MACHINE, in a general sense, signi fies any thing which serves to increase or regulate the effect of a given force. Ma chines are either simple or compound. The simple machines, otherwise called the simple mechanical powers, are usually teckoned six in number ; namely, the lever, the wheel and axle, the pulley, the wedge, the screw,'and the funwular ma chine. See the respective terms.
Compound machines are formed by combining two or more simple machines. They are classed under different denom inations, according to forces by which they are put in motion, as hydraulic ma chines, pneumatic machines, electrical ma chines, &c. ; or the purposes they are in tended to serve, as military machines, ar chitectural machines, &e.
Although there are no limits to the combination and adaptations of machin ery, there are certain general principles which may be applied in estimating the effects of any machine whatever. When a machine attains its state of uniform mo tion, the momentum of the power is equal to that of the resistance, and is the same that would be in. equilibria with the resistance if there were no motion at all. From this principle, and from the consi deration that in all machines the work done is to be estimated not merely from the quantity of resistance which is over come, but from the quantity overcome in a given time, we can ascertain the relation that ought to subsist between the velo city and the load or resistance, in order that the effect of the machine may be a maximum. This maximum effect is pro duced when the two following conditions are fulfilled: 1. When the load or resist ante is about four ninths of that which the power, when fully exerted, is just able to balance, or that which would keep the machine at rest altogether; and, 2, when the velocity of that part of the ma chine to which the power is applied i8 one third of the greatest velocity of the power. These conditions are deduced
from the following empirical expression, which is adopted by Euler and other writers to represent the law of the mov ingpower : P=the power applied (or weight which the power, when fully ex erted, is just able to overcome) • R--=the resistance, or load, or weight to be over come ; e the greatest velocity, or that at which the power ceases to act ; other velocity : then the law of the mov ing power is the variables in this expression are R and a, and the effect is represented by the product R a; on making which a maxi mum, the rules of the differential calcu lus give v=1. c • whence the formula be comes R=4-9ths P.
From these expressions it follows, that when the moving power and the resist ance are both given, if a machine he so constructed that the velocity of the part to which the power is applied is to the velocity of the part to which the resist ance is applied in the ratio of 9 R to 4 P, the effect of the machine will be a maxi mum, or it will work to the greatest pos sible advantage. The above conditions apply equally to machines impelled by animal force and the agents of nature, as running water, steam, the force of gravi ty, &c. An animal exerts itself to the greatest advantage, or performs the great est quantity of work in the least time, when it moves with about one third of the utmost speed with which it is capal.le of moving, and is loaded with four ninths of the greatest load which it is capable of putting in motion. It has been supposed in the above remarks that the friction of the parts of the machine is included in the resistance.