body may influence the direction of its vibrations. If a little fine dry sand be strewed over a vibrating surface, it will be thrown into violent agitation by the force communicated to it in parti cular situations, but in other situations it will remain at rest, and it will thus enable the eye to distinguish the vibrating from the quiescent parts. Thus, if vibrations be excited in a plate of glass or metal, by drawing the bow of a violin across its edge, it will emit a musical sound, and the sand will immediately arrange itself in certain lines regularly disposed, where it will accumulate from other parts, and remain at rest. It is thus found that the adjacent divisions of the surface are in different states of vibration, some being always elevated while others are depressed; and the oppositely vibrating parts are separated by lines of rest. These lines of rest are termed nodal lines, and they vary in form and position with the part where the bow is drawn across; but the point by which the plate is held being necessarily in a state of rest, must be included in a nodal line (14). Similar points of rest, or nodal points, are found on a vibrating string; and pieces of paper placed at the half, third, fourth, or other aliquot points of its length, will remain on it during its vibration, but will instantly fly off from any intermediate points. They are points of equilibrium between two adjacent oppositely vibrating parts. Indeed all vibrating bodies have a tendency to divide themselves into a certain number of parts which perform their vibrations independently of each other.

§ 55. The amount of force which may be accumulated from the frequent and regular repetition of minute impulses to the particles of elastic solids is very great, just as momentum may be accumulated in a pendulum by frequent small impulses (§ 29); and the cohesion of glass itself has been known

(14) If a plate of glass, a b c d, be held horizontally at its centre, E, between the finger and a thumb, and sand be scattered over its upper surface, upon causing it to emit a musical note, by drawing a violin-bow along its edge, the sand will arrange itself in lines constituting regular figures, the form of which will depend upon the pitch of the note. The lines a E, b E, c E, d E, in the figure, repre sent a common arrangement of these nodal lines; the point, E, by which it is held, will be, of course, quiescent.

6

to yield under the intense vibrations of a musical note. If we pass our moistened fingers lightly along a glass tube, two or three yards in length, and from three-fourths of an inch to an inch in diameter, we may generate a force which will be sufficient to move a leaden ball placed within it, and even to draw it up against the action of gravity, when the tube is inclined several degrees to the horizon. Or if we fix a small glass tube into a beam of wood, and cause it to vibrate longitudinally, in the same way, the successive and periodic impulses will be sufficient to agitate the beam throughout its mass, and to produce vibrations of such an extent that whole handfuls of sand thrown upon it will be projected upon the lines of rest, which will thus be accurately defined.

§ 56. These vibrations alter the molecular arrangement and strength of bodies while they last, so that if a weight of 90 pounds be suspended from a copper band of three yards in length, 0.4 inch wide, and 0.04 inch thick, it will remain unchanged for any length of time; but if made to vibrate, it will become lengthened six or seven inches. M. Savart measured the lengthening of rods of glass and brass by the act of vibration, under the friction of a damp cloth, and ascertained the amount of mechanical force which would be required to be directly applied to produce the same effect, and found it to be in the first case, (the diameter of the cylinder being 1.14 inches,) equal to a weight of 2000 pounds; and in the second, (the diameter being 1.38 inches,) 3800 pounds. The facts are of the utmost practical consequence with regard to structures in metal which are destined to support great weights, and are at the same time exposed to regular oscillations and vibrations.

We will now direct our attention to the forces of homogeneous attraction and repulsion.

IV. HOMOGENEOUS ATTRACTION AND

REPULSION.

§ 57. THE force of COHESION in bodies is measured by the amount of any force which may be required to separate their particles, or break them, and may be ascertained by experiment. The opposing force may be applied in various ways. (1) It may tend to tear the body asunder, in the direction of its fibres; (2) it may tend to break the body across; (3) it may tend to

crush the body; (4) it may tend to separate the particles by means of torsion or twisting. The investigation of the strength of materials, and the different degress in which they resist the action of force, so variously applied, belongs to mechanical science. The following table shows the force of cohesion from experiment of a few solids, as indicated by the weights required to tear them asunder, and to crush them.

TABLE II. Of Strength of Materials.

§ 58. The force of cohesion is opposed to mechanical force in the case of the surfaces of two solids of the same substance moving upon each other, and is estimated by the resistance to the motion, which is denominated friction.

Friction is greatest between rough surfaces, and diminishes with the degree of polish given to them.

All other circumstances being equal, it is directly proportioned to the pressure of the two bodies. Friction also arises from a similar opposition of the force of adhesion, in the case of the two surfaces in motion being of dissimilar matter; but it is greater between homogeneous substances than between heterogeneous ones.

§ 59. The subject of FRICTION, again, is purely mechanical; but we re-enter within the strictest limits of our department in considering next, those adjustments of the two antagonist powers of homogeneous attraction and repulsion, which constitute the physical states of solid, liquid, and aëriform. The best, because the most familiar, illustration of these three different states may be derived from our every day observation of the changes which water undergoes. Every one knows that by abstracting heat from water, or cooling it to a certain point, we

can convert it into a solid which we call ice; we diminish the repulsive force, and the attractive gains the ascendancy. The amount of this cohesion we can estimate by the mechanical force required to disintegrate it; but pound it, and comminute it as we will, we can never by these means totally overcome the attraction which constitutes its solidity; we can never so far unloose its constituent molecules as to give them freedom of motion amongst each other. The application of warmth will, however, gently and quietly loosen the tie; the ice will dissolve, and the liquid particles will yield in all directions to the slightest impulse.

§ 60. It is in consequence of the almost perfect manner in which cohesion is suspended in liquids that pressure is communicated by them in all directions alike. Solid bodies gravitate in masses, and exert no lateral pressure; but the particles of fluids gravitate independently of each other, and press against each other in every direction, not only downwards, but upwards and sideways. It is in consequence of this lateral pressure that water flows from an opening in the side of a vessel in which it is contained; and the lateral pressure is the result of the downward pressure of the liquid above, and exactly equal to it; consequently, the lower the orifice is made in the vessel the greater will be the velocity of the water running out of it, and the further it will be projected from it (15). It is the same

(15) If D be a hole made in the

side of the vessel of water, A, the water at D would only be pressed by the simple weight of the perpendicular column. of water from A to D; but when the orifice at D is open, and the water permitted to spout out, its motion throws its whole column into action, and it will now press upon and discharge the water from D, with the same force as if the water had been a solid descending from A to D, which would be as the square root of

B

the height AD: and, for the same reason, water issuing from other orifices, c and B, would run in quantities and velocities proportionate to the square root of their depths below the surface of the fluid. If D be four times as deep below the surface, A, as B, it will discharge twice the quantity of water which can flow from B in the same time; and if D were nine times the depth of B, three times the quantity would issue from it.

pressure acting upwards which occasions water, when poured into one leg of a siphon, to rise to the same height in the other (16).

§ 61. But it is not only the pressure of their own particles which is thus equally distributed throughout masses of fluids, but external force or pressure is communicated in the same way. In the Bramah's press an immense accumulation of force is brought to bear upon a particular point by pressure applied to a small column of water, reacting upon a larger mass placed under the surface of a moveable piston in a large barrel (17).

(16) This figure represents the arrangement of an experiment which commonly goes by the name of the Hydrostatical Paradox. a b is a narrow tube connected with the extensible vessel, c d e; when water is poured into the tube, the weight upon the surface will be raised by the pressure of the column of water in the tube, which will act with the same force as a column of water of the same height, whose base would have an equal area with the surface of the vessel. If a person stand upon the board be, and blow into the tube a, he may raise his own weight by the force of his breath.

e

F

(17) This figure represents a section of the press. D is a small but strong pump-barrel, fitted with the piston, Q, which is worked by the lever, K L By this pump water is raised from the reservoir, E, and injected under the large piston, A, M, fitting tightly in the barrel, H, N, and to which the pressplate, F, is attached; any force which is exerted upon the piston, q, is multiplied upon the piston, м, in direct proportion of the area of the latter to the former, and any substance placed between the plates I, F, thus becomes violently compressed. The pressure is immediately relieved by turning the screw, N, by which the water is allowed to flow back into the reservoir.

E

M

E