existence-time and space. Succession is the simplest fact; an unvarying contact accompanied with a movement, is enough for that. But co-existence is highly complex. The chief points involved in it are those now mentioned,—a series of contacts, and the inversion of the series by an inverted movement. The repetition of these, with the same mental effects, constitutes that notion of permanence, or of fixity of arrangements, implied in the object world, the universe as co-existing in Space.*

By drawing the hand over a surface, as, for example, twelve inches of wire, we have an impression of the quality of the surface, and also of its length. On transferring the hand to another wire thirty-six inches long, the increased sweep necessary to reach the extremity, is the feeling and the measure of the increased extent. By practising the arm upon this last wire, we should at last have a fixed impression of the sweep necessary for a yard of length, so that we could say of any extended thing, whether it was within or beyond this standard. 'Nay more, whenever anything brought up a yard to our recollection, the material of the recollection would be an arm impression, just as the material of the recollection of greenness is a visual impression.

If we pass from length to two dimensions, as, for example, the surface of a pane of glass, we have only a greater complexity of movement and of the corresponding impression. Moving in one direction we get the length; in the cross direc

• Mr. Herbert Spencer has analyzed the relation of co-existence and sequence with great clearness and felicity. He remarks:-'It is the peculiarity alike of every tactual and visual series which enters into the genesis of these ideas, that not only does it admit of being transformed into a composite state, in which the successive positions become simultaneous positions, but it admits of being reversed. The chain of states of consciousness, A to Z, produced by the motion of a limb, or of something over the skin, or of the eye along the outline of an object, may with equal facility be gone through from Z to A. Unlike those states of consciousness constituting our perception of sequence, which do not admit of an unresisted change in their order, those which constitute our perception of co-existence admit of their order being inverted-occur as readily in one direction as the other.'-Principles of Psychology, p. 304.

tion, we bring other muscles into play, and get an impression of movement on a different portion of the moving system. In this way we should have the impression of a right angle, or a builder's square. The full impression of the pane of glass would arise through movements from side to side over its whole length, or from movements round the edge and several times across, such as to leave behind the feeling of a possibility of finding contact anywhere within certain limits of length and breadth. In this embodiment, and in no other that I know of, would an extended surface be conceived by the mind through muscularity and touch. (The action of vision will be afterwards discussed.)

A cubical block, exemplifying all the three dimensions of solidity, presents nothing radically new. A new direction is given to the hand, and a new class of muscles are brought to contribute to the feeling. The movement must now be over the length, over the breadth, and over the thickness, and the resulting impression will be a complication of the three movements. To get a hold of the entire solidity, it is necessary to embrace all the surfaces one after another, which makes the operation longer, and the notion more complex and more difficult to retain. But the resulting impression, fixed by being repeated, is of the same essential nature as the notion of a line or a superficies; it is the possibility, the potentiality, of finding surface in three different directions within given limits. A cubical block of one foot in the side means that, commencing at an angle, and going along one edge, a foot range may be gone over before the material ceases; that the same may then be done across, and also downwards; and that, between every two edges, there is an extended resisting surface.

The multiplying of points of contact, by our having a plurality of fingers, very much shortens the process of acquiring notions of surface and solidity. In fact, we can, by means of this plurality, come to measure a length without any movement; the degree of separation of the fingers, made sensible by the tension of their muscles, being enough.

Thus I can appreciate a distance of six or eight inches by stretching the thumb away from the fingers, as in the span of the hand. By keeping the fingers expanded in this way so as to embrace the breadth of an object, and then drawing the hand along the length, I can appreciate a surface by a single motion combined with this fixed span of the thumb and fingers. I may go even farther; by bringing the flexibility of the thumb into action, I can keep the fingers on one surface and move the thumb over another side, so as to have a single impression corresponding to solidity, or to three dimensions. We are, therefore, not confined to one form of acquiring the notion, or to one way of embodying it in the recollection; we have many forms, which we come to know are equivalent and convertible, so that where we find one, we can expect another. But the most perfect combination of perceiving organs is the embrace of the two hands. The concurrence of the impressions flowing from the two sides of the body, produces a remarkably strong impression of the solidity of a solid object. The two separate, and yet coinciding, images support one another, and fuse together in such a way as make the most vivid notion of solidity that we are able to acquire by means of touch. The parallel case of the two eyes is equally striking.

The notion of solidity thus acquired is complex, being obtained through a union of touch and muscularity, and combining perception of surface with perception of extended form. Space, or unoccupied extension, is movement in vacuo, from one fixed point to another; by the inverted operation, and by repetition giving the same contacts, this is considered to mean extension (as opposed to mere sequence in time). Empty space means the power of movement without contact or resistance, except at the extreme terms. Resistance and empty space are correlatives. In passing from the sense of the resisting to unresisted movement, we make the transition that developes the two cognitions of Body and of Space, under the common object property of Extension.

14. Distance, direction, and situation, when estimated by

DISTANCE.-DIRECTION.-SITUATION.

187

touch, involve, in the very same manner, the active organs; the tactile sensations merely furnishing marks and startingpoints, like the arrows between the chain-lengths in landmeasuring. Distance implies two fixed points, which the touch can ascertain and identify; the actual measurement is by means of the sweep of the hand, arm, or body, from the one to the other. Direction implies a standard of reference; some given movement must fix a standard direction, and movement, to or from that, will ascertain any other. Our own body is the most natural starting point in counting direction; from it we measure right and left, back and fore. For the up and down direction we have a very impressive lead, this being the direction of gravity. When we support a weight we are drawn downward; when not sustaining the arms by voluntary effort, they sink downward; when our support gives way, the whole body moves downward. Hence we soon gain an impression of the downward movement, and learn to recognize and distinguish this from all others. If a blind man is groping at a pillar, he identifies the direction it gives to his hand, as the falling or the rising direction. Circumstances do not, perhaps, so strongly conspire to impress the standard directions of right and left, but there is an abundant facility in acquiring them too. The right deltoid muscle is the one chiefly concerned in drawing the right arm up and away from the body, and without our knowing anything about this muscle, we yet come to associate the feeling of its contraction with a movement away from the body to the right. All directions that call forth the play of the same muscles, are similar directions as respects the body; different muscles mean different directions. The great pectoral bringing the arm forward, the deltoid lifting it away from the side, the trapezius drawing it backward, indicate to our mind so many different positions of the guiding object; and we do not confound any one with the others. We learn to follow the lead of each of these indications; we make a forward step to succeed the contraction of the pectoral, a step to the right the deltoid, a step backward the trapezius.

Situation, or relative position, is known, if distance and direction are known. The idea of position implies three points. Two points might give extension, but relative position implies that we pass from A to B, from B to C, and from A to C. Such movements often repeated, both in the direct and in the inverse order, impart the idea of permanent co-existence in relative position, which amounts to an experience of Extension. The multiplication of these is the enlargement of our education in the co-existing and extended, from which at last, by an exercise of abstraction, we rise to the notion of Space or Extension in general.

Form or shape is determined by position. It depends upon the course given to the movements in following the outline of a material body. Thus we acquire a movement corresponding to a straight line, to a ring, an oval, &c. This is purely muscular. The fixed impressions engrained upon the organs, in correspondence with these forms, have a higher interest than mere discrimination. We are called upon to reproduce them in many operations-in writing, drawing, modelling, &c.; and the facility of doing so will depend, in great part, upon the hold that they have taken upon the muscular and nervous mechanism. The susceptibility and the retentiveness of impressions necessary to draw or to engrave skilfully, are principally muscular endowments.

15. So much for the qualities revealed to us by touch, either alone or in conjunction with movement. The accompaniment of activity belongs to every one of the senses; it serves to bring about, or increase, the contact with the objects of the sense. There is in connexion with each of the senses, a particular verb, or designation, implying action; to taste implies the movement for bringing the substance upon the tongue; to smell, or to snuff, means an active inhalation of the odorous stream; to feel signifies the movement of the hand or other organ over the surface in search of impressions; in like manner, to hear and to see are forms of activity. In the cases of taste and smell, the action does not contribute much to the sensation or the knowledge; in the