26 



MECHANICS. 



which will modify the effect of the power 

 so as to make it conformable to the va- 

 riation in the resistance to be overcome. 

 This will probably be better under- 

 stood by an example. Suppose that the 

 power is a spiral spring of tempered steel, 

 (Jig. 39.) placed in a barrel A, (fig. 40.) 



Fig. 39 



to which one end of the spiral spring is 

 fixed, while the other end is attached 

 to the axis on which the barrel A re- 

 volves. A chain is coiled round the 

 barrel A, one end of which is fixed 

 on the barrel, and the other end is 

 attached to a fusee B, which is a coni- 

 cal figure, also capable of turning on 

 an axle, and on which a spiral channel 

 or thread is cut to receive the chain after 

 it has been rolled off from the barrel A. 

 Let us suppose that the resistance, 

 whatever it be, is uniform, and that it 

 is applied to the axle of the fusee, or to 

 a wheel connected with that axle ; and 

 that when the chain is rolled upon the 

 spiral thread of the fusee, the spring 

 within the barrel A is stretched to its 

 utmost intensity. It is this which gives 

 the barrel A a tendency to recoil, which 

 tendency is communicated by the chain 

 to the fusee B, and acts in turning the 

 fusee by the leverage of the highest part 

 of the conical figure. With this leverage 

 the tension of the chain acts upon the 

 resistance, and its effect is to be esti- 

 mated by multiplying the tension of the 

 chain, or, what is the same, the inten- 

 sity of the spring, by the radius of that 

 part of the cone on which the chain 

 acts. As the fusee revolves, and the 

 chain rolls off the fusee B and on the 

 barrel A, the spring gradually loses its 

 intensity ; and consequently the tension 

 by which the chain acts upon the fusee 

 is gradually diminished, while the re- 

 sistance to be overcome by that tension 

 remains the same. It is, however, to be 

 considered, that as the chain is rolled 

 off the fusee, the part on which it acts, 

 coming nearer to the base of the cone, 



becomes constantly thicker. The tension 

 of the string, therefore, acts by a con- 

 stantly increasing leverage, and there- 

 fore with a constantly increasing me~ 

 chanical efficacy. Now, the tapering 

 form given to the cone may evidently 

 be so regulated, that the advantage 

 which is gained by the gradually in- 

 creasing leverage, by which the tension 

 of the string acts upon the fusee, shall 

 be exactly equal to that which is lost by 

 the gradually decreasing intensity of the 

 spring ; so that these two opposite ef- 

 fects producing a mutual compensation, 

 an'uniform action upon the resistance 

 will be the result. 



An instance of the application of this 

 beautiful principle will be seen in the 

 construction of a watch. 



CHAPTER VII. Complex Wheel- 

 work Force transmitted by Friction 

 Straps Tooth and Pinion-^- Shape 

 of Teeth their number Lantern ' 

 and Trundles Spur, Crown, and 

 bevelled Gear. 



(61.) IT does not always happen that 

 the end to be accomplished can be at- 

 tained with convenience by the simple 

 wheel and axle ; and it frequently be- 

 comes necessary to transmit the effect 

 of the power to the resistance, through 

 a system of wheels and axles mutually 

 acting upon each other. As the wheel 

 and axle is only a modification of the 

 lever, so a system of such machines 

 acting one upon another is only another 

 form of the compound lever, and the 

 conditions of equilibrium are exactly 

 the same in both. 



In complex wheel- work, the power is 

 applied to the circumference of the first 

 wheel, which transmits its effect to the 

 circumference of the first axle. This 

 circumference is made to act, by various 

 means, which we shall presently explain, 

 upon the circumference of the second 

 wheel, which again transfers the effect 

 to the circumference of the second axle, 

 which acts upon the circumference of 

 the third wheel, and this in the same 

 way transmits the effect to the circum- 

 ference of the third axle ; and thus the 

 transmission of the force is continued, 

 until it has arrived at the circumference 

 of the last axle to which the weight or 

 resistance is applied. 



Each separate wheel and axle being a 

 lever, the effect of such a combination 

 as we have described is the same as that 

 of a series of levers, whose longer arms 



