224 
ASTRONOMY. 
attraction, what can be demonstrated of no other, and what 
qualifies the dangers which arise from cross but unavoidable 
influences, that the action of the parts of our system upon 
one another will not cause permanently increasing irregu¬ 
larities, but merely periodical or vibratory ones; that is, 
they w : ll come to a limit, and then go back again. This we 
can demonstrate only of a svstem, in which the following 
properties concur, viz. that the force .shall be inversely as 
the square of the distance; the masses of the revolving bo¬ 
dies small, compared with that of the body at the centre; the 
orbits not much inclined to one another; and their eccen¬ 
tricity little. In such a system the grand points are secure. 
The mean distances and periodic times, upon which depend 
our temperature and the regularity of our year, are constant. 
The eccentricities, it is true, wiil still vary, but so slowly, 
and to so small an extent, as to produce no inconveniency 
from fluctuation of temperature and season. The same as 
to the obliquity of the planes of the orbits. For instance, 
the inclination of the ecliptic to the equator will never 
change above two degrees, (out of ninety,) and that will 
require many thousand years in performing. 
It has been rightly also remarked, that if the great 
planets, Jupiter and Saturn, had moved in lower spheres, 
their influences would have had much more effect, as to 
disturbing the planetary motions, than they now have. 
While they revolve at so great distances from the rest, they 
act almost equally on the sun and on the inferior planets; 
which has nearly the same consequence as not acting at all 
upon either. 
If it be said that the planets might have been sent round 
the sun in exact circles, in which case, no change of dis¬ 
tance from the centre taking place, the law of variation of 
the attracting power would have never come in question, 
one law would have served as well as another; an answer 
to the scheme may be drawn from the consideration of these 
same perturbing forces. The system retaining in other 
respects its present constitution, though the planets had 
been at first sent round in exact circular orbits, they could 
not have kept them: and if the law of attraction had not 
been what it is, or, at least, if the prevailing law had trans¬ 
gressed the limits above assigned, every evagation would 
have been fatal: the planet once drawn, as drawn it neces¬ 
sarily must have been, out of its course, would have wan¬ 
dered in endless error. 
(*) V. What we have seen in the law of the centripetal 
force, viz. a choice guided by views of utility, and a choice 
