16 _ PHYSICS. 
directions, whence arises a retarded or accelerated differential: motion; the 
theory remains the same, however, in all cases. . 
With regard to the statical condition of the screw, equilibrium takes bt 
when the power is to the resistance or weight as the height of a turn of the 
thread, or the distance between two threads, is to the circumference of the 
circle described by the power. Hence it follows that by prolonging the lever 
used in producing the rotation, or by diminishing the height of the threads, 
the greatest resistance can be overcome by a moderate power ; here; how- 
ever, the universal law presents itself, that what is gained in power is lost 
in time. | 
An endless screw is a spindle containing only a few turns, which catch 
either in a half open female screw, cut in the circumference of a disk, or in 
a wheel whose teeth are placed obliquely to the axis of the wheel, and in 
the direction of the obliquity of the thread, or in a rack-work with similarly 
situated teeth. The application of the endless screw to a windlass has been 
selected as an illustration, and figured in pl. 16, fig.34. Upon the axle 
BC, turned by the winch A, are to be found at D several turns of a screw, 
which, immovably fastened to the axle, turn with it without advancing. In 
these turns of the thread, the oblique teeth of the wheel, F, catch,. thus 
moving along the inclined plane of the thread, and causing the wheel to 
turn. As there are always as many teeth of the wheel caught by the screw 
as the latter has complete turns, and as for the turns going out at one side, 
new ones are constantly entering at the other, the motion is endless. This 
machine, it will readily be perceived, is a combination of the screw with the 
wheel and axle, and its statical condition will be P x AB x rad. F=W x 
height of a turn of the thread X rad. of azle. 
The screw, in its various varieties and modifications, finds innumerable 
applications in machinery ; we shall here briefly mention a single one, the 
differential screw of Hunter, represented in pl. 17, fig. 4. . EF is a plate of 
metal in which the screw D works, having, for example, ten turns to the 
inch. The inside of the screw is hollow, and forms at LM a nut, in which 
works the smaller screw, NO, having perhaps eleven turns to the inch, and 
forced by the frame, EFGH, to take part in the motion.of the screw, D. 
Suppose now that by méans of the handle BC, the screw D is turned round 
ten times, then A will rise one inch, and will raise the point K to an equal 
height. ‘Turning the screw NO ten times in the opposite direction, the point 
K. will descend 1° of an inch, and the result of the whole will be an elevation 
of j, of an inch. Now, hewever, while the screw D turns ten times, the 
turning of NO is hindered ty the square shoulder at K, and the result is the 
same as ii NO had been turned ten times in the other direction, and K. will 
consequently ascend only ;; of an inch: for a single revolution of the screw 
this will amount to ;5 of 7), or ;1, of an inch, whitih is the actual ascent 
or descent of the screw. Suppose the length of the lever, AB, to be only 
six inches, then to produce equilibrium the power must be to the resistance 
asl to 110 X6X27=4146.912. 
With respect to the simple machines, it is to be remarked, that to,pro- 
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