VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 29 



weak to resist any considerable violence. For example, if DC have 5 threads in 

 an inch, and de 6, and if the handle ckl be afoot in length, the power gained 

 by the engine will be nearly as (a 2 + a) X 6b = 2l60 to 1; whereas, to have 

 the same force by means of the common screw, it must have 30 threads in an 

 inch, and so must yield under a resistance which the other screw would overcome 

 without any difficulty. On this principle, the screw may be applied with advan- 

 tage in presses of different kinds, by fixing one of the plates of the press to the 

 end of the screw at e. 



If the screw de be intended to carry an index which must turn round at the 

 same time that it rises upwards, the common screw is preferable; for though I 

 can see a method by which the machine before described may be made to answer 

 this purpose, I am almost afraid to propose it. I mean, that within the screw 

 de another still smaller should be made to play, and be connected with the 

 screw cd, so as to move round along with it. It must have a 2 + a -f- 1 threads 

 in an inch, and they must be in the contrary direction to those of cd, so that 

 when they are both turned together, and cd moves upward, this other one 

 may move downward. At one turn of the handle this will move upward 



— - — X -3 -7 = 4 , o 3 ~, a i i — °f an mcn J a "d at the same time will move 



a* + a a 2 + a + I a* + 2a 3 + 2u* + a 



round in a circular direction. For example, let cd have 5 threads (= a) in an 

 inch, de 6 (= a + l), and a third screw within de, but connected with cd so 

 as to partake of its motion, 31 (= a' -f « + 0- At one turn of the handle, 

 this screw will rise upwards j X{ X -rr = mhr of an inch ; but this appears too 

 complicated for use, and the least inaccuracy in the construction would hinder it 

 from moving. 



But, on the other hand, if while the point e rises it is of consequence that 

 it be kept from going round, the machine under consideration will best answer 

 this purpose. On this principle it may be useful in several respects: for instance, 

 let a (fig. 3) represent a magnifying lens, and let it be moveable on the screw bc 

 of l6 threads in an inch, which turns within the larger screw cd of 15 threads 

 in an inch, and that again moves within the plate ef in the end of the cylinder 

 gf.* To use the instrument, fix the object to be magnified on the pin gl, and 

 then turn the lens A on the screw bc, till it be nearly at the proper distance from 

 the pin, and opposite to it. You may then adjust the distance more accurately 

 by turning the screw dc, at each turn of which the lens will recede from, or 

 approach to, the pin -^-^ of an inch. This it will do and not turn aside, but 

 still remain opposite to the pin lg. A double microscope might be fitted on in 



* The screw bc is restrained from moving along with cd by the small pillar uk, which slides back- 

 wards and forwards in a groove in the cylinder gf.— Orig. 



