435 
absolute motions (which on geometrical principles is necessarily correct) 
there is no error in treating the moon as describing an ellipse round the 
earth, perturbed by the difference of sun’s force on earth and on moon ; and 
there is no error in speaking of the moon’s relative velocity round the earth 
as the small velocity in such an ellipse. 
The failure in your reasoning is simply the want of the steps for inferring 
relative force and relative motion from absolute force and absolute motion ; 
and this seems to go through the whole. 
You can perhaps understand that, as a very closely occupied man, I 
cannot enter further into this matter. 
I am, Sir, 
Your obedient Servant, 
Gr. B. AIRY. 
To James Reddie, Esq. 
[The Reply to this letter is not inserted, as its substance will be found in 
the paper On the Motion of the Moon , Note D.] 
NOTE D. (§§ 2, 31, 33.) 
The Paper alluded to in the text as submitted to Section A of the British 
Association at Bath, in August, 1864, having been referred to two of our 
Vice-Presidents, Mr. Mitchell and Dr. Thornton, is now here printed upon 
their recommendation, with the approval of the Council of the Victoria 
Institute, that it may be discussed along with the foregoing Paper, should 
any prefer doing so. It is as follows : — 
ON THE MOTION OF THE MOON, AND THE SUN’S REPUL- 
SIVE INFLUENCE, AS THE PROBABLE CAUSE OF THE 
VARIATIONS OF THE MOON’S MOTIONS, &c. 
1. The time which the moon occupies in passing through the shadow of 
the earth during an eclipse is, roughly speaking, four hours ; and — taking the 
earth’s diameter at 8,000 miles, and assuming the breadth of the earth’s 
shadow, plus that of the moon’s disk, to be the same as the breadth of the earth 
itself, — it has hence been deduced, that the moon in passing through the 
earth’s shadow is moving at the rate of 2,000 miles an hour : so, calculating 
her path for a day or for a month of thirty days at the same rate, we have 
48,000 miles as the extent of her daily path, and 1,440,000 miles as her path 
during each lunation. These figures and calculations, however, are only 
approximative. The moon’s velocity is stated by the Astronomer Royal of 
England, in his well-known Six Lectures on Astronomy , to be more pre- 
cisely 2,288 miles an hour, and her path each lunation 1 ,500,450 miles ; and 
even in old works on Astronomy, such as Ferguson’s, it will be found that 
the velocity of the moon is given as “ about 2,290 miles an hour.” 
2. From the same simple data, the moon’s mean distance from the earth 
has been deduced. Assuming her path in a month to be a circle of 
1,500,450 miles in circumference, we have only to divide these figures 
by 3T415...(the well-known ratio of the diameter to the circumference of 
