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 suflices, 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 21,758 days, the line of conjunction travels 
through an are of 8°, it follows that in 892 years the conjunction of 
the two planets will have advanced from Pp, P/ to R, R/. In reality, the 
time of travelling 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, qi to R, R/ 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 will 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 verséd. We have supposed that the orbits 
of both planets are situate in the same plane. In reality, however, 
they 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.— Tvanslator. 
