9. Gravity is that force by which all bodies endeavour to descend towards the centre of the earth.

AXIOMS, OR PLAIN TRUTHS.

Ir a body be at rest, it will remain at rest; and if in motion, it will continue that motion, uniformly in a straight line, if it be not disturbed by the action of some external

cause.

The change of motion takes place in the direction in which the moving force acts, and is proportional to it. The action and reaction of bodies upon one another, are equal.

LAWS OF MOTION.

Uniform motion is caused by the action of some force. by one impulse, on the body :—and if

b signify the quantity of matter to be moved,
f the force which caused the body's motion,
v the velocity with which the body moves,
m the momentum of the body in motion,
s the space passed over by the moving body,
t the time of describing that space;

and if b = 3, m = 6, v = · 2, ƒ = 6, s = 4, t = 2: then the figures in the examples will show the application of the theorems.

OF ACCELERATED MOTION.

If the moving force continues to act all the while that the body is in motion, then that motion will be uniformly accelerated such is the case with bodies falling to the earth, as the force of gravity acts constantly. Now, it has been found by experiment, that a body falling through free space, in the latitude of London, will, by the force of gravity, fall through 16:095 feet in the first second of time; and as forces are measured by the effects they produce, this 16·095 may be taken as the measure of the force of gravity; and as this quantity does not differ materially from 16 feet, we shall neglect the fraction 095 in our calculation of the circumstances of falling bodies.

The subjects of consideration here are, the time that the falling body is in motion, the space it falls through in that time, and the velocity which it has acquired in falling through that space, or that velocity with which it would continue to move, supposing gravity to cease its action, and the motion of the body becoming uniform.

The time is always supposed to be taken in seconds, and the space in feet.

The velocity acquired

The time of falling

=

32 x time of falling, or =√(64 × space fallen through)

Ex. If a body falls through 100 feet, then
✓(64 x 100) = 80 the velocity acquired

80

32

=

216 = 2.5= the time of falling.

If the space described be 64 feet, then

32 × 2 = 64 = the velocity acquired.

If the space descended be 400, then

✔(400 × 64) = 160 the velocity acquired,

=

A

B

C

IF two bodies, A and B, in motion, weigh respectively 5 and 3 lbs., and their velocities respectively 3 and 2 before they strike, then will 3 x 5 be the momentum of A, and 2 x 3 that of B, before the stroke; also, 5 + 3 = 8 is the sum of their weights; then, 1st. If the bodies move the same way, the quotient arising from the division of the sum of the momentums of the two bodies, by the sum of their weights, will give the common velocity of the two bodies after the stroke. 2d. If the bodies move contrary ways, then the quotient arising from the division of the difference of their momentums, by the sum of their weights, will give the common velocity after the stroke. 3. If one of the bodies be at rest, then the quotient of the momentum of the other body, divided by the sum of the weights of the two bodies, will give the common velocity after the stroke. Hence, assuming the numbers given above, 15+ 6

we have, in the first case,

=

23; in the second

8

When the bodies are perfectly elastic, the theorems become more complicated.

If the weight of the one body be A, and the velocity V; ' the weight of the other body B, and its velocity v: then, 1st. If the bodies move in the same direction before the stroke,

(2Bxv)-(A—B×V)

A+B (2AxV)+(A-B×v) A+B

the velocity of A after the stroke.

the velocity of B after the stroke.

2d. If B move in the contrary direction to A before the stroke,

3d. If the body B had been at rest before it was struck by A, then

A+ B

2 A

X V

= the velocity of A after the stroke.

× V = the velocity of B after the stroke. A X B

Ex.-If the weight of an elastic body A be 6 lbs., and its velocity 4, and the weight of another body B be 4 lbs., and its velocity 2; then we have these results: in the first

case,

(2×4×2)+(6—4×4)

6 + 4 (2×6×4)+(6-4×2) 6 + 4

=8= velocity of A after the stroke.

5.2 velocity of B after the stroke.

The sum of these two velocities, viz. 5.2 and ⚫8= = 6, which was the sum of the velocities 2 and 4 before the stroke; and this is a general law. The reader may exercise himself with the rules for the other cases.

It is to be observed, that when non-elastic bodies, that is, bodies which have no spring, strike, they will both move in the direction of the motion of that body which has the greater momentum; but if they are elastic, they will recoil after the stroke, and move contrary ways.

THE COMPOSITION AND RESOLUTION OF FORCES.

Ir a body be acted upon by two forces, one of which would cause it to move from A to B in any given time, and the other would cause it to move from A to C in

the same time; then if these forces act upon the body at one instant, it will move in neither of the lines AB, AC, but in the line AD, which is the diagonal of the parallelogram of which the two lines AB and AC are containing sides; and by the action of the two forces, the body will be found at D, at the end of the time that it would have been found at B or C, by the action of either of the forces singly This important fact in mechanical science, is usually called the parallelogram of forces. From this statement it will be seen, that if we have the quantity and direction of any two forces urging a body at the same instant, we can find the resulting motion, both in quantity and direction.

It will not be difficult to understand, that if the two forces which act upon a body, act not at an angle, but in the same straight line, and in contrary directions, the resulting motion will be in that straight line, and in the direction of the greater force; but if the forces be equal, the body will remain at rest. If, while a body A is urged by a force in the direction AB, which would carry it to A, it be acted on by another force in the direction AC which would carry it to C, and a third force in the direction DA, which would carry it over a space as great as that from D to A, these being the sides and diagonals of a parallelogram, the body A will remain at rest. Also, if a body A has a tendency to move in the direction AB, but is counteracted by a force DA, and if we wish to keep the body A from moving, altogether, we must apply another force AC, forming the other side of the parallelogram of which AB is one side and AD the diagonal.

If there be three forces acting on a body at the same time, make the sides of a parallelogram represent any two of them; then the diagonal of this parallelogram, together with the third force as the two sides of another parallelogram, will give a diagonal which will be the result of the three forces acting at once on the body.

If the two forces which urge the body, both produce a uniform motion, the resulting motion will be in a straight ine; but if one of them act by impulse, which would produce a uniform motion, and the other act constantly so as to produce an accelerated motion, the resulting motion will be in a curve. Thus, if the ball of a cannon were sent in ? horizontal direction, it would never deviate from this raight line unless acted on by some external force. The