245] Stability of the Solar System 317 



Stated biiefly, the results established by the two astro- 

 nomers were that the changes in axis, eccentricity, and 

 inclination of any planetary orbit are all permanently re- 

 stricted within certain definite limits. The perturbations 

 caused by the planets make all these quantities undergo 

 fluctuations of limited extent, some of which, caused by the 

 periodic disturbing forces, go through their changes in 

 comparatively short periods, while others, due to secular 

 forces, require vast intervals of time for their completion. 



It may thus be said that the stability of the solar system 

 was established, as far as regards the particular astronomical 

 causes taken into account. 



Moreover, if we take the case of the earth, as an in- 

 habited planet, any large alteration in the axis, that is in 

 the average distance from the sun, would produce a more 

 than proportional change in the amount of heat and light 

 received from the sun ; any great increase in the eccentricity 

 would increase largely that part (at present very small) of 

 our seasonal variations of heat and cold which are due to 

 varying distance from the sun ; while any change in position 

 of the ecliptic, which was unaccompanied by a corresponding 

 change of the equator, and had the effect of increasing the 

 angle between the two, would largely increase the variations of 

 temperature in the course of the year. The stability shewn 

 to exist is therefore a guarantee against certain kinds of 

 great climatic alterations which might seriously affect the 

 habitability of the earth. 



It is perhaps just worth while to point out that the 

 results established by Lagrange and Laplace were mathe- 

 matical consequences, obtained by processes involving the 

 neglect of certain small quantities and therefore not perfectly 

 rigorous, of certain definite hypotheses to which the actual 

 conditions of the solar system bear a tolerably close re- 

 semblance. Apart from causes at present unforeseen, it is 

 therefore not unreasonable to expect that for a very con- 

 siderable period of time the motions of the actual bodies 

 forming the solar system may be very nearly in accordance 

 with these results ; but there is no valid reason why certain dis- 

 turbing causes, ignored or rejected by Laplace and Lagrange 

 on account of their insignificance, should not sooner or later 

 produce quite appreciable effects (cf. chapter xin., 293). 



