22d April 1866.
SLR—The statement herewith is offered as a condensed and easily. com- prehensible view of the pr of that the moon turns on her • own axis- in the same period that she moves around the earth.
Mr. Symons fails to solve accurately the problem of the moon's rotation on her own axis coincident with her rotatory motion in her orbit, because he starts with the incorrect assumption that the relation of the moon to the earth is the same as that of a point on the circumference of a wheel rotating on an axis.
The relation of the moon to the earth is not of this purely physical kind, but is in truth dynamical. While rotating around the earth in her own orbit, she moves in space freely, and unattached, if such an expression may be allowed. In this rotation she is acted on by two forces ; one centrifugal, which impels her at a tangent to her orbit ; the other, gravity, acting at right angles to the former. The product of the two forces is reresented• by a curve corresponding to her orbit. If that orbit be• divided into, say, four equal arcs, at points called respectively, A, B, C, D, it will be seen that the moon moving in her orbit without any rotation on -her axis would not uniformly turn the same face to the earth. But the telescope tells us that the same face is always towards the earth : ergo, she rotates on her
axis as she moves in her monthly orbit. G.
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