VOL. LIII.] , PHILOSOPHICAL TRANSACTIONS 711 



Mr. F. takes occasion to mention what he calls a general error in the manner 

 of placing the axis of the lever under the beam. A balance, having its centre of 

 motion underneath, and equal weights at each end, being placed horizontally, 

 will remain in that position ; as both weights are equidistant from the centre of 

 gravity, which is'perpendicular to the centre of motion ; but when it is made to 

 incline to either side, it will continue to move on that side, till it becomes pa- 

 rallel to the horizon, with the centre of motion above the balance: for when 

 either end is depressed in the least degree, it becomes more distant from the 

 centre of gravity ; and the opposite end, which is raised in proportion, is brought 

 nearer to it, though both ends still continue equidistant from the centre of 

 motion. The lever of this engine is 2 feet g inches from the upper part of the 

 beam to the centre of its axis placed underneath; and weighs with its arch-heads 

 about 5 tons. When it was placed in a horizontal position, it required but QS^- 

 lb. to overcome the resistance from friction in the pivots; but when either end 

 was depressed 4 feet below the level, at which distance the springs are fixed, it 

 required 534 lb. to be applied to the opposite end to bring it back again: so that 

 a power = 4404- was required, on account of the centre of gravity being so much 

 changed by the position of the axis underneath. 



To avoid this general error, Mr. F. had the axis placed on the upper side of 

 the lever, and fixed by proper bolts and screws to a bar of iron equally strong, 

 placed underneath: and in order to reduce the quantity of friction, which is in 

 proportion to the space rubbing on a dead surface in equal time, he had them 

 made in a form, by which they are equally strong, though the rubbing part is 

 but 1-1- diameter; so that by changing only the form of the pivots, the friction 

 is reduced to -f of its original quantity. He applied two quadrants, or friction- 

 arches, to each of these pivots, whose radii are 2 feet 6 inches, by which the 

 whole friction of the pivots of the axis of the lever, are transferred to the pivots 

 of the quadrants, which are 14^ inch diameter. These quadrants are equal in 

 effect to wheels 5 feet diameter ; the radius of which is V to the semidiameter 

 of its pivot, and reduce the friction in the pivots of the quadrants to -^Lth part of 

 what it was in the pivots of the axis; which multiplied by f, the reduction made 

 by changing the form of the pivots, gives '-f° : by which means the friction that 

 was in the pivots of the great axis, which was = 425 lb., is reduced to ^4-^, or 

 somewhat less than 2f lb. On trial, the lever, that before required a power of 

 95 lb. to overcome the least resistance from friction, was as easily effected by the 

 application of -| pound ; and the resistance from friction occasioned by a weight 

 of 6 tons is of so little consequence, that the lever may be swung with a slight 

 thread, and will continue in a state of vibration for several minutes after. The 

 original quantity of friction in the pivots of the lever a, which when loaded 

 with its full weight 22 tons, required a power = 425 lb. to overcome its resist- 



