MECHANICS. The force of a body at rest is that which we conceive to be in a body lying still on a table, or hanging by a rope, or supported by a spring, and is called by the names of pressure, vis mor tua, &c. the measure of this force being the weight with which the table is press ed, or the spring bent.
The force of a body in motion, called moving force, via motrix, and vis viva, to distinguish it from the vis mortua, is al lowed to be a power residing in that body so long as it continues its motion, by means of which it is able to remove ob stacles lying in its way, to surmount any resistance, as tension, gravity, friction, &c. and which, in whole or in part, conti nues to accompany it so long as the body moves.
We have several curious, as well as useful observations, in Desagulier's " Ex perimental Philosophy," concerning the comparative forces of men and horses, and the best way of applying them. A horse draws with the greatest advantage when the line of direction is level with his breast ; in such a situation, he is able to draw 200 lb. eight hours a-day, walking about two miles and a half an hour. And if the same horse is made to draw 240 lb. he can work but six hours a-day, and cannot go quite so fast. On a carriage, indeed, where a friction alone is to be overcome, a middling horse will draw 1000 lb. But the best way to try a horse's force is, by mak ing him draw up out of a well, over a single pulley or roller ; and, in such a case, one horse with another will draw 200 lb. as already observed. Fivr men arc found to be equal in strength to one horse, and can with as much ease push round the horizontal beam of a mill, in a walk forty feet wide ; whereas three men will do it in a walk only nineteen feet wide. The worst way of applying the force of a horse is, to make him carry or draw up hill ; for if the hill be steep, three men will do more than a horse, each man climbing up faster with a burden of 100 lb. weight, than a horse that is loaded with 300 lb.; a difference which is owing to the position of the parts of the human body being better adapted to climb than those of a horse. On the other hand, the best way of applying the force of a horse is in a horizontal direction, wherein a man can exert least force ; thus, a man weigh ing 140 lb. and drawing a boat along by means of a rope coming over his shoul ders, cannot draw above 27 lb. or exert above one-seventh part of the force of a horse employed to the same purpose. The very best and most effectual posture in a man is that of rowing, in which he not only acts with more muscles at once, for overcoming the resistance, than in any other position ; but as he pulls backward, the weight of his body assists by way of lever.
FoncE accelerative, or Retardive Force, is that which respects the velocity of the motion only, accelerating or retarding it; and it is denoted by the quotient of the motive force, divided by the mass or weight of the body. So, if m denote the
motive force, and b the body or its weight, andf the accelerating or retarding force, then is f as j'. Again, forces are either constant or variable. Constant forces are such as remain and act continually the same for some determinate time. Such, for example, is the force of gravity, which acts constantly the same upon a body while it continues at the same distance from the centre of the earth, or from the centre of force, wherever that may be. In the case of a constant force F, acting upon a body b, for any time t, we have these following theorems ; puttingf = the constant accelerating force = F 4- b; = the velocity at the end of the time t; = the space passed over in that time, by the constant action of that force on the body : and g- = 16 feet, the space ge nerated by gravity in 1 second, and calling the accelerating force of gravity 1; then is = to = g = v 2 23 4 g 2 = V 4 t =2 gf, = V— v s t g t' = 4 e s' FoneEs variable, are such as are con tinually changing in their effect and in tensity ; such as the force of gravity at different distances from the centre of the earth, which decreases in proportion as the square of the distance increases. In variable forces, theorems similar to those above may be exhibited, by using the fiuxions of quantities, and afterwards tak ing the fluentsof the given fluxional equa tions. And herein consists one of the great excellencies of the Newtonian or modern analysis, by which we are enabled to manage and compute the effects of all kinds of variable forces, whether accele rating or retarding. Thus, using the same notation as above for constant forces, viz. f, the accelerating force at any instant ; t, the time a body has been in mo tion by the action of the variable force; the velocity generated in that time ; s, the space run over in that time ; and • v v feet; then is s vt; 8 • • • = 4 g t; ==87) • V =,, v 25f z In these four theorems the force f, though variable, is supposed to be constant for the indefinitely small time t ; and they are to be used in all cases of variable forces, as the former ones in constant forces ; viz. from the circumstances of the problem•under consideration, deduce a general expression for the value of the force f, at any indefinite time t ; then sub stitute it in one of these theorems, which shall be proper to the case in hand ; and the equation thence resulting will deter mine the corresponding values of the other quantities in the problem. It is also to be observed, that the foregoing theorems equally hold good for the de struction of motion and velocity, by means of retarding or resisting forces, as for the generation of the same by means of accelerating forces.