The mechanism consists of a train-arm, T, which turns upon the vertical
pivot, P, fixed in the stand. In this arm, T, are the bearings of two
cranks, B and C. equal in length to each other and to a third crank, A,
which is stationary, being fixed to the pivot, P, by a pin, p. To the
crank-pin of A is secured a reverted arm, A', which supports the earth,
E, and keeps it also stationary. The three cranks are connected by the
rod, R, like the parallel rod of a locomotive: to which is fastened by a
steady-pin, o, the bevel wheel, D, concentric with the crank-pin, b. The
head of this crank-pin is first made spherical, then faced off at an
angle with the axis of b, and in the sloping face is firmly fixed the
long screw, S, forming the support for the moon, M, which is caused
to rotate about the axis of S, by means of the wheel, F, equal to
and engaging with D. The upper end of S projects slightly through a
perforation in the moon, and to it the hemispherical black shell or cap,
G, is fixed by the screw, K; this cap represents the unilluminated part
of the moon, and since G, s, b, and B, are in effect but one piece, the
cap moves precisely as the crank does.
Now as the train-arm, T, is carried round, the cranks, B and C, will
turn in their bearings; but by their connection with A, they are
compelled to remain always parallel to themselves, and thus the axis of
the moon receives a motion of translation. But since during this action
the wheel D turns relatively to the pin b, the moon evidently rotates
about its axis with an angular velocity precisely equal to that of its
orbital motion.
The black shell however has the motion of translation only, and thus
exhibits the phases of the moon, on the supposition that the source
of light is infinitely remote and the rays come always in the same
direction, which is not strictly true, of course; but the reasons of the
varying appearance are as clearly shown as if it were absolutely exact.
The same may be said in regard to the phenomena of libration; the
inclination of the moon's axis to the plane of her orbit is really
small, but is purposely exaggerated in this apparatus in order to make
the results apparent; in the position represented, it is quite obvious
that an observer upon the earth can see a little past one pole, and
cannot quite see the other, as well as that this condition will be
reversed after half a revolution.
The action in reference to the phases is clearly shown in the small
diagram on the right. The one on the left illustrates the manner in
which the libration in longitude is made apparent. It will be noted that
the center of M is not directly over the axis of the bearing of the
crank, B, so that after half a revolution the moon will be farther from
the earth than she is here shown. Her orbit here is circular, whereas,
in fact, it is an ellipse; but the earth not being in the center, her
angular velocity in relation to the earth is variable, the result
of which is that, when she is near her quadrature, the actual force
presented to the earth is slightly different from that presented when in
conjunction or opposition.
Thus these various peculiarities of the motion of our satellite are
exhibited by comparatively simple means--the number of moving parts
being, it is believed, as small as it can be made; and the substitution
of a crank motion for the usual train of wheels, we think, is a new
device.
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