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 120 deg., and
since in a period of three synodic revolutions or 21,758 days, the line
of conjunction travels through an arc of 8 deg., it follows that in 892
years the conjunction of the two planets will have advanced from P, P'
to R, R'. In reality, the time of travelling 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 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 versa_. 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.--_Translator_.

[35] The utility of observations of the transits of the inferior planets
for determining the solar parallax, was first pointed out by James
Gregory (_Optica Promota_, 1663).--_Translator_.

[36] Mayer, from the principles of gravitation (_Theoria Lunae_, 1767),
computed the value of the solar parallax to be 7".8. He remarked that
the error of this determination did not amou