MECHANICS. 



excess of .^th of an inch above ^th of 

 an inch ; that is, by ; A 5 th of an inch. 



To render the explanation clearer, we 

 have here supposed things to happen in 

 succession, which really happen toge- 

 ther. The same motion which advances 

 the screw A downwards, draws the screw 

 B upwards ; but the final effect is the 

 same as if these two motions took place 

 in succession. 



It is plain, therefore, that the effect of 

 this machine is the same as that of a sim- 

 ple screw in which the distance between 

 the threads is equal to the difference 

 of the distances between the threads of 

 the two screws A and B; and, therefore, 

 that the ratio of the power to the weight 

 is the difference between the distances of 

 the threads of the two screws to the 

 circumference described by the power. 



The mechanical efficacy is, therefore, 

 increased by diminishing the difference 

 of the distance between the threads of 

 the screws. If the circumference de- 

 scribed by the power be 20 inches, and 

 one screw have twenty threads to an 



inch, and the other twenty-one, the 

 power will be to the weight as the dif- 

 ference between 5^ and S ' T , or 3 1 5 to 20, 

 or as 1 to 8400. If, however, one screw 

 have 30 threads and the other 31 to an 

 inch, then the power is to the weight as 

 the difference between & and 3 ' T , or 5 |<j 

 to 20, or as 1 to 18600. 



The threads of each screw may be 

 constructed of any size and strength 

 which may be required, and yet so very 

 nearly equal, that any degree of power 

 may be imparted to the machine. Thus, 

 by the preceding investigation, it ap- 

 pears that two screws, constructed with 

 30 and 31 threads in a foot, are equiva- 

 lent to a single screw with 930 threads 

 in a foot. 



(101.) The thread of the screw, in- 

 stead of urging forward the nut, some- 

 times is made to act upon the teeth of 

 a wheel, as in fig. 86. In this case it 

 is called a perpetual screw. The ma- 

 chine in this figure is complex, being 

 composed of the screw and the axle in 

 the wheel. The relation between the 



Fig. 86. 



power, and the weight is easily investi- r the radius of the axle, and W the 



gated. Let P be the power, and let x weight or resistance ; and let C be the 



be its effect on the wheel GE. Let R circumference described by the power, 



be the radius of the wheel, D the dis- By what we have established respecting 



tance between the threads of the screw, the screw, 



