328 LAPLACE. 



shine, with a brighter lustre. Still, the question remained 

 undecided. The inutility of such efforts seemed to sug- 

 gest only a feeling of resignation on the subject, when 

 from two disdained corners of the theories of analysis, 

 the author of the Mecanique Celeste caused the laws of 

 these great phenomena clearly to emerge. The varia- 

 tions of velocity of Jupiter, Saturn, and the Moon flowed 

 then from evident physical causes, and entered into the 

 category of ordinary periodic perturbations depending 

 upon the principle of attraction. The variations in the 

 dimensions of the orbits which were so much dreaded re- 

 solved themselves into simple oscillations included within 

 narrow limits. Finally, by the powerful instrumentality 

 of mathematical analysis, the physical universe was again 

 established on a firm foundation. 



I cannot quit this subject without at least alluding to 

 the circumstances in the solar system upon which depend 

 the so long unexplained variations of velocity of the 

 Moon, Jupiter, and Saturn. 



The motion of the earth around the sun is mainly 

 effected in an ellipse, the form of which is liable to vary 

 from the effects of planetary perturbation. These altera- 

 tions of form are periodic ; sometimes the curve, without 

 ceasing to be elliptic, approaches the form of a circle, 

 while at other times it deviates more and more from that 

 form. From the epoch of the earliest recorded observa- 

 tions, the eccentricity of the terrestrial orbit has been 

 diminishing from year to year ; at some future epoch the 

 orbit, on the contrary, will begin to deviate from the form 

 of a circle, and the eccentricity will increase to the same 

 extent as it previously diminished, and according to the 

 same laws. 



Now, Laplace has shown that the mean motion of the 



