Here I must take the liberty of remarking, that neither the measure of momentum nor that of any other kind of power, has any relation whatever to time; for momentum simply expresses the quantity of power in a moving body at a particular instant, without reference to the rate of accumulation, or to the effect it would produce; and similar remarks apply to other species of power.

[D. 72.] It is further necessary, both for practical and scientific purposes, to have a term to designate, that power which is equivalent to momentum, when the velocity is uniform. Smeaton employed the term mechanical power for this purpose; and since this term is sanctioned by the language of all writers on the first principles of mechanics; and the simple machines, by means of which such power is modified to produce the desired effect, have always been called the mechanical powers. I think it will be found desirable to use the term mechanical power in preference to any

other that has been proposed. The term impetus is objectionable, because it indicates a degree of violence in the action of power, which does not agree with what takes place in the most common applications of mechanical power. And it is questionable, whether its proposer did not intend it to be a measure of effect.

I must now attempt to inform the reader, more particularly, of the circumstances to which these different modifications of power apply, and in so doing, I shall have occasion to place a most interesting department of mechanical science in a different light from what it has been regarded by my predecessors.

[E. 72.] Force is immediately comparable with the weight of a quiescent body. Its intensity, direction, and equilibrium, are the proper objects of that part of mechanics called statics, or hydrostatics, and aerostatics, when the body exerting force is fluid.

[F. 72.] Momentum, or the force of a moving body, is proportional to the quantity of matter in the body, multiplied by its velocity at that instant when the comparison is made. Its rate of increase and decrease, its direction, and equilibrium, are the proper objects of those parts of mechanics called dynamics and hydrodynamics. In fact, statics is only that particular case. of dynamics when the velocity is nothing. In like manner we simplify an important part of the science of mechanics by separating all problems in which the velocity is uniform; because in that case the length of the line the body moves over, is proportional to the velocity.

[G. 72.] Mechanical power then is, a particular name for the momentum of a body in uniform motion, in that case, it is proportional, to the quantity of matter in motion, multiplied by the length of the line through which it acts; consequently, in all problems where the motions are uniform, (and there can be no difficulty in distin

guishing such problems) this measure of power may be employed, and its motion, equilibrium, and direction, determined accordingly. Every person conversant with the management of such problems must be aware of the advantage of this mode of investigation; it applies to the motion of water-wheels, of wind-mills, of rivers, the resistance of fluids, &c. &c. and in general to the motion of machines. It has often been partially applied in considering the equilibrium of mechanical powers, (see Wood's Mechanics, prop. xxx, and xxxi.) but I am not aware of its having been previously pointed out as a general principle, with the object of forming a distinct branch of mechanics. Some writers have confounded measure of power with measure of effect so far as to suppose, that mechanical power is identical with the quantity of matter multiplied into the square of its velocity; I hope the true nature of mechanical power is here so defined as to prevent a recurrence of a like mistake.

It is much to be regretted that power has not been made the basis of all mechanical science, in the place of motion; for motion is merely an affection or mode of matter acted upon by unbalanced force. For, in the practical application of mechanics it would prevent error; and in the theory of mechanics that interesting phenomenon, the accumulation of power, must have been forced upon the attention of philosophers. (Ed).