induction. But before the inquiry can make any considerable progress, it will plainly be needful to form some clear and definite conception with regard to the real nature of both these kinds of substance, and the laws of mutual action which must be supposed to exist between them. Such will be the first object of the present investigation. It will then be endeavoured to trace out, in order, the main consequences of the fundamental hypothesis, and their correspondence with the known phenomena of physical change.

CHAPTER I.

ON MATTER AND ETHER.

1.

EVERY particle of matter attracts every other particle, with a force varying inversely as the square of the distance between them.

This is the great discovery of Newton, which must form the natural starting point for every further advance in physical science. The history of Astronomy for two centuries has consisted mainly in the development of its results. But rich and fertile as its consequences, in one direction, have proved to be, those which flow from it in another have never been traced with sufficient clearness. When examined narrowly, it points to conclusions of great importance and scientific value.

2. Every particle is either a mathematical point, or else contains such a point, as the true centre from which the attraction proceeds.

By the fundamental law, the attractive power varies inversely as the square of the distance. But distances cannot be measured from a space of finite dimensions. They must be measured from some point only. Hence, if the attractive forces exerted by a particle on every other are determinate, then the point from which they emanate, or

from which all the distances are reckoned, must be determinate also.

3. There is no reason for admitting, in the particles of matter, a solid sphere of repulsion, enclosing the true centre of force, and distinct from it.

First of all, such an assumption is very complex and arbitrary, and thus violates the first and second Axioms of inductive inquiry. A central force, emanating from a definite point or centre, is proved to exist. The hypothesis introduces these further elements; an arbitrary radius of the solid nucleus, an arbitrary shape of the atom, a surface of abrupt and infinite repulsion, a structure unalterably rigid, and also an arbitrary relation of the centre of force to the supposed solid nucleus. None of these things can be rightly assumed, while there is no clear necessity for the supposition.

Again, two of these assumptions are opposed to all the conclusions from experience. They would rest a scientific datum upon a popular impression, which exact science disproves. In compound bodies, repulsion always begins at some distance from the surface. A sudden change, then, from attraction to infinite repulsion, has no analogy in its favour. The most solid bodies, also, have always some elasticity, and a case of perfect rigidity is not to be found. The hypothesis, then, of a rigid, solid nucleus, not only finds no warrant in the law of gravitation itself, but is also opposed to all known analogy. Hence, by Axiom II. it is inadmissible, until it can be shewn that a simpler hypothesis, the natural result of the law alone, fails to satisfy the actual phenomena.

4. The simplest view of matter, derived at once from the law of gravitation, is that it consists of monads, or move

able centres of force, unextended, but definite in position, which attract each other with a force varying inversely as the square of the distance between the centres.

This conception, of points that are centres of force, results plainly and unavoidably from the nature of the law of gravitation. Any further conception of the constitution of matter is an unproved addition. Also the conception, in this simplest form, involves no greater metaphysical difficulty than may be shewn to exist equally in every other conception of primitive or constituent atoms.

5. The particles of matter, so constituted, could never coalesce with each other, and thus lose their individual being, or disappear.

Let us suppose two particles to fall from rest in the line joining their centres. Unless all other particles were disposed with perfect symmetry in reference to this line, and were also at rest, there must be some lateral disturbance. But in this case they will describe ellipses round their centre of gravity, and after their nearest appulse, will recede again. Hence it is plainly impossible that any two particles, so formed, should coalesce together.

6. The law of gravitation, in matter so constituted, will not alone account for the cohesion and solid structure of bodies.

Let us assume one thousand millionth of the earth's radius (= in. or 63 millimetres nearly) for a linear unit. Assume further that a small sphere of this radius, and of the density of the earth, has its particles symmetrically placed, and 10" for the number in its radius, or its mean linear density. The attraction of this sphere on an atom at its surface will be 109 less than the atom's weight. traction of atom on atom at that distance will be

The at

n

less than the weight of an atom, and at their own mean distance π.10" less than the weight. Hence two atoms must be 64720×102 nearer to each other than this mean distance, that one may have a cohesive action on the other equal to its own weight, so as to retain it in permanent connection. There is plainly no arrangement of the particles which can satisfy this condition, and retain the least semblance of a solid structure. We must therefore look elsewhere for the explanation of cohesive force and solidity.

Two alternatives are possible. Either the law of gravitation must be modified for small distances; or there must be some other substance, distinct from common matter, on which the phenomena of cohesion depend.

7. A self-repulsive ether, wholly distinct from common matter, also exists, and is diffused widely throughout all known space.

The closing words of the Principia are like a prophecy, and shew in what direction the second main series of physical discovery must be attained.

"I might add something about a certain very subtle spirit, which pervades dense bodies and lies hid in them; by the power of which, bodies at very small distances attract each other, and when brought close together, cohere; and electrical bodies act at greater distances, attracting and repelling neighbouring bodies; and light is emitted, refracted, and reflected, and warms bodies; and sensation is excited, and the limbs of animals are moved at will, through vibrations of this spirit, propagated through the nerves to the brain, and from the brain to the muscles. But these things cannot be expounded in few words; nor is there extant a sufficient abundance of