VOL. XIV.] PHILOSOPHICAL TRANSACTIONS. 6l 



rant QD, but hangs on the train of wheel-work 1, 2, 3, 4, it evidently follows 

 that if its power be superior to the resistance of the train, then the whole body 

 of the movement must needs descend towards E in fig. 3. By this it appears 

 that there are two offices assigned to the weight or power represented by P. 

 The first is, to be a counterpoise to the excess of the weight of LED, above 

 LQD; the second is, that it be of force sufficient to put the train into a mo- 

 tion, so adjusted as may exactly comport with the time assigned for the revolu- 

 tion of the whole body. So that if there be any difficulty remaining, it consists 

 in such an exact stating of the weight and power of P, that it may adequately 

 serve both these intentions. And how easy this is, will appear from the follow- 

 ing propositions. 



1. That whatever the intrinsic weight of P shall be, as suppose it 4 ounces 

 Troy, yet the power of that weight will be augmented or diminished, according 

 to the different degrees of its elevation in the quadrant TQ. Thus, considering 

 PM as a lever, its fulcrum is M, the point where it exerts its power on the 

 train, is at V ; then whatever power it has on the point V in its present eleva- 

 tion of 45 degrees, it will acquire a greater by being raised to 50 or 55, &c. and 

 the greatest of all in QO degrees, at Q : and on the contrary, let it sink to 40 

 or 35, &c. its power on the point V will still be diminished, insomuch that in 

 T it will be quite extinguished ; and therefore if P be of a competent weight to 

 move the train at all, it will certainly move it in some degree of elevation or 

 other in the quadrant QT. 2dly, if the weight P be considered as to its office 

 of being a counterpoise to the body of the movement, it will perform this no 

 less while it hangs by the lever M P, than if it were fast rivetted in the same 

 place to the case of the movement : so in whatever point of the quadrant it 

 moves the train, it may be also a counterpoise to the body of the movement. 

 For, 1. At whatever point of the circle LETQ, fig. 6, the line of declivity DE 

 makes an angle of contact; on the same point will the diameter SD fall at right 

 angles with DE. 2. The line of direction LD will always fall on the point of 

 contact D, making an angle with the diameter, as SDL. 3. The angle SDL 

 will be always equal to DEH, in fig. 3, i. e. as great as is the elevation of the 

 line of declivity DE above the horizontal EH, so great will be the angle of 

 distance be between the diameter SD and the line of direction LD, fig. 6. 

 4. The greater the angle of declivity is, the less will be the section LQD; and 

 so, on the contrary, the less that angle is, the greater the section. And there- 

 fore, 5. The excess of the weight of LED above LQD must be also greater, 

 by raising up the stage with the screw at S ; and that excess less, by screwing it 

 down. 6. The lighter that part of the body is, which is represented by the. 



