222 Mb AIRY ON A NEW CONSTRUCTION OF THE GOING-FUSEE. 



One important point to which I have not yet alluded is the manner of 

 winding up. It has been supposed all along that the act of winding up 

 simply relieves the barrel from the pressure of W. This cannot be done 

 by a square and winch upon the axis b in the usual way. For the action 

 of the hand in winding up would then produce a force which may be 

 resolved into a couple acting on the barrel and a force of variable direction 

 acting at b : which differs entirely from our supposed relief of the pressure 

 of W. But it can be done easily by inseparably attaching a toothed-wheel 

 // to the barrel, and mounting a toothed-wheel k with its centre of motion 

 on the clock-plate, so that the center of k shall be in the same horizontal 

 line with a, and that the teeth of k may work in those of h: the 

 winding-up-key being applied to the axis of k. For then the act of turning 

 It produces no effect on the barrel except a pressure upwards at the very 

 point where the weight of W produces a pressure downwards (any in- 

 cidental pressure in the direction of a radius of the barrel, arising from the 

 slope of the surface of the teeth, evidently having no effect on the angular 

 motion about a). And therefore, as that pressure upwards must necessarily 

 be equal in magnitude to the pressure produced by W, it follows that we 

 may consider the pressure of Was simply relieved in this way of winding 

 up the clock. The wheel k, it is to be observed, may be of any size or any 

 number of teeth whatever. 



The going-fusee is now complete in its action, so far as regards the use 

 of a determinate weight W. But by a trifling alteration it will be made 

 perfect for any weight whatever, without requiring any other change when 

 the weight Wis changed. 



Suppose the lever-frame to be so loaded at cl that the lever-frame when 

 carrying the barrel and toothed-wheel may be nearly in equilibrium about 

 a. Then the weight w must be in a constant proportion to W. Now it 

 will be possible always to arrange the suspension of a single weight by a 

 line with pulleys attached to the barrel and to cl, so that the tension of the 

 line acting on cl shall be to the tension of that acting upon the barrel in the 

 constant proportion which may be assumed. 



Consequently the action of that single weight, whatever be its amount, 

 will then produce two forces such as are proper for the action of this going- 



