380 PHILOSOPHICAL TRANSACTIONS. [aNNO 1730. 



18 grains were sufficient. When p is = 2-i-, and w = 5, the additional weight 

 marked -l, was 4 penny-weight and 2 grains. 



It is plain from this, that Mons. Perault's experiments were very inaccurately 

 made, and therefore not to be depended on. 



A further Examination of M. Perault's Machine, said to be without Friction. 

 By the same. N°412, p. 228. 



As some have endeavoured to render this engine more useful, by causing it 

 to roll up an inclined plane, instead of making it rise directly up in the man- 

 ner described, and condemned in the former paper; it is here shown what 

 must be the loss of the power in proportion to the inclination of the plane ; 

 which is, that in every inclination of the plane, if the sine of the angle of 

 inclination be taken in parts of the radius of the axle, or roller, the power will 

 be to the weight :: as the radius of the roller -\- the sine of inclination, to 

 the radius of the wheel — the said sine of inclination; that is, in the fig. 10, 

 p = 1 : w = 3 :: dk : ak. 



In the present experiment be is an inclined plane, on which the roller c is 

 to roll up, touching the said plane at the point c; am is the wheel behind that 

 plane, another such plane, and equally inclined, being also supposed behind 

 the wheel, to support the other end of the roller. 



The lines of direction of the power and weight being ap and dw, through 

 the point of contact, or centre of motion, c, draw ad parallel to the horizon, 

 and perpendicular to ap and dw ; through the centre of the engine, c, draw ad 

 parallel to ad. Suppose the angle bca of the plane's inclination to be 30°, the 

 right sine will then be equal to half the radius; therefore dividing c2, the radius 

 of the roller, into 2 equal parts at k, if you draw kc and cc, the angle kcc will 

 be equal to bca, and its sine will be ck. Now since it is evidently the same 

 thing to make use of ad for a lever, whose centre of motion is at k, as of ad, 

 equal and parallel to it, with its centre of motion at c; it follows that in this 

 inclination of the plane, the distance of the weight dk is greater than do (the 

 distance of the weight in the common use of this engine) by the addition of 

 the quantity ck, the sine of the angle of inclination; and ka, the distance of 

 the power, is less than ca (the distance of the power in the common way) by 

 the subtraction of the said quantity or sine ck: consequently that, on an inclined 

 plane, the power is to the weight :: as dc : to ca. q. e. d. 



Carol. 1. — Hence it follows, that the radius of the wheel and the radius of 

 the roller being given, tlie loss of power may be found in any inclination of 

 the plane. Thus, as here, the power, which in the common way would be 



