uniform motion forever, unless disturbed by the action of an external cause.

The same cause produces the same effects. This proposition, so far as it goes, is identical with the first of the three great laws of motion, which is, "A body must continue forever in a state of rest or of uniform motion, in a straight line, if not disturbed by the action of an external cause.' If this be true of bodies both at rest and in motion, the proposition is truc as regards bodies in motion, and as true when considered apart from the direction of the motion as it is when the law defines the line of motion.

4. All motion is in proportion to the force which produces it.

The degree of the effect is in proportion to the cause; in other words, add to or take from the force in action upon given matter, the quantity of motion is changed propor tionally. The second of the three laws is: "Every change of motion produced by the external (objective) cause is proportional to the force impressed, and in the direction of a straight line in which the force acts." The proposition affirms the first clause of the law, and this is necessarily true independently of the truth of the latter clause.

We draw from this proposition the following as corrollaries: 1st, that force is divisible, different quantities or degrees. of it acting at different times on the same matter; 2d, force is transferable, for otherwise, that is, without transfer of force, there could be no increase or diminution of motion.

5. The absolute condition of the transfer of force is its presence with matter not susceptible of motion by it.

The essential property of force being action, wherever it

is, it acts, or from its nature it is transferred from matter which cannot be moved to matter having space for motion.

6. The degree or velocity of the motion of a mass deponds on the degree of force which acts upon cach atom constituting the moving mass. It appears self-evident, that every atom, perhaps in a degree according to its clement or kind, requires always the same force to move it with the same velocity, and the motion of the mass depends on the degree of force relative to the number of its atoms.

7. Every atom of the solar system is in continued motion, orbital and rotary.

IIence it follows, that it is force which determines the position of every atom, mass, and world, and determines their position positively in space. It also determines the relative position of all things.

8. Matter occupies but one place in space at the same time, and consequently no atom can have motion but in one line of direction at the same time.

Hence it follows, that all motion is orbital, rotary, curvilinear; for, all atoms being in curvilinear motion, no addition of rectilinear motion can change the curve into the straight line, there will ever remain the element of the curve. The contrary opinion indicates infinity, and is unintelligible. The foundation principle of geometry is the measure of all angles by arcs of the circle, and the measurement of the circle or curve conversely by the inscribed straight lines or angles.

Hence the fixed relation between the diameter of the circle and its circumference, and the measure of motion by

the diameter of the circular orbit. We assume that the harmonic motion of the heavenly bodies bears a certain proportion to the orbit, that this velocity has a fixed ratio to the diameter, and that this ratio mathematically determined is proportional to the square of the distance of the circumference from the centre.

The velocity of bodies moving in free space being in a fixed ratio to the orbit, it is the present force, the active principle, which determines the orbit. A change of the degree of force would enlarge or diminish the orbit. In all free motion, therefore, the motion is uniform and harmonic. Two atoms moving in the same orbit will move with the same velocity; in different orbits will preserve that relative position which is determined by the difference of orbit, and the difference of the line of direction; so that mathematically the relative position of any body can be deduced, given as the elements of calculation its orbit and direction of motion.

9. Rectilinear motion, or motion in a straight line, cannot be affirmed of any atom belonging to or in harmony with the solar system, or with the system of worlds. The horizontal line on the surface of the globe is curvilinear. So from any one point to another, in, on, and about the earth, the moving body takes the curved line. In the old philosophy, circular motion was deemed the natural motion; but the new philosophy conceives of circular motion as constrained by the operation of conflicting forces.

10. The supposed perpendicular descent of a falling body is a curvilinear motion. This is not practically admitted, but mathematically deduced; the fall is termed a "cubical

parabola." The supposed attraction of the earth does not draw in straight lines, falling bodies preserving ever their rotary motion.

11. Bodies in rotation with the earth, on receiving additional force, must either take a higher level of rotation, or use the force received in additional motion in a new direction.

12. In the act of falling whereby a lower level of rotation is assumed, force must be transferred from the falling body when its motion is suspended.

The motion of falling is added to the rotary motion, thereby giving action to the present force. This motion being suspended, only rotary motion in a smaller orbit remaining, force will be transferred. Hence arises spare force of descent. The spare force of descent will be measured by the degree of descent. Hence the spare force of falling bodies is measured by the square of the time of descent, equal times giving equal distances of descent. Thus most distinctly is presented the law of falling bodies, or motion begetting motion, which, indistinctly understood, caused the great controversy between the schools of Des Cartes and Leibnitz, and which to this day has obscured mechanical science, by making the occasional abnormal motion of falling bodies the element of calculation of harmonic motion.

13. The motion of the heavenly bodies being harmonic with fixed velocity according to orbit, their velocity is the immediate measure of the velocities of retarded or accelerated motion; that is, the abnormal motion is detected and

measured by the normal, the motion of bodies in confined space being determined by the velocity of bodies in free space.

Time is the indirect measure of velocity; the motion of the earth which measures time, the direct measure of velocity. Hence all velocity is known by and measured by the rotation of the earth. A body which moves thirty miles in one hour moves over the given space isochronously, or while the earth has moved one twenty-fourth part of her rotary circle. Time, therefore, has no reference to force and motion so as to increase or diminish them, and motion refers to time only as indicating the extent of the motion of the earth.

14. There is beside the consentaneous motion of the atoms of the mass, or the progressive motion of the mass, an atomic or molecular motion of every atom composing the

mass.

This proposition will receive its most perfect demonstration by the facts and phenomena of nature; but is believed from analogy, that the same law governs the minute as well as the extended, also from the fact that there is space between all atoms, that force is primarily in action on the atoms. If force be present with atoms, and there be space for motion, motion is affirmed. We leave this propo sition mainly upon these general statements, recurring, in this place, to one most significant fact: "The expansion of volume of small bodies by dilatation from heat, may be obtained without sensible error by trebling the number which expresses its increase in length.” Daniell's Introduction to Chemical Philosophy. The trebling of the diameter, it will be perceived, gives nearly the circumference of the circle of motion.