386 SOME MATHEMATICAL CALCULATIONS. 



can be annihilated, but to be metamorphosed, and group 

 themselves elsewhere in a different order.* 



* From these slow movements, which have been designated the " secular 

 inequalities," we might with some probability infer the end of the world, 

 which even Newton regarded as certain, at least, unless "the Great 

 Architect at times retouched His work." The inequalities or secular 

 variations affect the elements of the orbits, such as the inclination of the 

 plane of the orbit, the semi-major axis of the ellipse, or the mean dis- 

 tance of the planet from the sun, the eccentricity of the ellipse, or the 

 relation between the distance which separates the forces from the centre 

 and the semi-major axis assumed to be unity, and the movements of the 

 perihelions and the nodes. These elements change with extreme slowness. 

 Thus, the inclination of Jupiter diminishes by 8" in a century ; and that of 

 Saturn increases by 9" ; but the very ecliptic varies, it diminishes 33" in 

 a century. 



The variations of the eccentricities are scarcely computable by centuries ; 

 their effect is, that the ellipses insensibly approach or recede from a cir- 

 cular form. 



It is demonstrated by mathematical analysis that these variations are 

 periodical, and confined within narrow limits, in such wise that "the 

 planetary system can oscillate only round a certain mean, from which it 

 never departs except by a very small quantity." But may not this very 

 mean, which we have taken to be constant, oscillate round a more distant 

 and still more constant mean ? 



Observation had long ago detected a continual acceleration in the 

 movement of Jupiter, and a not less certain diminution in the movement 

 of Saturn. Now, to say of a star that its velocity augments, is to declare 

 that it draws nearer its centre of movement. To say that its velocity de- 

 creases, is to affirm that it is retiring from that centre. 



It would seem, therefore, that Jupiter, 1 the greatest of our planets, is 

 destined to be swallowed up, or absorbed, in the incandescent mass of the 

 Sun, while Saturn, 2 with its belt and eight satellites, will gradually wander 



1 The equatorial diameter of Jupiter in English miles is 56,065 ; its density is '24 of 

 the Earth's; its distance from the sun, 494,270,000 miles ; inclination of its orbit to the 

 ecliptic, i 18' 51". 



2 The equatorial diameter of Saturn in English miles is 79,147 ; its density, "12, the 

 Earth = i ; its distance from the sun, 906,200,000 miles ; and the inclination of its orbit 

 to the ecliptic, 2 29' 36". 



