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POPULAR SCIENCE REVIEW. 
motions of Jupiter’s satellites, but who was no adept in the 
higher branches of mathematics, found as the result of observa- 
tion that the relation above described was so closely approxi- 
mated to, that 1,317,900 years would have to elapse before the 
three satellites could be in conjunction. This result affords an 
interesting measure of the accuracy of observation up to War- 
gentin’s day, since Laplace has shown that the relation is 
absolutely exact. Librations may take place on either side of the 
mean state (though the most careful modern observations exhibit 
no trace of such libration), but there is no possibility of 
accumulative change, save by the influence of effective agencies 
external to the system. It is somewhat singular that the comet 
of 1767 and 1779 passed through the middle of Jupiter’s 
system, without producing any observable derangement of the 
mean motions of the satellites, — a fact which proves conclusively 
that the mass of the comet must be small, its density incon- 
ceivably minute. 
In Ferguson’s astronomy it is stated that the motion of the 
fourth satellite presents no approach to a relation of commen- 
surability with those of the others. A simple relation exists, 
however, with a closeness of approximation which is quite remark- 
able. In fact, throughout the whole solar system there is no 
relation of commensurability which brings closely following 
conjunction-lines so near to each other as this does.* The 
relation is this three times the period of the fourth satellite 
is 50d. lh. 36m. 33*8 13s., and seven times the period of the 
third is 50d. lh. 57m. 53*520s. ; the difference 21m. 19*707s. 
is less than one-1 123rd part of the period of the fourth satellite. 
Thus when the third satellite has travelled round seven times 
from a given conjunction-line "with the fourth, the fourth has 
gone round three times and in addition one-1 123rd part of a 
circumference, that is less than 20', and the third overtakes the 
fourth before the latter has passed over 15' more (since 
15 : 35 :: 3 : 7). This conjunction-line, then is separated from 
a preceding one (the fourth preceding) by less than 35'. The 
remarkable relation which causes the u Great Inequality ” of 
Saturn and Jupiter, brings neighbouring conjunction-lines 
nearly 8-J° apart, a distance fourteen times as great as the above. 
From the connection between the motions of the first three 
satellites, it follows of course that the periods of the two inner 
satellites also approximate to commensurability with the period 
of the fourth. We have, in fact, fourteen revolutions of the 
second, or twenty-eight revolutions of the first, nearly equal to 
* Since the above was written, I have found that some tables of elements 
of the Saturnian system give such periods to the satellites Dione and Ence- 
ladus as to produce a yet closer approach than that of the two satellites of 
J upiter whose motions are here discussed. 
