the law of Kepler) which would be the exact copy in miniature of the orbit of Mars, relatively to the sun.

In the figure, B represents a base, from which rises vertically the pivot C (in dotted outline). Turning freely on this pivot, is a flanged or spool-shaped eccentric pulley D, to which the horizontal arm A is rigidly secured which carries the revolving body P. The arm A is set in motion by means of a cord wound around the eccentric pulley D and drawn from it by winding on the other pulley H, which is driven by some steady power; the pulley D being of the proper eccentricity and ellipticity to give the radius vector, or arm A, its proper motion for describing equal areas in equal times while it is being so driven.

The planet P is in the form of a car, its wheels having perfect anti-friction bearings and concave rims, running on a pair of knife edge rails E. The car body is fitted with a shot receptacle, by which its weight may be varied. It is drawn centreward by the cord h winding on the eccentric pulley W,

to which a rotary force is given by a coiled spring S; the pulley W being regulated by stops to turn just half way round; one half of its circumference exactly equaling the difference between perihelion and aphelion, or the least and greatest distances of the planet P from the centre.

The tension of the coiled spring S, and the eccentricity of the pulley W are so adjusted that a spring weighing scale attached to the car P, and drawn outward, will register a centreward attraction, which is inversely as the square of the distance from the centre.

While the arm A is strictly level, yet the rails E are adjustable for grade, and when they are also level, the car P, when made to revolve around the pivot C, is only affected by the two conditions—its unequal propulsion in its orbit, and the centreward traction of the cord h. But by slightly elevating the outer end of the rails E, we also give the car a gravity tendency toward the centre, which is uniform from end to end of the rails. This supplies what is called the

"Newtonian constant;" which is increased or diminished, as the rails are more or less inclined.

I made many careful experiments with this apparatus, both with the rails E level, and with them variously inclined; but they all gave practically the same results-when the orbital motion of P was just sufficient to start it from the perihelion stop p, in the fastest portion of its orbit, it would roll out toward the aphelion stop a, but return to p again on or before reaching the slowest, or the aphelion portion of its orbit, and remain there till it neared the fastest, or perihelion portion of its orbit again; and when the orbital motion was slightly increased to gain better results, it would roll out to a, and remain there; manifesting a disposition to leave the system, but for the restraint of the cord h, and stop a; thus clearly demonstrating that Kepler's second law furnishes another instance in which theory and practice do not join hands.

The fallacy of this law may however be illustrated without resort to the mechanical

experiment which we have described, by the use of the following diagram:

In this figure, S represents the sun, or centre of force, and M a planet at the perihelion point of its orbit, revolving around S in the direction of the arrows-its radius vector describing equal areas in equal times.

As the central attraction must necessarily be a little stronger than the tangential tendency of a revolving body, to keep it in its orbit, we will (referring to the diagram) let 10 represent the centrifugal force of the planet M, gained from its orbital velocity, at P; and 11 the combined focal attraction due to the "Newtonian constant" and the general law of gravitation, (assuming the Newtonian constant to be 1.)

At a, with the velocity of the planet and the focal attraction diminished, let 9 represent the centrifugal, and 9 plus 1,—or 10, the centripetal force affecting it; at b, let 8 and 9 represent the two forces; at c, 7:8, and at A, 6:7.

The planet has, at A, reached its lowest velocity, and from this point on toward P again (according to Kepler) its orbital motion, and therefore the centrifugal force will gradually increase, and the centripetal force also reassert itself.

From P to A, the influence of the two opposite forces on the planet was steadily diminishing; but through the assistance of