SCREW. 



af the fcrew, the weight is fo much lifted up, or the refiftance 

 fo much moved, or the thing to be prefted is fqueezed fo 

 much clofer together, as is the diftance between two imme- 

 diate fpirals ; and in the fame time, the power is fo much 

 moved, as is the compafs defcribed by the faid power in one 

 turn of the fcrew. Wherefore the velocity of the weight 

 (or whatfoever anfwers thereto) will be to the velocity of 

 the power, as is the faid diftance between the fpirals to the 

 compafs defcribed by the power, in one revolution or turn- 

 ing round of the fcrew ; fo that the gaining in power is here 

 recompenfed by the lofs in time. 



2. As the diftance between two threads, B I, is lefs ; 

 the power required to overcome the faid refiftance is lefs ; 

 therefore the finer the thread, the eafier the motion. 



3. If the male fcrew be turned in the female, at reft, 

 a lefs power will be required to overcome the refiftance, as 

 the lever or fcytala C D {Jig. 3.) is the longer. 



4. The diftance of the power from the centre of the fcrew, 

 C D, the diftance of the two threads I K, and the power to 

 be apphed in D, being given, to determine the refiltance 

 it will overcome : or, the refiftance being given, to find the 

 power necefTary to overcome it. 



Find the periphery of a circle defcribed by the radius C D ; 

 then to the diftance between the two threads, the periphery 

 juft found, and the given power ; or, to the periphery found, 

 the diftance of the two threads I K, and the given refiftance, 

 find a fourth proportional. This, in the former cafe, will 

 be the refiftance that will be overcome by the given power ; 

 and, in the latter, the power iieceftary to overcome the re- 

 fiftance. 



E. gr. Suppofe the diftance between the two threads, 3, 

 the diftance of the power from the centre of the fcrew C D, 

 25, and the power 30 pounds ; the periphery of the circle 

 to be defcribed by the power, will be found 157. There- 

 fore, as 3 : 157 ;: 30 : 1570, the weight to which the 

 refiftance is equal. 



5. The refillance to be overcome by a given power being 

 given ; to determine the diameter of the fcrew, the diltance 

 of the two threads I K, and the length of the fcytala, or 

 handle : the diftance of the threads, and the diameter of the 

 fcrew, may be an"umed at pleafure, if the male be to be 

 turned in the female by a handle. Then, as the given power 

 is to the refiftance it is to overcome, fo is the diftance of the 

 threads to a fourth number, which will be the periphery to 

 be defcribed by the handle C D, in a turn of the fcrew. 

 The femidiameter of this periphery, therefore, being fought, 

 we have the length of the handle C D. But if the female 

 fcrew be to be turned about the male, without any handle, 

 then the periphery and femidiameter found will be very 

 nearly thofe of the fcrew required. 



E. gr. Suppofe the weight 6000, the power 100, and 

 the diftance of the threads 2 lines ; for the periphery to be 

 pafled over by the power, fay 100 : 6000 :: 2 : 120 ; the 

 femidiameter of which periphery being Jd of 120=^.40 

 lines, will be the length of the handle, if any be ufed ; 

 otherwife the fide of the female fcrew muft be 40 lines. 

 Mr. Hunter has defcribed a new method of applying the 

 fcrew with advantage in particular cafes. Phil. Tranf. 

 vol. Ixxi. part i. p. 58, &c. 



A cylindrical fcrew is bored, and made at the fame time 

 a tubular fcrew, with a little difference in the diftances of 

 the threads, fo that when it is turned within a fixed nut, it 

 rifes or finks a little more or lefs than the internal fcrew, 

 which perforates it, would rife or fink by the aftion of its 

 own threads ; and a weight attached to this internal fcrew 

 afcends, in each revolution, only through a fpace equal to 

 the difference of the height of. the two coils. Here the 



machine is analogous to a very thin wedge, of which th? 

 thicknefs is only equal to the difference of the diftancee of 

 the threads, and which of courfe adls with a great mecha- 

 nical advantage. It might, in fome cafes, be more conve- 1 

 nient to make two cylindrical fcrews of difi^erent kinds, [ 

 at different parts of the fame axis, rather than to perforate 

 it. The friAion of fuch machines is, however, a great im- 

 pediment to their operation. 



Screw, Endlefs. If a fcrew be fo fitted as to turn a 

 dented wheel D F {Jig. 4. ) it is called an endlefs, or per. 

 petual fcreiu, becaufe it may be turned for ever, without 

 coming at an end. From the fcheme, it is evident enough, 

 that while the fcrew turns once round, the wheel only ad- 

 vances the diftance of one tooth. 



ScREVf, DeSrine of the EnJ/eJs. I. If the power applied 

 to the lever, or handle of an endlefs fcrew A B, be to the 

 weight, in a ratio compounded of the periphery of the axis 

 of the wheel E H, to the periphery defcribed by the power 

 in turning the handle, and of the revolutions of the wheel 

 D F, to the revolutions of the fcrew C B, the power will be 

 equivalent to the weight. 



Hence, I. As the motion of the wheel is exceedingly 

 flow, a fmall power may raife a vaft weight, by means of an 

 endlefs fcrew ; for this reafon, the great ule of the endlefs 

 fcrew is, either where a great weight is to be raifed through 

 a little fpace ; or, where a very flow gentle motion is 

 required. On which account it is very ufeful in clocks and 

 watches. 



2. The number of teeth, the diftance of the power from 

 the centre of the fcrew A B, the radius of the axis H E, 

 and the power, being given ; to find the weight it will 

 raife. 



Multiply the diftance of the power from the centre of 

 the fcrew A B, into the number of teeth : the produft is 

 the fpace of the power pafled through, in the time the 

 weight pafles through a fpace equal to the periphery of the 

 axis. Find a fourth proportional to the radius of the axis, 

 the fpace of the power now found, and the power. This 

 will be the weight which the power is able to fuftain. Thus, - 

 if A B = 3, the radius of the axis H E = i ; the power 

 100 pounds, number of teeth of the wheel D F 48 ; the 

 weight will be found 14,400; whence it appears, that the 

 endlefs fcrew exceeds all others in increafing the force of a 

 power. 



A machine for (hewing the power of the fcrew, may be 

 contrived in the following manner. Let the wheel C (Jig. 5.) 

 have a fcrew a 6 on its axis, working in the teeth of the 

 wheel D, which we may fuppofe to be forty-eight in num- 

 ber. It is plain, that for every revolution of the wheel C, 

 and fcrew a b, by the winch A, the wheel D will be moved 

 one tooth by the fcrew ; and, therefore, in forty-eight revo- 

 lutions of the winch, the wheel D will be once turned 

 round. Then, if the circumference of a circle, defcribed 

 by the handle of the winch, be equal to the circumference 

 of a groove e round the wheel D, the velocity of the handle 

 will be forty-eight times as great as the velocity of any given 

 point in the groove. Confequently, if a line G goes round 

 the groove e, and has a weight of forty-eight pounds hung 

 to it below the pedeftal E F, a power equal to one pound 

 at the handle will balance and fupport the weight. To prove 

 this by experiment, let the circumferences of the grooves of 

 the wheels C and D be equal to one another ; and then, if a 

 weight H of one pound be fufpended by a line going round 

 the groove of the wheel C, it will balance a weight of forty- 

 eight pounds hanging by the line G ; and a fmall addition to 

 the weight H will caufe it to defcend, and fo raife up the 

 other weight. If the line G, inftead of going round the 



groove 



