Ma AIRY ON A NEW CONSTRUCTION OF THE GOING-FUSEE. 223 



fusee : and therefore upon any change in that weight there will still be two 

 forces such as are proper for that action ; and an alteration in the suspended 

 weight therefore will not require any other alteration in the adjustments of 

 the mechanism. 



If it be required, for instance, that the forces corresponding to Wand 

 w shall be equal, we must adopt the construction represented in figure 4, 

 which, for its simplicity, may be considered preferable to any other. If 

 it be required that the force corresponding to w shall be double that 

 corresponding to W, we must adopt the construction of figure 5. This 

 is the construction adopted by the mechanic who (under my general 

 direction) constructed the clock-work of the Northumberland Telescope. 

 The wheels h and k are, for clearness, omitted in figures 4 and 5. 



The length and inclination of the arm ad will depend upon the hori- 

 zontal distance between the verticals through a and d : and this horizontal 

 distance will be found by such a calculation as the following. Suppose, (for 

 instance) the diameter of the barrel to be half that of the toothed-wheel. 



W 



The force W acting on the barrel will produce a force — at c, and the 



3 W 



pressure at b will therefore be — — . This pressure acting on the arm ba 



of the lever whose fulcrum is a, is to be balanced by the pressure w acting 



3 W W 3 



at d: or — — - x ba = w x al. Consequently al = — x -ba. Thus in the 

 2 * * w 2 



W 3 



instance of fig. 4, where — — 1, al must = -ba; in the instance of fig. 5, 



W 1 3 



where — = -, al must = -ba. In determining the inclination to be 



w 2 4 ° 



adopted for the arm ad the mechanic must be guided only by the following 

 considerations : that if ad be nearly horizontal, the failing of power in the 

 action of the going-fusee (similar to the weakening of a spring by expan- 

 sion) will be small, but the angle through which the lever-frame must turn, 

 in order to correct any small error of adjustment, will be large : whereas, 

 if a d be greatly inclined to the horizon, the action of the going-fusee fails 

 rapidly during the suspension of the action of W, but a small error of 



