CHAPTER XIX.

ON THE DISCOVERIES IN PHYSICAL ASTRONOMY.

334. THE astronomical knowledge, that existed before the time of Sir Isaac Newton, was derived from long and tedious observations, which had been continued through many ages. The various discoveries, such as the elliptical motions of the planets, the law of the periodic times, the precession of the equinoxes, the direct motion of the apogee of the moon's orbit, the retrograde motion of its nodes, the variation and evection of the moon, were apparently so many unconnected circumstances.

It was Newton who first, from a few general laws of matter and motion, by help of mathematical principles, shewed the origin and connexion of these different phænomena, and that they were simple results of the general properties which the Creator has ordained should belong to matter and motion. Before his time Physical Astronomy did not exist. The attempts of Kepler, Des Cartes, and others, to explain several astronomical phænomena from physical principles, now scarcely deserve notice.

335. It would be incompatible with the plan of this work to enter into any detail of the mathematical principles of physical astronomy. But the discoveries in physical, are so connected with plane astronomy, and so important, that it was not possible to avoid the mention of many of them, when occasion offered; and it may not be deemed improper to conclude with

a short account of the general advantages, the science of astronomy has received from the application of physical principles.

Sir Isaac Newton has shewn that all the bodies of the solar system mutually attract each other. That the gravitation or the force of attraction exerted by, or toward any body, is in proportion to the mass of the attracting body. That this force, is greater or less, according as the distance from the attracting body is less or greater, and that in proportion to the square of the distance.

a

336. Of the immediate cause of gravitation, he confesses himself ignorant. He says, that gravity must be caused by an agent acting constantly according to certain laws: but whether this agent be material or immaterial, he did not attempt to decide. He reflected much on this subject, but it does not appear that he ever came to any conclusion which satisfied himself. At this day we are not advanced one step farther toward the knowledge of the proximate cause of gravity, than Newton himself had advanced.

The knowledge of the proximate cause, however, is not necessary to ascertain the existence and laws of the action of gravity. The latter are collected from a variety of facts.

From the laws of the action of gravity combined with laws of matter and motion, deduced from observations on terrestrial matter, Newton explained the motions observed in the solar system.

The sun situate in the midst of the planets attracts them all toward itself, while they also attract the sun, but from the greater mass of the sun, the effect of the planets in moving the sun is very small, compared with the attraction of the sun on the planets.

a Letter to Dr. Bentley, page 438, vol. 4. Works.

Horsley's Edition of Newton's

Had no other impulse been given to each of the planets, they and the sun would have come together in consequence of their mutual attraction. But a proper impulse was given to each planet in a direction either perpendicular, or nearly perpendicular to a line joining the sun and planet. In consequence of this impulse, and of the attraction of the sun, each planet continues to revolve round the sun in an elliptical orbit not differing much from a circle, that is, not very eccentric. These impulses must have been given at the creation. These impulses required, to use the words of Newton,a "the Divine Arm to impress them according to the tangents to their orbits."

The simple laws of matter and motion, which the Almighty has been pleased to ordain, are sufficient to preserve the motions of the system for a length of time, to which our bounded intelligence cannot put a limit.

337. The preparatory steps of Newton consist, principally, in shewing, that a body projected, and attracted to a fixed centre, describes equal areas in equal times, about that centre, and in investigating the laws of the variation of the force by which a body attracted toward a given point, may be made to move in a given curve.

He particularly shews by an interesting application of mathematical principles, that a body moving in an ellipse and describing equal areas in equal times, about one of the foci, must be attracted toward that focus, by a force varying inversely as the square of its distance from the focus: that the squares of the periodic times of bodies, moving in different ellipses about a common centre of force in the common focus, are as the cubes of the greater axes.

He also, conversely, proves that a body attracted to a fixed

a Third Letter to Dr. Bentley.

centre, by a force varying inversely as the square of the distance, and projected in a direction, not passing through the centre, with a velocity, not exceeding a certain limit, will describe an ellipse about the fixed centre. The increase, or decrease of velocity, generated by the attractive force, is so exactly combined with the velocity of projection, that the efficacy of the attractive force in drawing it from the tangent of the curve, in which tangent it would continue, were the attractive force to cease, is such as always to retain it in the circumference of the ellipse.

After considering a variety of cases about a fixed centre, he considers two or more bodies, mutually attracting each other.

He also demonstrates that if a globe consist of particles each of which attracts with a force varying inversely as the square of the distance, that the united forces of all the particles, compose a force tending to the centre of the globe, and varying inversely as the square of the distance from the centre of the globe.

338. The application of his investigations to the system of the world, may be briefly stated as follows.

The effort by which all bodies within our reach, tend toward the surface of the earth, we call gravity. If left to themselves, bodies fall toward it in a right line, but if projected, they tend toward it in a curvilinear course.

By gravity also a pendulum, when removed from a vertical position, tends to it again, and so vibrates.

Experiments on the motions of falling bodies and the vibrations of pendulums, after proper allowances made for the resistance of the air, shew that this force of gravity, measured by the velocity produced in a given time, is nearly the same in the same place, at any distance from the surface to which our experiments can reach.

But along with the knowledge of this fact, we also arrive at another, of great importance, viz. that however dissimilar bodies are in their visible properties, yet they are all equally affected

by gravity, that each particle of a body is acted upon by the same force, that the component parts of air and gold, are equally impelled toward the earth. This knowledge is derived from observing that all bodies, at the same place, describe, in falling toward the earth, equal spaces in equal times, abstracting from the resistance of the air.

To these laws of gravity, we are enabled also by experiment to add a third; that the gravitation toward the earth is the united effect of gravitation toward its separate parts, or that each particle of matter attracts; from whence it follows, that the attraction of gravitation between terrestrial matter is mutual. Several strong arguments induced Newton to adopt this, as an Hypothesis, but it seems not to have been fully verified, till long after his death. No facts, proving it, were known to him.

Although we are ignorant of the cause of gravitation, yet we can inquire whether it be a principle which has no other connexion with the earth, than that of impelling bodies toward its centre, or whether it be a principle attached to each particle of matter, and so whether the force by which bodies are impelled towards the centre of the earth, arises from the joint attractions of the particles of which the earth is composed. Newton, as

a If the Earth had been originally a fluid of uniform density, it would have followed from the mutual attraction of its parts, and from its rotation on its axis, that the increase of the length of a pendulum vibrating seconds would have been nearly as the square of the sine of latitude. Also if the Earth had been originally a fluid of unequal density, the denser parts would have so arranged themselves towards the centre, that the law of increase of the length of the pendulum would still be as the square of the sine of latitude. Now we know that the interior of the Earth is denser than the surface, and a great number of experiments have shewn, that in both hemispheres the increase of the length of the pendulum is as the square of the sine of latitude. From hence it has been inferred that the Earth was originally in a fluid state.

The above is one of the results of analysis and experiment that, according to Laplace, ought to be ranked among the few certainties that Geology furnishes.