292 



THE INCLINED PLANE, WEDGE, AND SCREW. 



lost, the machine will acquire an efficacy limited by nothing but the sraallness 

 of the difference between the two threads. 



Fig. 13. 



This principle was first applied in the manner represented in fig. 13. A is 

 the greater thread, playing in the fixed nut ; B is the lesser thread, cut upon a 

 smaller cylinder, and playing in a concave screw, cut wilhin the greater cyl- 

 inder. During every revolution of the screw, the cylinder A descends through 

 a space equal to the distance between its threads. At the same time, the 

 smaller cylinder B ascends through a space equal to the distance between the 

 threads cut upon it : the effect is, that the board D descends through a space 

 equal to the difference between the threads upon A and the threads upon B, 

 and the machine has a power proportionate to the smallness of this difference. 



Thus, suppose the screw A has twenty threads in an inch, while the screw 

 B has twenty-one : during one revolution, the screw A will descend through 

 a space equal to the twentieth part of an inch. If, during this motion, the 

 screw B did not turn within A, the board D would be advanced through the 

 twentieth of an inch ; but because the hollow screw within A turns upon B, 

 the screw B will, relatively to A, be raised in one revolution through a space 

 equal to the twenty-first part of an inch. Thus, while the board D is depressed 

 through the twentieth of an inch by the screw A, it is raised through the twen- 

 ty-first of an inch by the screw B. It is, therefore, on the whole, depressed 

 through a space equal to the excess of the twentieth of an inch above the 

 twenty-first of an inch that is, through the four hundred and twentieth of an 

 inch. 



The power of this machine will, therefore, be expressed by the number of 

 times the four hundred and twentieth of an inch is contained in the circum- 

 rence through which the power moves. 



In the practical application of this principle at present, the arrangement is 

 somewhat different. The two threads are usually cut on different parts of the 

 same cylinder. If nuts be supposed to be placed upon these, which are ca- 

 pable of moving in the direction of the length, but not of revolving, it is evi- 

 dent that by turning the screw once round, each nut will be advanced through 

 a space equal to the breadth of the respective threads. By this means the 

 two nuts will either approach each other, or mutually recede, according to the 

 direction in which the screw is turned, through a space equal to the difference 

 of the breadth of th,e threads, and they will exert a force either in compressing 

 or extending any substance placed between them, proportionate to the small- 

 ness of that difference. 



A toothed wheel is sometimes used instead of a nut, so that the same qual- 

 ity by which the revolution of the screw urges the nut forward is applied to 

 make the wheel revolve. The screw is in this case called an endless screw, 



