544 PHILOSOPHICAL TRANSACTIONS. [aNNO 172!. 



will never be the cause of the wheel's going round. Such a machine is men- 

 tioned by the Marquis of Worcester, in his Century of Inventions, N'^ 56. 



The consequence of this, and similar machines, is nothing to a perpetual 

 motion; and the fallacy is this: the velocity of any weight is not the line which 

 it describes in general, but the height that it rises up to, or falls from, with 

 respect to its distance from the centre of the earth. So that when the weight 

 in fig. 17, describes the arc Aa, its velocity is the line ac, which shows the 

 perpendicular descent, or measures how much it is come nearer to the centre 

 of the earth; likewise the line bc denotes the velocity of the weight b, or the 

 height that it rises to, when it ascends in any of the arcs Bb instead of the arc 

 BD ; so that in this case, whether the weight b in its ascent be brought nearer 

 the centre or not, it loses no velocity, which it ought to do, in order to be 

 raised up by the weight a. Nay, the weight in rising nearer the centre of a 

 wheel, may not only not lose of its velocity, but be made to gain velocity, in 

 proportion to the velocity of its counterpoising weights, that descend in the 

 circumference of the opposite side of the wheel; for if we consider two radii 

 of the wheel, one of which is horizontal, and the other, fastened to and mov- 

 ing with it, inclined under the horizon in an angle of 60*^, fig. 19, and by the 

 descent of the end b of the radius bc, the radius cd by its motion causes the 

 weight at d to rise up the line pp, which is in a plane that stops the said weight 

 from rising in the curve da, that weight will gain velocity, and in the beginning 

 of its rise it will have twice the velocity of the weight at b ; and consequently, 

 instead of being raised will overpoise, if it be equal to the last-mentioned 

 weight. And this velocity will be so much the greater, in proportion as the 

 angle acd is greater, or as the plane pp, along which the weight d must rise, 

 is nearer the centre. Indeed if the weight at b, fig. J 7, could by any means 

 be lifted up to |3, and move in the arc (3b, the end would be answered; because 

 then the velocity would be diminished, and become (3c. 



Experiment. — Take the lever bcd, fig. I9, whose brachia are equal in length, 

 bent in an angle of 120° at c, and moveable about that point as its centre; in 

 this case, a weight of 2 lb. hanging at the end b of the horizontal part of the 

 lever, will keep in equilibrio a weight of 4 lb. hanging at the end d. But if a 

 weight of 1 lb. be laid on the end d of the lever, so that in the motion of d 

 along the arc pA, this weight is made to rise up against the plane pp, which 

 divides in half the line ac equal to cb, the said weight will keep in equilibrio 

 2 lb. at b, as having twice the velocity, when the lever begins to move. This 

 will be evident, if you let the weight 4 hang at d, while the weight I lies above 

 it; for if you then move the lever, the weight 1 will rise 4 times as fast as the 

 weight 4. 



