from the body.—­Does it act any where else?—­No; then it certainly exists in this part of space, and no where else; that is, it hath figure; namely, the figure of the nervous system, which is nearly the figure of the body.  When the idea of solidity is excited, as above explained, a part of the extensive organ of touch is compressed by some external body, and this part of the sensorium so compressed exactly resembles in figure the figure of the body that compressed it.  Hence, when we acquire the idea of solidity, we acquire at the same time the idea of FIGURE; and this idea of figure, or motion of a part of the organ of touch, exactly resembles in its figure the figure of the body that occasions it; and thus exactly acquaints us with this property of the external world.

Now, as the whole universe with all its parts possesses a certain form or figure, if any part of it moves, that form or figure of the whole is varied:  hence, as MOTION is no other than a perpetual variation of figure, our idea of motion is also a real resemblance of the motion that produced it.

It may be said in objection to this definition of motion, that an ivory globe may revolve on its axis, and that here will be a motion without change of figure.  But the figure of the particle x on one side of this globe is not the same figure as the figure of y on the other side, any more than the particles themselves are the same, though they are similar figures; and hence they cannot change place with each other without disturbing or changing the figure of the whole.

Our idea of TIME is from the same source, but is more abstracted, as it includes only the comparative velocities of these variations of figure; hence if it be asked, How long was this book in printing? it may be answered, Whilst the sun was passing through Aries.

Our idea of PLACE includes only the figure of a group of bodies, not the figures of the bodies themselves.  If it be asked where is Nottinghamshire, the answer is, it is surrounded by Derbyshire, Lincolnshire and Leicestershire; hence place is our idea of the figure of one body surrounded by the figures of other bodies.

The idea of SPACE is a more abstracted idea of place excluding the group of bodies.

The idea of NUMBER includes only the particular arrangements, or distributions of a group of bodies, and is therefore only a more abstracted idea of the parts of the figure of the group of bodies; thus when I say England is divided into forty counties, I only speak of certain divisions of its figure.

Hence arises the certainty of the mathematical sciences, as they explain these properties of bodies, which are exactly resembled by our ideas of them, whilst we are obliged to collect almost all our other knowledge from experiment; that is, by observing the effects exerted by one body upon another.

3. Of the Penetrability of Matter.