THE LEVER AND WHEELWORK. 257 



therefore this power, when the diameter of the wheel is given, does not, as in 

 the ordinary wheel and axle, depend on the smallness of the axle, but on the 

 smallness of the difference of the thinner and thicker parts of it. The axle 

 may, therefore, be constructed of such a thickness as to give it all the requisite 

 strength, and yet the difference of the diameters of its different parts may be so 

 small as to give it all the requisite power. 



It often happens that a varying weight is to be raised, or resistance over- 

 come, by uniform power. If, in such a case, the weight be raised by a rope 

 coiled upon a uniform axle, the action of the power would not be uniform, but 

 would vary with the weight. It is, however, in most cases desirable or neces- 

 sary that the weight or resistance, even though it vary, shall be moved uni- 

 formly. This will be accomplished if by any means the leverage of the weight 

 is made to increase in the same proportion as the weight diminishes, and to 

 diminish in the same proportion as the weight increases ; for in that case the 

 moment of the weight will never vary, whatever it gains by the increase of 

 weight being lost by the diminished leverage, and whatever it loses by the 

 diminished weight being gained by the increased leverage. An axle, the sur- 

 face of which is curved in such a manner that the thickness on which the rope 

 is coiled continually increases or diminishes in the same proportion as the 

 weight or resistance diminishes or increases, will produce ttyis effect. 



It is obvious that all that has been said respecting a variable weight or re- 

 sistance is also applicable to a variable power, which, therefore, may, by the 

 same means, be made to produce a uniform effect. An instance of this occurs 

 in a watch, which is moved by a spiral spring. When the watch has been 

 wound up, this spring acts with its greatest intensity, and, as the watch goes 

 down, the elastic force of the spring gradually loses its energy. This spring 

 is connected by a chain with an axle of varying thickness, called a fusee. 

 When the spring is at its greatest intensity, the chain acts upon the thinnest 

 part of the fusee, and, as it is uncoiled, it acts upon a part of the fusee which is 

 continually increasing in thickness, the spring at the same time losing its elas- 

 tic power in exactly the same proportion. A representation of the fusee, and 

 the cylindrical box which contains the spring, is given in fig. 20, and of the 

 spring itself in fig. 21. 



Fig. 20. Fig. 21. 



When great power is required, wheels and axles may be combined in a 

 manner analogous to a compound system of levers, explained in fig. 9. In this 

 case the power acts on the circumference of the first wheel, and its effect is 

 transmitted to the circumference of the first axle. That circumference is placed 

 in connexion with the circumference of the second wheel, and the effect is 

 thereby transmitted to the circumference of the second axle, and so on. It is 

 obvious, from what was there shown, that the power of such a combination 

 of wheels and axles will be found by multiplying together the powers of the 

 several wheels of which it is composed. It is sometimes convenient to com- 

 pute this power by numbers, expressing the proportions of the circumferences 

 or diameters of the several wheels, to the circumferences or diameters of the 

 several axles respectively. This computation is made by first multiplying the 

 numbers together which express the circumferences or diameters of the wheels, 



VOL,. II. 17 



