SPRI NGS C1OCK-WOEK. ] 



APPLIED MECHANICS. 



839 



its increased centrifugal force, to some such position as 

 that indicated by the dotted lines. When at this distance, 

 the radius of its orbit D E was greater than the former 

 radius B C ; and therefore the speed with which the disc 

 w as driven throu gh the air was proportionately greater, and 

 the resistance of the air to its motion increased accordingly. 

 The momentary increase of velocity, therefore, produced 

 a considerable increase of resistance, and thus reduced 

 itself to its average rate ; and, conversely, a decrease oi 

 velocity diminished the resistance, and thus restored 

 itself. By a proper adjustment of the disc as to area, 

 the length of the arm by which it swung, and a weight 

 on that arm, the apparatus served to move the cylinder 

 for many minutes with a velocity in which there was not 

 the slightest appreciable irregularity. A piece of paper 

 was fixed on the cylinder, and a pencil, connected with 

 a spring-balance acted on by the pressure to be measured, 

 traced on the paper as it revolved a diagram, indicating the 

 intensity of the pressure at every instant of the motion. 



When the elasticity of a solid body is employed as a 

 force for moving machinery, the body is called a spring, 

 Fig. 138. and generally consists 



of a strip of steel 

 wound into a spiral 

 form round an axis A, 

 as shown in Fig. 136 ; 

 one end of the strip 

 being fixed to the axis, 

 and the other at B to 

 the side of the cylin- 

 drical box in which the 

 spring is contained. 

 When the box is fixed, 

 as in a Geneva watch, 

 the axis is turned 

 round by a key, and 

 the spring is thus 

 drawn into closer convolutions. A wheel is fixed on the 

 axis, and is connected by gearing with the escapement, 

 and hands of the watch. The effort of the spring to 

 unwind itself causes the axis to revolve in the direction 

 O[-posite to that in which it was wound, and thus puts 

 the train of wheels in motion. It is the property of all 

 elastic bodies to exert a force which is nearly proportional 

 to the amount of strain to which the body has been sub- 

 jected. As we wind up the spiral spring of a watch, we 

 apply greater and greater strain the farther we wind ; 

 and so when the spring unwinds itself it exerts the great- 

 est force at first, and gradually decreases in power, the 

 farther it is unwound. This decrease of force is an irre- 

 gularity which no modification of the form of spring can 

 obviate, but which may be considerably diminished by 

 making the spring with a great number of convolutions. 

 Thus, we may suppose that a spring of 20 convolutions, 

 or turns, is wound up from its neutral condition to the 

 full power required, by 10 revolutions of the axis. In 

 unwinding itself it would lose by the first revolution 

 T \jth of its force, by the second revolution another ^th, 

 and so on, until by five revolutions backwards it would 

 lose /jjths or ^ of its full force. But if we suppose the 

 spring had forty convolutions, and that we wound it up 

 by 20 revolutions on the axis to the same force as the 

 former spring, in unwinding itself it would lose by the 

 first revolution Ath, by the second another 2 l oth, and so 

 on till by the fifth it would lose Aths or jth of its full 

 force. The decrease of power in the second instance is 

 only half that in the first, the axis performing in each 

 case an equal number of revolutions. It is, therefore, 

 important to give all springs which are required to exert 

 a tolerably equal force throughout their recoil as great a 

 number of convolutions as possible, and to employ as 

 few revolutions of the axis as possible for moving the 

 machinery. In other watches, where smallness of bulk 

 is not so much studied, and in clocks moved by springs, 

 the axis of the spring is fixed, and the box c (Fig. 137) 

 containing it is caused to revolve by the recoil of the 

 spring, and to wind upon its outer surface a small chain 

 a attached to a fusee a. This fusee is a conical barrel, 

 with a screw groove cut in its surface to receive the coils 



of the chain. When the spring is beginning to recoil, 

 and therefore acting with its greatest force, the chain 



Pig. 137. 



pulls the fusee round at its upper part where the di- 

 ameter is smallest, and therefore acts with least leverage 

 on the train. As the spring loses force, the chain is 

 pulled from a larger diameter of the fusee, and acts with 

 more and more leverage on the train as its tension be- 

 comes less. By properly proportioning the increase in 

 the diameter of the fusee to the diminution in the force 

 of the spring, the power applied to the train can thus be 

 made perfectly regular throughout the whole range of 

 the spring's recoil. The fusee is not a regular cone, the 

 outline of its section being part of a hyperbolic curve, 

 that being the form which f uruishes the proper proportion 

 of increase of diameter to diminution of spring force. 



In machinery moved by springs, modes of regulating 

 the speed may be employed as in machinery moved by 

 weights. Thus, in spring watches and clocks, the 

 balance-wheel and pendulum are used for governing the 

 time-keeping train, and the fan for governing the striking 

 part. In musical-boxes the fan is also employed, and 

 serves to give the movement of the barrel sufficient 

 regularity to suit the regular time of the music. 



Mr. Froude, to whom we have already referred, con- 

 trived a very ingenious regulating apparatus for 

 machinery moved by a spring, employing the resistance 

 of the air as a retarding force in a manner somewhat 

 similar to that we have described, but with a difference 

 in the details, made with a view to render the apparatus 

 portable and capable of acting justly, without regard to 

 level. The regulating part of the apparatus consisted 

 of an axis with a longitudinal slot cut through it, 

 mounted in bearings at A A (Fig- 138), and connected 

 with the train of machinery. Within the slot there was 

 fitted a short transverse spindle B, to which were fixed 



Fig. 138. 



two thin blades, kept in the position indicated in the 

 igure by means of a small spring made to act on their 

 spindle. When this apparatus was made to rotate with 

 considerable velocity in the bearings A A, the blades 

 ;ended, by their centrifugal force, to fly outwards to 

 some such position as that marked by the dotted lines, 

 and thus encountered more resistance from the air. By 

 ;he proper adjustment of the area and weight of these 

 jlades and of the spring which acted on their spindle in 

 opposition to their centrifugal force, extreme regularity 

 in the motion of the train was maintained. 



In general, for moving machinery with regular speed, 

 weights are preferable to springs, because the force of a 

 weight is constant, while that of a spring varies according 

 its tension. But weights act only vertically, while 

 prings act in any direction. For all portable apparatus 

 which cannot be maintained in a constant level so as to 

 make the direction in which the weight acts constant, 



