28 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 



weeks, to the beginning of December, when the Aherramantah season again 

 commences. 



V. A New Method of applying the Screw. By Mr. IVm. Hunter, Surg. p. 58. 

 The method is somewhat similar to Nonius's division of the circle. In cer- 

 tain cases it may be attended with some advantages to a greater degree than by 

 those commonly practised. Let ab (rig. 2, pi. 1) be a plate of metal in which 

 the screw cd plays, having a number of threads in an inch equal to a. Within 

 the screw cd there is a female screw, by which is received the smaller screw de 

 of a + 1 threads in an inch. This screw is retained from moving round along 

 with the screw cd by means of the apparatus at afgb. Now, if the handle ckl 

 be turned a times round the screw, cd will advance upwards an inch, and if we 

 suppose the screw de to move round along with cd, the point e will also advance 

 an inch. If we now turn the screw de a times backward, the point e will move 



a 



downwards of an inch, and the result of both motions will be to lift the 



a + i 



point e upward (1 =) of an inch. But if, while the screw cd is 



1 a + 1 ' a + I 



turned a times round, de be kept from moving, the effect will be the same as if 

 it had moved a times round with cd and been a times turned back, that is, it 



will advance of an inch. At one turn therefore of the handle ckl it will 



a + I 



move upwards ( X =) -; of an inch. If then we suppose the handle 



r v a + 1 a ' a- + a rr 



ckl to be b inches long, the power gained by the machine will be as (a 2 -|- a) 

 X 6.2832 b to unity. 



To illustrate this by a particular example, let the screw cd have 10 threads in 

 an inch, and de 1 1 ; then, while the handle ckl is turned 10 times round, the 

 point d will rise 1 inch above its former situation. But at 10 turns it can only 

 pass over 10 threads of the screw de, and consequently it will advance on that 

 screw 4-f of an inch. The point e therefore must rise V4- of an inch, that the 

 point d may have room to rise a complete inch above its former place: therefore, 

 at one turn of the handle, the point e will rise -H-o of an inch; and if the handle 

 be supposed half a foot long, the power, to produce an equilibrium, must be to 

 the weight, as 1 to 110 X 6.2832 X 6 = 4146. 012, which is the very number 

 expressed by the general theorem, viz. (c a + a) X 6.2832 b, calling a = 10 

 and b = 6. 



Now let us compare, according to the rules before laid down, this method of 

 using the screw with the common one. And first, in order to have the same 

 power by means of the common screw that is exerted by this machine, it must 

 have a number of threads in an inch equal to a 1 + a, which would render it too 



