268 HISTORY OF SCIENCE. 



cipitated upon the earth. The dates at which these catastrophes 

 would happen could not be precisely calculated, but it was known 

 that they were very distant. It was probably for this reason that 

 those results, so startling to astronomers, raised no alarm in the popular 

 mind. The scientific world, however, realized more clearly the de- 

 struction to which our planetary system was tending, and the roost 

 profound mathematicians were invited to study these threatening per- 

 turbations. Euler, Lagrange, and others attempted in vain to discover 

 any counteracting influences, and it appeared as if nothing remained 

 but resignation to the inevitable. In this state of the question La- 

 place drew from certain hitherto overlooked branches of mathematical 

 analysis the means of investigating the variations of the velocities of 

 the moon, Jupiter, and Saturn ; and he showed that these were after 

 all nothing but oscillations of long periods, and that, like the rest, 

 they were due to the action of gravitative attraction. The orbit of 

 the earth round the sun is in the main an ellipse; but this ellipse is 

 liable to change its form, on account of the attraction of the earth by 

 the other planets. Now, from the time of the earliest recorded ob- 

 servations the orbit of the earth has been becoming less elliptical, its 

 figure approaching continually nearer to the circular form, and for 

 some indefinite period it will continue to do this, without actually 

 becoming a circle ; and at some future time it will be resuming its 

 more elliptical form, according to the same laws by which it is at 

 present becoming less elliptical. Now, Laplace showed that the 

 changes of the motion of the moon depend upon these changes in the 

 form of the earth's orbit, a diminution of the eccentricity necessarily 

 producing an increase of the moon's velocity, and vice versa; and he 

 proved that the observed amount of the moon's acceleration from the 

 earliest ages is accounted for by these causes. The perturbations of 

 Jupiter and Saturn were shown by Laplace to be due to the action of 

 these planets upon each other ; and these inequalities run through a 

 period of about nine hundred years, during one-half of which the 

 united action of the planets retard the one and accelerate the other, 

 and during the other half has the reverse effect. 



Laplace's theoretical calculations concerning Saturn and its ring 

 are remarkable as predictions, which W. Herschel's observations con- 

 firmed. The ring, as every one knows, is entirely detached from the 

 body of the planet. The distance between is 20,000 miles, and the ring 

 is 54,000 miles broad, while its thickness is only 250 miles. With the 

 exception of some concentric streaks (which are now considered to 

 indicate several detached rings), the most skilled observers had failed 

 to detect any mark in the ring which could indicate its period of revo- 

 lution, if any. From theoretical considerations Laplace concluded that 

 the ring must revolve in its own plane, and that the period of its revo- 

 lution ought to be 10 hours 33 minutes 36 seconds. By very delicate 

 and careful observations Sir W. Herschel concluded that the ring re- 



