174 LECTURE XV. 



irregular, and the machinery would be destroyed by the strain. (Plate XIV. 

 Fig. 184.) 



On the other hand it must be observed, that the force applied to a ma- 

 chine may, in general, be divided into two portions; the one employed in op- 

 posing another force, so as to produce equilibrium only, the other in generat- 

 ing momentum. With respect to the first portion, a single crank has the 

 inconvenience of changing continually the mechanical advantage of the ma- 

 chine; with respect to the second, its motion in the second quarter of its re- 

 volution is accelerated, instead of being retarded, by the inertia which this 

 portion of the force is intended to overcome: and from a combination of both 

 these causes, the motion must necessarily be rendered very irregular. They 

 may, however, be completely removed by employing always cranks in pairs, 

 one of them being fixed so as to make a right angle with the other, which 

 is also the best position for two winches to be turned by two labourers ; since 

 the point of the circle, in which a man can exert his greatest strength, is 

 nearly at the distance of a right angle, or a little more, from the point at 

 which his force is smallest. 



An alternate motion may be comunicated to a rod, so that the force may 

 be either uniformly exerted, or varied according to any given law, by means 

 of an inclined surface, formed into a proper curve, and acting on a friction 

 wheel fixed to the rod ; and a single plane surface, placed obliquely, would 

 answer sufiiciently well for this purpose. But in such cases, as well as when 

 a crank is used, it is necessary to employ other means for supporting the 

 rod in its proper situation; this may either be done by additional friction 

 wheels, or in a more elegant manner, by such an arrangement of jointed 

 rods, as will cause the extremity of one of them to move in a curve Avhich 

 does not sensibly differ from a right line. If we fix two pins in a beam, so 

 as to connect to it two equal rods, of which the extremities are joined by a 

 third, and the end of this third rod which is nearest to the centre of the 

 beam be connected to a second beam of a proper length, the oj^osite end of 

 the rod will initially describe a right line; and for this purpose the length of 

 the second beam must be to the distance of the nearest pin from the centre 

 as that distance is to the distance of the pins from each other. The same 

 effect may also be produced by means^ of a frame, made of two pieces, each a 



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