134 LECTURE XV. 



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 

 opposing another force, so as to produce equilibrium only, the other in 

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

 has the inconvenience of changing continually the mechanical advantage of 

 the machine ; with respect to the second, its motion in the second quarter 

 of its revolution is accelerated, instead of being retarded, by the inertia 

 which this portion of the force is intended to overcome : and from a com- 

 bination 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 communicated 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 ob- 

 liquely, would answer sufficiently 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 which 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 opposite 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 yard long, united by joints to each 

 other, and to two other pieces of a foot each ; one of the first pieces being 

 fixed, if the shorter piece opposite to it be produced to the length of four 

 feet, its extremity will move at first in a right line. The proportions of 

 the rods may also be made more convenient than these, and others may be 

 added to them, if it be required, which may make a line move so as to 

 remain always in parallel directions. (Plate XIV. Fig. 185... 188.) 



But of all the modes of communicating motion, the most extensively 

 useful is the employment of wheelwork, which is capable of varying its 

 direction and its velocity without any limit. 



Wheels are sometimes turned by simple contact with each other ; some- 

 times by the intervention of cords, straps, or chains, passing over theni ; 

 and in these cases the minute protuberances of the surfaces, or whatever 

 else may be the cause of friction, prevents their sliding on each other. 



