MECHANICS. 



Fig. 48. 



7, " '' 



9 ^m 



their formation depends, may be con- 

 ceived by imagining two cones to be 

 applied side to side, as in Jig. 49. If 

 their surfaces have sufficient friction, 



and one of them be turned upon its axis 

 by a mechanical force, it will compel 

 the other to revolve : and if the bases 

 of the cones be equal, each will revolve 

 in the same time ; as in Jig. 49. But 

 if the diameter of the base of one 

 be equal to any number of times the 

 diameter of the base of the other, as in 

 Jigs. 48 and 50, then the lesser cone will 



revolve as many times in one revolution 

 of the greater. It is evident that what 

 we have observed of the entire cones, 

 will be equally true of any parts of them, 

 a, b, c, &c. equally distant from their 

 common vertex, and therefore would 

 be true of wheels, the edges of which are 

 parts, c d, of the conical surfaces. 



If the friction of the conical surfaces 

 be insufficient to transmu: the force, the 

 surfaces may be fluted, as in Jig. 5 1 ; 



Fig. 51 



and if the conical surfaces be incom- 

 plete, the breadth being F c, they will 

 become bevelled-wheels. 

 It will be easily perceived that the use 



of bevelled-wheels is to produce a rota- 

 tory motion round one axis by means of 

 a rotatory motion round another which 

 is oblique to it ; and, provided that the 

 two axes are in the same plane, this 

 may always be accomplished by two 

 bevelled-wheels. A system of wheels 

 of this kind is represented in/g. 52. 



Fig. 52 



CHAPTER VIII. Of the Pulley 

 Fixed Pulley Single moveable Pul* 

 ley Spanish Burtoas Systems 

 with a single Rope their defects 

 White's Pulley Systems with se- 

 veral Ropes. 



(71 .) THE machines, the theory of which 

 has been explained in the preceding 

 chapters, derive their whole efficacy 

 from the supposed inflexibility of the 

 materials of which they are constructed. 

 The effect of weights acting on a lever 

 is to bend it over the fulcrum, and if 

 the lever yields to this, and suffers itself 

 to be bent, it loses its mechanical effi- 

 cacy. The same observation may be ap- 

 plied to all the machines which we have 

 hitherto described. It may be said that 

 there are no materials of which such 

 machines can be constructed which are 

 perfectly inflexible. This is true ; but 

 we have before observed, that the most 

 easy method of teaching the science, is 

 to suppose, in the first instance, this 

 perfect inflexibility, and subsequently 

 to apply to the results corrections which 

 will adapt them to cases where small 

 degrees of flexibility are found, at least 

 to those cases where the flexibility pro- 

 duces any effect sufficiently great to 

 affect the practical accuracy of the 

 result. 



On the other hand, the machine to 

 whose properties we are now to call the 

 attention of the student, is one whose 

 efficacy depends on the perfect flexibility 

 of the material. On this supposition our 

 theory will necessarily be founded, and 



