All this supposes these bodies to be sound and good throughout; but none of these should be put to bear more than a third or a fourth part of the weight, especially for any length of time.

From what has been said, if a spear of fir or a rope, or a spear of iron of d inches diameter, was to lift the extreme weight, then,

The fir would bear 8 dd hundred weight.

The rope 22 dd hundred weight.

The iron 63 dd ton weight.

PROP. LXXX. (Fig. 1. Pl. XII.)

MOTION OR PRESSURE IN A FLUID IS NOT PROPAGATED IN RIGHT LINES, BUT EQUALLY ALL AROUND IN ALL MANNER OF DIREC TIONS.

If a force act at a in direction ab, that motion can be directed no further than these particles lie in a right line as to c. But the particle c will urge the particles d, f obliquely, by which that motion is conveyed to e, g. And these particles e, g, will urge the particles n, p, and r, s obliquely, which lie nearest them. Therefore the pressure, as soon as it is propagated to particles that lie out of right lines, begins to deflect towards one side and the other; and that pressure being farther continued, will deflect into other oblique directions, and so on. Therefore, the pressure and motion is propagated obliquely ad infinitum, and will, therefore, be propagated in all directions.

Cor. (Fig. 2. Pl. XII.) If any part of a pressure propagated through a fluid, be stopped by an obstacle, the remaining part will deflect into the spaces behind the obstacle. Thus, if a wave proceeds from C, and a part goes through the hole A, it expands itself, and forms a new wave beyond the hole, which moves forward in a semi

circle whose centre is the hole.

For any part of a fluid pressing against the next is equally rea ted on by the next, and that by the next to it, and so on; from whence follows a lateral pressure (equal to the direct pressure) into the places behind the obstacle.

PROP. LXXXI. (Fig. 3. Pl. XII.)

A FLUID CAN ONLY BE AT REST WHEN ITS SURFACE IS PLACED IN

A HORIZONTAL SITUATION.

For, let ABCD be a vessel of water or any fluid; and let AB be parallel to the horizon. Suppose the surface of the liquor to be in the position FE. Then, because the parts of the fluid are easily moveable among themselves; therefore (by Ax. 7.) the higher parts at E will, by their gravity, continually descend to the lower places at F. Also the greater pressure under E and the lesser under F, will cause the parts at E to descend, and those at F to ascend. And thus the higher parts of the fluid at E descending, and spreading themselves over the lower parts at F, which are at the same time ascending; the surface of the fluid will at last be reduced to a horizontal position AB. But being settled in this position, since there is no part higher than another, there is no tendency in any one part to descend, more than in another; and, therefore, the fluid will rest in an horizontal position.

Cor. 1. (Fig. 4. Pl. XII.) If the fluid does not gravitate in parallel lines, but towards a fixed point or centre C; then the fluid can only be at rest when its surface takes the form of a spherical surface AB, whose centre is C.

For if any parts of the surface of the fluid A or B, were further from C than the rest, they would continually flow down to the places nearer C, towards which their weights are directed; till at last they would be all equi-distant from it.

Cor. 2. Any fluid being disturbed, will of itself return to the same level, or horizontal position.

Cor. 3. (Fig. 5. Pl. XII.) Hence, also, if a different fluid ABEF rest upon the fluid ABCD; both the surface FE, and the surface AB that divides them, will lie in a level or horizontal situation, when

at rest.

For, if any part of the surface AB be higher than the rest, it will descend to the same level; and şince FE is also level, and, therefore, the heights AF, BE in every place equal; the pressure of it on all the parts of the horizontal surface AB, will be equal. And, therefore, it cannot descend in one place more than another, but will continue level.

Cor. 4. Hence, water communicating with two places, or any way conveyed from one place to another, will rise to the same level in both places; except so far as it is hindered by the friction of the channel it moves through, or, perhaps, some very small degree of tenacity or cohesion.

PROP. LXXXII. (Fig. 6. Pl. XII.)

IN ANY FLUID REMAINING AT REST, EVERY PART OF IT, AT THE SAME DEPTH, IS IN AN EQUAL STATE OF COMPRESSION.

For, let the plane EF be parallel to the surface AB. Then, since the height of the fluid at all the points of EF, is equal; therefore the weights standing upon any equal parts of EF are equal; and, therefore, the pressure in all the points of EF is equal also.

Cor. 1. A fluid being at rest, the pressure at any depth is as the depth.

For this pressure depends on the weight of the superincumbent fluid, and, therefore, is as its height.

Cor. 2. In any given place, a fluid presses equally in all directions.

For (by Prop. LXXX.) as the pressure in any place acts in all directions, it must be the same in all directions. For if it were less in one direction than another, the fluid would move that way, till the pressure becomes equal. And then the fluid would be at rest, and be equally compressed in all directions.

Cor. 3. The pressure is equal in every part of a plane drawn pa

rallel to the horizon.

Cor. 4. When a fluid is at rest, each drop or particle of it is qually pressed on all sides, by the weight of the fluid above it.

PROP. LXXXIII. (Fig. 6. Pl. XII.)

If a fluid be AT REST IN ANY VESSEL, WHOSE BASE IS PARALLEL TO THE HORIZON, THE PRESSURE OF THE FLUID UPON THE BASE, IS AS THE BASE AND PERPENDICULAR ALTITUDE OF THE FLUID,

VESSEL.

WHATEVER BE THE FIGURE OF THE CONTAINING

CASE I.

Let ABCD be a cylinder or prism, then (by Cor. 1. Prop. LXXXII.) the pressure upon a given part of the base (as a square inch) is as the depth. And the pressure upon the whole base is as the number of parts, or inches, contained in it; and, therefore, is as the base and altitude of the fluid.

CASE II. (Fig. 7. Pl. XII.)

Let the heights and bases of the vessels ABC, DEF be equal to those of the cylinder ABCD (Fig. 6. Pl. XII.); then, since any part of the bases AB or DE is equally pressed, as an equal part of the base CD; (Fig. 6. Pl. XII.) therefore the whole pressure upon the bases AB or DE is equal to the whole pressure upon the base CD, (Fig. 6. Pl. XII.); and, therefore, is as the base and perpendicular height.

Cor. 1. If two vessels ABC, DEF, of equal base and height, though never so different in their capacities, be filled with any the same fluid, their bases will sustain an equal quantity of pressure, the same as a cylinder of the same base and height.

Cor. 2. The quantity of pressure at any given depth, upon a given surface, is always the same, whether the surface pressed be parallel to the horizon, or perpendicular, or oblique; or whether the fluid continued upwards from the compressed surface, rises perpendicularly into a rectilinear direction, or creeps obliquely through crooked cavities and canals; and whether these passages are regular or irregular, wide or narrow. And hence,

Cor. 3: (Fig. 8. Pl. XII.) If ABDCF be any vessel containing a fluid; and BL, ED, HFÓK, and GC be perpendicular to the horizon, and GHAB the surface of the liquor; and FL, COD parallel to AB.; then the pressure at L and F is as BL or HF; at D, O and C, as ED; at K as HK; and, therefore, the pressure at L and F is the same; and the pressures at D, O, C are equal.

Cor. 4 (Fig. 8. Pl. XII.) The pressure is every where directed perpendicularly against the inner surface of the vessel. Therefore at Kit is directed downward at L sideways, and at F upwards. By Prop. IX.

Cor. 5. (Fig. 9. Pl. XII.) If two vessels AB, CD, communicate with one another by the tube BC, and if any liquor be poured into one AB, it will rise to the same height in the other CD, and will stand at equal heights in both; that is, AD will be a horizontal line.

For if the fluid stand at unequal heights, the pressure in the higher will be greater than in the lower, and cause it to move towards the lower.