433 
fallacious, unless the hypothesis that the earth goes round the sun is 
abandoned. 
Again, on p. 184 of the Lectures, and in fig. 59, the whole argument is 
only tenable if based upon the hypothesis that the earth is stationary, and 
the moon moving in an oval “ orbit ” round it every month. In §§ 60-63 of 
Victoria Toto Ccelo will be found a sketch of the line of reasoning to be 
adduced against this. 
On p. 185 of the Lectures an allusion is made to what is previously ad- 
vanced at pp. 85-87, to which I should not at present have cared otherwise to 
advert ; but I cannot help considering that what is there stated can scarcely 
have been stated intentionally, and I have no wish to take advantage in 
argument of what it would appear may have been an oversight. In Viet 
Toto Coelo, § 11, I have pointed out that the motion of the moon in the quasi- 
ellipse, in which she has thus been represented to move, is in certain respects 
unlike the elliptical motions of the other heavenly bodies ; the moon’s motion 
being described as least at the apsides of her orbit, where the curvature is 
greatest, and greatest when in syzygy where the curvature is least. This 
— which is not the case, however, as regards the hypothetical ellipses described 
by the planets and comets round the sun — is nevertheless stated to be so 
(and it is even repeated) in the Lectures. For instance (p. 86) it is stated, 
“ The greater its (the planet’s) speed, the less its path is curved,” referring 
to k in fig. 30, where the curvature is obviously greatest, the planet being 
then in perihelion, and moving round the lower focus of the ellipse with its 
greatest velocity. 
In p. 85 of the Lectures, and the same figure (30), I regret that I may also 
be obliged to point out, that the tangential velocity or “ force,” “ that part ” 
[“ of the force ”] “ which acts in the direction om parallel to the orbit,” is said 
to “ accelerate the planet’s motion in its orbit.” But in “ resolving the force 
ms into two, km and om,” an unusual and unreal element is introduced 
into the demonstration. According to the first and second propositions of 
the Principia, and the ordinary methods of exhibiting the effects of centri- 
petal forces, ms, the central force, is — besides om, the tangential velocity — 
the only force affecting the body ex hypothesi. nm is therefore purely fic- 
titious, and could only have been real, had the orbit (instead of an ellipse) 
been a perfect circle, when nm would have been merely sm, the radius 
vector, produced beyond the circumference of the orbit ; in which case, also, 
there would be no “accelerative force,” as the circle would be described 
with a uniform velocity. I point out this for the sake of accuracy and ad 
hominem only, not as myself adopting any mode of demonstration that would 
seem to prove that gravitating bodies could ever revolve either in circles or 
ellipses round centres of attraction ; which I affirm, and claim to have 
proved elsewhere, to be demonstrably impossible. 
To revert to the motion of the moon. I will only further trespass upon 
your time by observing that when the moon is in conjunction, and when (as 
stated in the Lectures) the sun’s attraction upon it is greatest, it is precisely 
then (the moon’s real path being regarded) that the moon begins to move 
away from the sun with increasing velocity, as if repelled. It is also when the 
moon as it were has dipped within the earth’s orbit, between her last and 
first quarter, and when nearest the sun in conjunction, that her real motion 
is necessarily slowest, for then she ultimately falls behind the earth’s motion 
in its orbit ; and it is only when she rises beyond the earth’s path, between 
her first and last quarter, and when her distance from the sun is greatest in 
opposition, that her motion is greatest ; in other words, the reverse of what 
is stated in the Lectures, and of what may appear when a fictitious elliptical 
path is constructed for her, as with the earth at rest in its centre ; also the 
reverse of what would result were there really an attractive influence exer- 
2 g 2 
