A NEW LUNARIAN.
By Prof. C. W. MACCORD, Sc.D.
The construction of apparatus for illustrating the motions of the heavenly bodies has often occupied the attention of both mathematicians and mechanicians, who have produced many very ingenious, and in some cases very complicated, combinations. These may be divided into two classes; the object of the first being to represent exactly what occurs--to reproduce the precise movements of the various bodies represented in their true proportions and relations to each other, in respect to distances, magnitudes, times, and phases. When the absolute complexity of the movements of the bodies composing the solar system is considered, it is not so much a matter of wonder that a planetarium which shall thus imitate them is a very delicate and complicated machine as that it should lie within the limits of human ingenuity.
In the second class, the object is to show the nature and the causes of specific phenomena, without regard to others perhaps, and without necessarily paying attention to exact proportions of distances and dimensions. Indeed, it is often the case that the illustration is made clearer by exaggerating some of these and reducing others; thus, for example, the causes of the variation in the lengths of the days and nights, and of the changes in the seasons, can be exhibited to much better advantage by an apparatus in which the diameter of the sun and its distance from the earth are enormously reduced than they possibly could be were they of their proper proportionate magnitudes; nor is the presence of any other planet, or the attendance of a satellite, at all necessary or even desirable for the purpose named.
It is apparent that machines of this class can be made much more simple than those of the first, while at the same time it may safely be asserted that for educational purposes they are far more useful.
In both classes, the action involves the use of some sort of epicyclic train, since the motions to be explained are both orbital and axial. The planetary body is carried round by a train-arm, and its rotation about its axis is usually given it by a train of gearing, the inner or central wheel of which is stationary, being fastened to the fixed frame supporting the whole.
AN IMPROVED LUNARIAN.
The lunarian which we herewith present belongs to the second of the classes above named; in its construction an attempt has been made to show by as simple means and in as clear a manner as possible the nature of the following phenomena, viz.:
1. Apogee and perigee.
2. The moon's phases.
3. The rotation on her axis, by reason of which she always presents nearly the same face to the earth.
4. The inclination of her axis to the plane of her orbit, and her consequent libration in latitude.
5. Her varying angular velocity, and consequent libration in longitude.
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.