14(1 LAPLACE. 



\Yo have just explained bow Laplace demonstrated that the solar sys- 

 tem can experience only small periodic oscillations around a certain 

 mean state. Let us now see in what way he succeeded in determining 

 the absolute dimensions of the orbits. 



What is the distance of the sun from the earth ? No scientific ques- 

 tion has occni)ied, in a greater degree, the attention of mankind ; mathe- 

 matically speaking, nothing is more simple. It sultices, as in common 

 oi)erations of surveying, to draw visual lines from the two extremities of 

 a known basr to an inaccessible object. The remainder is a process of 

 elementary calculation. Unfortunately, in the case of the sun, the dis- 

 tance is great, and the bases which can be measured upon the earth are 

 comparatively very small. In such a case the slightest errors in the di- 

 rection of the visual lines exercise an enormous influence upon the 

 results. 



In the beginning of the last century, Halley remarked that certain in- 

 terpositions of Venus between the earth and the sun, or, to use an ex- 

 l)ression applied to such conjunctions, that the transits of the planet 

 across the sun's disk, would furnish at each observatory an indirect 

 means of fixing the position of the visual ray very superior in accuracy 

 to the most perfect direct methods.* 



Such was the object of the scientific expeditions undertaken in 17G1 



junction of the two planets will occur at P, P' when they have both described around S an 

 additional arc of about 8°. In the same way it may be shown that the two succeeding con- 

 junctions will take place at the points q, q' r, r' respectively 8° in advance of Q, Q', R, R'. 

 Thus we see that the points of conjunction will travel with extreme slowness in the same 

 direction as that in which the planets revolve. Now, since the angular distance between P 

 and R is ]'2(l°, and since in a period of three synodic revolutions, or yi,7')8 da5-s, the line 

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

 tlie two planets will have advanced from P, P' to R, R'. In reality the time of traveling 

 from P, P' to R, R' is somewhat longer from the indirect 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, R' and from R, R' to P, P'. During the half of this period 

 the perturbative oiTect resulting from every triple conjunction will lie constantly in one di- 

 rection, and during the other half it will lie in the contrarj- direction; that is to say, 

 during a period of 4G0 years, the mean motion of the disturbed planet will be con- 

 tinually 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 

 inequalitj' 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 wliile the mean motion of one planet is in- 

 creasing, that of the other is diminishing, and vice versa. We have supposed that the or- 

 bits of both planets arc situate in the same plane. In reality, however, they are inclined 

 to cadi other, and this circumstance will produce an eti'ect exactly analogous to that de- 

 pending on the eccentricities of the orbits. It is plain tliat the more nearly the mean motions 

 of the two ])lauets approach a relation of commeusurability, the smaller will be the displace- 

 ment of every third conjunction, and consequently the longer will be the duration, and the 

 i;reater the ultimate accumulation, of the inequality. — Tuanslatok. 



* The utility of observations of the transits of the inferior planets for dcterunniug the 

 ^olar parallax was first pointed out by James Gregory. (Optica Promota, IGW.)— Tkans- 

 i.ATOU. 



