ON THE MOTIONS OF CONNECTED BODIES. 89 



a slow motion. Thus, if we have a stream of water, fiUing a single reservoir, 

 which is to raise a weight by means of its descent, the proportion here as- 

 signed will be the best for performing the most work in a given time; but if 

 we chose to double our machine, so that'one reservoir should be filled during 

 the descent of another, it would be proper to proportion the weights in such a 

 manner, that the whole time required for filling one of the reservoirs should 

 be occupied in the descent and the reascent of the other. 



In all these cases, if great accuracy were required, it would be necessaiy 

 in the calculation to add to the mass to be moved, the quantity of moveable 

 matter in the machine, reduced to a mean distance from the fulcrum or centre, 

 according to its rotatory power, in the same manner as the centre of gjTation 

 is determined. But there is seldom occasion for such a degree of precision. 

 The magnitude of the pressure which is exerted on the fulcrum, during the 

 motion of the connected bodies, may always be determined, by comparing 

 the actual velocity of the centre of gravity with that of a body descending 

 without resistance. 



These propositions and experiments must be allowed to require an attentive 

 consideration from those who are engaged in practical mechanics ; and it is 

 natural to suppose that the proportions laid down may be adopted w^th safety, 

 and employed with success, and that we may sometimes derive important ad- 

 vantages from their application. But on more mature consideration, we shall 

 find some practical reasons for caution in admitting them without material 

 alterations. 



If a machine were constructed for raising a solid weight, and so arranged 

 as to perform its office in the shortest possible time with a given expense of 

 power, the weight would still possess, when it arrived at the place of its 

 destination, a considerable and still increasing velocity: in order that it might 

 retain its situation, it would be necessary that this velocity should be destroy- 

 ed; if it were suddenly destroyed, the machinery would undergo a strain which 

 might be very injurious to it: and if the velocity were gradually diminished, 

 the time would no longer be the same as is supposed in the calculation. In 

 the second place, the forces generally employed arc by no means uniformly 

 accelerating forces, like that of gravitation, to which the propositions which 



VOL. I. N 



