ON PRESSURE AND EQUltlBUIUM. 7J 



little more or less than the internal screw which perforates it would rise or 

 sink by the action of its own threads, and a weight attached to this internal 

 screw ascends, in each revolution, only through a space ecjual to the difference 

 of the height of the two coils. Here the machine is analogous to a very thip 

 wedge, of which the thickness is only equal to the difference of the distances 

 of the threads, and which of course acts with a great mechanical a<lvantage. 

 It might in some cases he more convenient to make two cylindrical screws, of 

 different kinds, at different parts of the same axis, rather than to perforate it. 

 The friction of such machines is, however, a gi«at impediment to their opera- 

 tion. (Plate V. Fig. 71.) 



In all the kinds of equilihrium that we have considered, and in all other 

 cases that can be imagined, it will be found that the forces, or rather weights, 

 opposed to each other, are so arranged, that if they were put in motion, their 

 momenta in the direction of f gravity would, in the first instance, be equal and 

 contrary, the velocity being as much greater as the magnitude of the weight 

 is smaller. Thus, if an ounce weight, placed on a lever, at the distance of four 

 feet from the fulcrum, counterpoise a weight of four ounces at the distance of 

 one foot, the velocity with which the ounce would descend, if the lever were 

 moved, would be four times as great as that with which the weight of four 

 ounces would descend. A single moveable pulley ascends with half the ve- 

 locity of the end of the rope which is drawn upwards, and acts with a force 

 twice as great ; a block of three shieves enables a weight to sustain another 

 six times as great ; but the velocity, with which this weight ascends, is only 

 one sixth of that with which the smaller weight must descend. When a 

 weight rests, on an inclined plane, of which the height is one half of the 

 length, it may be retained by the action of a weight of half its magnitude, 

 drawing it up the plane by means of a thread passing over a pulley; here if 

 the weight ascended or descended along the oblique surface, its velocity, re- 

 duced to a vertical direction, would be half as great as that of the smaller ■ 

 weight which balances it. 



Some authors have considered this law as affordins: a fundamental demon- 



o 



stration of the conditions of equilibrium in all possible cases. For since, 

 wherever two weights are in equilibrium, if one of them descended, the other 



VOL. I. T 



