VOL. XIV.] PHILOSOPHICAL TKANSACTIONS. " 5p 



stage, it is to be replaced at S, as before; which may be done in less than half 

 the time you are winding up a watch ; and if the stage be 6 feet long, no oftener 

 than once in a week. 



The way of adjusting this motion to the exact measure of an hour, and 

 rectifying its errors, is as follows: viz. by a screw inserted in the stage at S, by 

 the turning of which the stage may be elevated or depressed, the movement 

 will go faster or slower; faster if raised up; and slower if let down. And by 

 making the horary circle moveable, and inserting several small bosses or buttons 

 here and there upon its verge, with an easy touch of the finger it may be moved 

 to the right or left, as there shall be occasion, till the just time be brought to 

 the suspended index. 



Now because it may seem at first view a little surprizing that a circular body 

 should rest, or which in the present case is the same, move so imperceptibly 

 slow, on a descending plane, having no visible impediment either to stop or re- 

 tard the impetus of its own weight: therefore to explain this, let the circle 

 LODN, fig. 5, represent any circular body, whose centres of gravity and 

 magnitude are coincident at M; and let this circular body be placed on some 

 level plain GG: then it is evident that the angle of its contact with that plane 

 at a, will also be the point of its libration, and consequently it must rest there; 

 because the momentum and obstacle are equal. Let DE represent a descending 

 plane, making an angle of contact with this circular body at b, and here it is 

 manifest it cannot rest; because the line of direction ra, which while it insisted 

 on a level, divided the circular body by the centres of magnitude and gravity 

 into parts equiponderate, is now removed to LD; which line LD falling with- 

 out or beside the centre M, evidently destroys the equipoise of its parts, and 

 therefore must leave it to tumble down towards E; for the momentum exceeds 

 the obstacle. The reason therefore of its descent now being the overbalance 

 of the parts LND to the remaining section LDO, it must necessarily follow, 

 that if some weight, equal to the excess of LND above LOD, were affixed to 

 the limb of the quadrant O a, as at P; then the circular body would rest as 

 quietly at b, as it did before at a. The supposition cannot be denied, and the 

 consequence is unavoidable, because LDO + P = LND, i. e. the obstacle is 

 equal to the momentum. Nay this circular body will now resist a greater force, 

 and maintain its point of libration b, more firmly on the declivity DE, than it 

 could before, when it rested on the point a, in the level GG. The reason of 

 which is evidently this, that by the addition of the counterpoise P to the quad- 

 rant Oa, the centre of gravity falls lower in the line of direction LD, and is re- 

 moved from M to G, i. e. nearer to the point of libration b: and consequently 



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