Chap. 3. PHILOSOPHICAL DISCOVERIES. 14s

op be in (equilibria” . The second is, " to determine whatought to be the proportion of the power and weight to eachother, in a given engine, that it may produce the greatest effcEifojstbhy in a given time." All the writers on mechanics treatof the first of these problems, but few have considered thesecond ; tho’ in practice it be equally useful as the other. As-to the first, there is a general uniform rule that holds in all thepowers, is founded on the laws of motion, and is another in-stance of the beauty and harmony that results from the sim-plicity of the theory of motion described in the last chapter.Suppose the engine to move, and reduce the velocities of thepower and weight to their respective directions in which theyact; find the proportion of those velocities ; then if the powerbe to the weight, as the velocity of the weight is to the velo-city of the power, or, (which amounts to the fame thing) ifthe power multiplied by its velocity give the fame product asthe weight multiplied by its velocity, this is the cafe wherein thepower and weight sustain each other and are in (equilibria : lothat in this cafe, the one would not prevail over the other, ifthe engine was at rest ; and, if it is in motion, it would con-tinue to proceed uniformly, if it was not for the friction of its-parts, and other resistances. This principle has a plain analogy <to that by which the - equality of the motions, or forces, ofbodies was determined in general, in chap. 2. § 19. For, as,the motion of bodies are equal, and destroy each others effect,if their directions are contrary, when the first is to the second,as the velocity of the second is to the velocity of -the first,the greater velocity of the 1 ester body just compensating itsdeficiency in quantity of matter; fo the actions of the power,and weight are equal, and destroy each others effect upon theengine, when the power is to the weight, as the velocity ofthe weight is to the velocity of the power. But tho’ it is, . useful