VOL. XXXVI.] PHILOSOPHICAL TRANSACTIONS. 373 



portion to the difference of those Hnes, which must give a twitch to the person 

 who draws from r, or r, by a guide rope. 



If, to prevent this inconveniency, the pulley at q be removed back to q ; 

 then indeed the rope will run over the line c4, or t4, and consequently the 

 gibbet will be easily held in that situation; but if there is occasion to remove 

 the weight to 5, the rope touching the pulley at t, will make an angle with 

 c5, and again be subject to the inconveniency abovementioned. Besides, in 

 bringing the end of the gibbet from g to 4, the rope immediately applying 

 itself to the pulley al t, will come forward with a jerk, though it will be 

 twitched back again when at 5. 



If the pulley be set backwarder still, as may be seen at p, when you would 

 keep the weight under 8, it will tend to go on towards c, in proportion as the 

 rope at m8 is now shorter than the line n8; for now the weight descending a 

 little, the force of that descent added to the pull of him who draws the guide 

 rope, will cause the weight to swing towards the crane, so as sometimes to do 

 mischief, if the weight he very great, and the men careless. 



No position of the pulleys can mend the matter, there being only three situa- 

 tions of the gibbet in its whole traverse, where it can keep its place when 

 loaded. Therefore the wheel, y, and the wheel and pinion, xu, in fig. 1, are 

 of very considerable use when great weights are raised. 



Fig, 4, represents the double axis in peritrochio, or wheel and pinion used 

 instead of the walking wheel of fig. 7, c, c, is an axis with handles having a 

 pinion p which leads the wheel pr to wind the rope rz on the axle r. k, a, 

 part of the catch which stops the rope from running back again, w w, a 

 wooden wheel of some thickness, which, when the catch is up, is kept from 

 turning too swift, as the weight runs down, by pulling up the semicircular 

 part of the pall loi, so as to make it bear hard against the wheel below, to 

 regulate or stop the descent of the weight, cc, the pivots or centres of the 

 axle. LF, part of the lever, by which the pall is drawn up against the wheel 

 WW, by means of the rope fb. q, the weight to bring down the pall clear of 

 the wheel ww, when it is not pulled up. ioib, the end of the pall which is 

 applied to the wheel, the other end not being represented here. 



Fig. 5 shows the manner of letting down the weight swifter or slower as 

 there is occasion, representing that end of the axle on which the catch and 

 pall act alternately, pp and pp are two upright pieces, fixed to the frame of 

 the crane, in any manner that is most convenient for carrying the three centres 

 L, K, and k. 



When the rope Rrz, going over a pulley at r, or any where else, draws from 

 the axle in the direction Kr ; the catch, if its end is at a, keeps it immove- 



