432 
Annual Report of the Council of the Royal Astronomical Society, and pub- 
lished in the Monthly Notices for February last, that — “ strange as it may 
appear,” and notwithstanding the recent re-verification at the Royal Observa- 
tory of all the parallactic calculations hitherto supposed to justify the theory 
of the sun’s motion, — you, Sir, had arrived at the conclusion, “that the 
whole question of solar motion in space, so far at least as accounting for the 
proper motion of the stars is concerned, appears to remain at this moment in- 
doubt and abeyance ” ; but (3) I now venture mainly to address you, because 
I am about to write another paper intended to be hereafter published, elabo- 
rating more minutely and discussing more rigidly than before, the glaring 
fallacies, dating from the time of Newton, relating to the motion of the 
moon, which are briefly alluded to in the passages of Victoria Toto Ccelo to 
which I have ventured to direct your attention ; where you may observe I 
have frequently cited your admirably lucid Six Lectures on Astronomy , in 
justification of what I have advanced as to current views. 
I have taken the liberty to refer you to the printed matter in my book 
(the citations from which only occupy a few pages and will be more easily 
read than MS.) that I may thus be enabled to shorten this letter ; having 
now only further to acquaint you, — which I do as a duty and an act of 
courtesy towards you, — that finding nothing so distinct and clearly enunciated 
elsewhere on this subject, as in your Six Lectures, I shall write with special 
reference to one or two passages in them ; and these I will now point out, 
with a brief indication of the nature of the issues I intend to raise. 
I think this course the more proper on my part, as I am not unmindful that 
these lectures were originally delivered to a mixed audience in the country, 
though they appear to have been subsequently revised for publication — the 
preface to the 4th edition, which I shall cite, being dated from the Royal 
Observatory. 
In p. 176 of the lectures (fig. 56), it may be considered we have the 
working out of Prop, iv., Theor. iv., of Newton’s Principia, b. iii., and what 
constitutes the unfortunately false basis upon which the famous “ Problem of 
the Three Bodies ” has invariably been solved. I may briefly observe, that 
lhy primary argument against this, and the main principle of all my 
reasoning, will be that the physical or dynamical laws of astronomy can only 
deal with the real or absolute motions of the heavenly bodies, — not with 
mere relative or apparent motions, — and that the real motions of the moon, 
both as regards velocity and path, are utterly disregarded in these pro- 
positions. 
In p. 177 of the Lectures, the real motions of the moon being thus dis- 
regarded, her velocity is represented as only equal to 0'6356 of a mile in 
1"= 2,288 miles an hour (or 2,290 miles, as given in Ferguson’s Astronomy). 
I object, that on the heliocentric hypothesis, taking the radius of the earth’s 
orbit as = 95 million miles, and its mean motion as 68,000 miles an hour 
(as in the Lectures), then the moon’s motion is thirty times greater than 
above represented ; the motion of the moon being, in fact, upon the whole, 
greater than that of the earth. 
The “circumference of the moon’s orbit” is in the same place spoken of 
(as if it described a circular or oval path each lunation) and represented as 
only 1 ,500,450 miles in a month ; whereas the moon’s real path in a month 
is only an undulatory curve, crossing and re-crossing an arc of between one- 
twelfth and one-thirteenth part of the orbit of the earth, and, in round 
figures, is thirty times greater than represented, or equal to more than 
45,000,000 miles in a month. Every part of the reasoning based upon the 
moon’s fictitious “ orbit ” round the earth as a fixed centre, both as to the 
moon’s angular velocity, the direction of its motion, and its fall from the 
tangent (as well as the force of gravity thence deduced), is consequently 
