INEQUALITY OF JUPITER AND SATURN. 333 



What is the distance of the sun from the earth ? No 

 scientific question has occupied in a greater degree the 

 attention of mankind ; mathematically speaking, nothing 

 is more simple. It suffices, as in common operations of 

 surveying, to draw visual lines from the two extremities 

 of a known base to an inaccessible object. The re- 

 mainder is a process of elementary calculation. Unfor- 

 tunately, in the case of the sun, the distance is great and 

 the bases which can be measured upon the earth are 

 comparatively very small. In such a case the slightest 



distance between p and R is 120, and since in a period of three sy- 

 nodic revolutions or 21,T58 days, the line of conjunction travels 

 through an arc of 8, it follows that in 892 years the conjunction of 

 the two planets will have advanced from p, p' to n, R'. In reality, the 

 time of traA-elling from p, p/ to R, R' is somewhat longer from the in- 

 direct effects of planetary perturbation, amounting to 920 years. In an 

 equal period of time the conjunction of the two planets will advance 

 from Q, q> to R, P./ and from R, R' to P, P'. During the half of this 

 period the perturbative effect resulting from every triple conjunction 

 will lie constantly in one direction, and during the other half it will 

 lie in the contrary direction; that is to say, during a period of 460 

 years the mean motion of the disturbed planet Avill be continually 

 accelerated, and, in like manner, during an equal period it will be 

 continually retarded. In the case of Jupiter disturbed by Saturn, 

 the inequality in longitude amounts at its maximum to 21'; in the 

 converse case of Saturn disturbed by Jupiter, the inequality is more 

 considerable in consequence of the greater mass of the disturbing 

 planet, amounting at its maximum to 49'. In accordance with the 

 mechanical principle of the equality of action and reaction, it happens 

 that while the mean motion of one planet is increasing, that of the 

 other is diminishing, and vice versa. \Ve have supposed that the orbits 

 of both planets are situate in the same plane. In reality, however, 

 the/ are inclined to each other, and this circumstance will produce 

 an effect exactly analogous to that depending on the eccentricities of 

 the orbits. It is plain that the more nearly the mean motions of the 

 two planets approach a relation of commensurability, the smaller will 

 be the displacement of every third conjunction, and consequently the 

 longer will be the duration, and the greater the ultimate accumulation, 

 of the inequality. Translator. 



