LAW OF GRAVITATION. 219 



lates the central force, with other laws, not ob- 

 viously inadmissible, as for instance, the inverse 

 simple ratio of the distance, a considerable quan- 

 tity of calculation is found to be necessary in 

 order to trace the results, and especially the per- 

 turbations in the two cases. The perturbations, 

 in the supposed case have not been calculated ; 

 such a calculation being a process so long and 

 laborious that it is never gone through, except for 

 the purpose of comparing the results of theory 

 with those of observation, as we can do with regard 

 to the law of the inverse square. We can only 

 say, therefore, that the stability of the system, 

 and the moderate limits of the perturbations, 

 which we know to be secured by the existing 

 law, would not, so far as we know, be obtained 

 by any different law. 



Without going into further examination of the 

 subject, we may observe that there are some cir- 

 cumstances in which the present system has a 

 manifest superiority in simplicity over the con- 

 dition which would have belonged to it if the 

 force had followed any other law. Thus, with the 

 present law of gravitation, the planets revolve, 

 returning perpetually on the same track, very 

 nearly. The earth describes an oval, in conse- 

 quence of which motion she is nearer to the sun 

 in our winter than in our summer by about one- 

 thirtieth part of the whole distance. And, as 

 the matter now is, the nearest approach to the 

 sun, and the farthest recess from him, occur 



