface of 

 the earth. The force of that attraction being what it is, out 



