*4 ^be perpetual Screw, f Book f, 



the refiftance which the thread h of the fcrew oppofes 

 to the tooth of the wheel, keeping the direction h g per- 

 pendicular to the radius C h. This thread h therefore 

 acls by the radius, of the wheel C b, whilft the weight 

 P acts by the radius of the roller or windlafs C d ; fo 

 that to maintain an equilibrium, the force at h fhould 

 be to the weight P as C d> as the radius of the roller 

 rs to the radius of the wheel C h. Thus the re- 

 lation which the weight P Ihould have to the power 

 QJn cafe of an equilibrium, may be expreffed in this 

 manner. The weight is to the power as the product 

 of the radius of the wheel, multiplied by the circum- 

 ference which the radius of the handle defcribes, is 

 to the product of the radius of the windlafs, multiplied 

 by the height of the pace of the fcrew. 



The motion of the wheel being exceedingly flow in 

 proportion to that of the handle, it follows that a very 

 fmall power is capable of raifing a confiderable weight 

 by means of the perpetual fcrew. For example, fup- 

 pofe, as in fig. 8. a wheel C h t which has nine teeth, 

 and a fcrew which has but one thread, and which, at 

 each round, caufes only one toth of the wheel to pafs - t 

 fuppofe the circumference of the windlafs T to be 

 cme foot, and the circumference which the radius of 

 the handle E M defcribes to be five feet ; when the 

 wheel C h fhall have performed an entire round, the 

 weight P will be railed one foot, and the fpace run 

 through by the power Q^will be 19 times five feet or 

 95 feet. . The velocity of the power Q^will then be 

 to the velocity of the weight P as 95 is to one; con- 

 fequently this power, with the effort of I Ib. is capable 

 of railing 95 Ib. ; and if its effort v.as equal to 30 Ib. 

 it would" raife 2,850105. 



If the wheel C h had as many more teeth as it has, 

 ike radius E M of the handle were as long again, 



the 



