440 
a common impulse on any system of bodies affects not their relative motions ; 
but that they will continue to attract, impel, or circulate round one another, 
in the same manner as if there was no such impulse. The moon is so near the 
earth and both of them so far from the sun, that the attractive power of the sun 
may be considered as equal on both ; and therefore the moon will continue 
to circulate round the earth in the same manner as if the sun did not attract 
them at all. For bodies in the cabin of a ship may move round, or impel 
one another, in the same manner when the ship is under sail, as when it is 
at rest ; because they are all equally affected by the common motion of the 
ship.” (§ 268.) 
16. Now, had I anything better to produce on that side of the question, I 
should have been glad to do so. Unfortunately the point is not discussed at 
all in the Astronomer Royal’s lectures. Ferguson’s reasoning is not only 
very poor and inadequate, but it is self-contradictory. He first says, that 
when the moon is nearest the sun, “ her gravity towards the sun exceeds her 
gravity towards the earth” ; and he even repeats, that “ she is considerably 
more attracted by the sun than by the earth at that time ” ! But he after- 
wards says, that “ the moon is so near the earth, and both of them so far 
from the sun, that the attractive power of the sun may be considered as equal 
on both ; and therefore that the moon will continue to circulate round the 
earth as if the sun did not attract them at all ” ! The best answer I can give 
to this is the following words of the Astronomer Royal. He says : — ■“ The sun 
by the law of gravitation attracts bodies which are near with greater force 
than those which are far distant from it. Therefore, when the moon is nearest 
the sun, the sun attracts the moon more than the earth, and tends to pull 
the moon away from the earth” (p. 184). He afterwards clearly points out 
that it is only when the moon is in quadrature that the sun’s attraction upon 
her and the earth is nearly the same, as they are then both equidistant 
from it. 
17. But, unfortunately, while Ferguson is arguing upon these false notions 
as to the force of gravity, and with questionable logic throughout, though 
very properly with reference to the actual path of the moon on the helio- 
centric hypothesis, Professor Airy does not apply his sounder reasoning'fas 
to the sun’s attraction to the real motion of the moon at all, but only to her 
quasi “ motion” in an unreal circular path round the earth as a centre at rest. 
As he thus, when the moon moves slowest, has reversed the real direction of 
her motion between her quadratures, he by that means shows that the sun’s 
increasing attraction increases the moon’s velocity from her last quadrature as 
she is approaching nearer the sun to her place in conjunction ; which is 
directly contrary to the fact that the moon then really decreases her speed 
till nearest the sun, where she moves with her least velocity. It is in this 
manner alone he arrives at the following conclusion : — “ Therefore, when 
the moon is nearest the sun , and furthest from the sun, she is moving with 
the greatest velocity” ; which could only possibly be true were the earth at 
rest. 
18. Ferguson’s other argument is as follows : — “But this difficulty vanishes 
when we consider that a common impulse on any system of bodies affects not 
their relative motions, but that they will continue to attract, impel, or circu- 
late round one another, in the same manner as if there was no such impulse. 
For [he argues] bodies in the cabin of a ship may move round, or impel one 
another in the same manner when the ship is under sail and when it is 
at rest, because they are all equally affected by the common motion of 
the ship.” 
19. If Ferguson, or any other persons who have made use of this illustra- 
tion, had only carefully considered what is the cause or reason why all bodies 
in the cabin of a ship are necessarily affected by the motion which is truly 
