An endless screw consists of two or more spiral fillets or threads on a rod which is capable of being turned on its axis by a power applied to the beadle of a winch, or to a string passing over the circumference of a pulley attached to the rod. The threads work between teeth on the einnunference of a wheel, so that while the revolution of the rod con. aimed, the wheel turns on its own axis. If the radius of the winch or of the pulley on the screw.rod be 6 inches, and the distance between the threads of the screw be 1.10th inch, a power represented by unity at the circumference of the pulley will be in equilibria omitting the effectsof friction, with a resistance expensed by 6 x 10 x 2w, that is, (w being the half circumference of a circle whose radius is unity) applied at the threads of the screw or at the circumference of the wheeL If the lined c n, &c., were drawn on paper, and that paper were bent on the surface of a convex or concave cylinder, one spiral throaul would be formed by the union of A r, E K, &c., at their extremities, and another by the like union of e n, a m, : this is called a thrauled screw, and it it evident that its mechanical power depends upon the ratio of A B to a r, while that of the single-threaded screw depends on the ratio of A a to a n ; that is, with apparently an equal distance between the threads on both screws, the power of the latter is double that of the former.
From the high ratio which the resistance bears to the moving-power in the screw, the use of this machine for moving or compressing bodies is very great ; it is also extensively employed in the construction of philosophical instruments for measuring small angles or distances. [3licaomersa.] The ingenious screw-machine which was invented by Mr. Hunter, and is described in the ' Phil. Trans.' vol. 17, consists of one convex screw which works in the interior of another convex screw. The latter works in a concave screw which is fixed ; and the former Is capable of moving in a rectilinear direction only, being pre vented from turning on its axis with the rotation of the exterior screw. Also the number of threads in an inch on the convex surface of this Lust is less by one than the number in an inch on the convex surface of the other ; suppose the first number to be 10 and the other to be 11 ; then one revolution of the exterior screw would cause the whole machine to move forward through a space equal to inch, but in the same time the interior screw is carried backward through t4 inch. Therefore the forward motion of this last is equal to or inch ; and to produce an equal effect in a simple screw, the latter should have 110 threads in an inch.
Mr. Barlow of Woolwich mentions a compound machine of this kind in which the exterior screw had 100 threads in an inch, and the interior screw 101 threads ; .therefore one turn of the machine caused
the latter to move through the very minute extent of inch, and this space was further sutxlivided into hundredths by means of a micrometer head applied to the exterior screw.
The endless screw is a component part of graduating machines, counting machines, &c.; it is also employed in conjunction with a wheel and axle to raise heavy weights.
Serene, or 'Spiral, of Archimedes. The inventor of the machine so called is quite unknown, but both Diodorus Sieulus and Athennius ascribe the origin of It to the philosopher of Syracuse. The former relates (' Bibl. Hist:, lib. i., c. 34) that irrigation was facilitated in Egypt by a certain machine invented by Archimedes of Syracuse, and called Cochlias (Nexalar) from its form ; and the latter states (' Delpoosophistm; lib. v., p. 206, Casaub.) that Archimedes invented it for the purpose of removing the water from the hold of the great ship which was built by King hero of Syracuse. Vitruvius (` De Archi tecture,' lib. x., c. 11) described the machine under the name of cochlea. lie says that it consisted of four or eight laths bent spirally, and fixed at one edge against the axle, so as to form as many winding channels about it; and that the whole was covered by a cylindrical case, formed of planks, nailed over the exterior edges of the laths. The lower extremity was immersed in the water, which, rising along the channels by the 1. volution of the machine on its axis, was dis charged at the upper extremity. Vitruvius adds that it was turned by men walking on its outer circumference, probably on the conical surface of a bevelled wheel fixed to the axle.
By the account which Vitruvius has given of its disposition, the spiral laths were placed nearly at an angle of 45° with the axle, and the latter was incliued to the horizon in an angle of 36° 52'. The cause of the ascent of the water, and the limits of the inclination of the axle to the harizon, will be Been from the following details which refer to the modem form of Archimedes's spiral as it is also called. It may consist of either a flexible tube open at both ends and wound spirally on the exterior surface of a cylinder ; or it maybe a plate of metal coiled about an axis, like the threads of a screw, and enclosed within a hollow cylinder so as to be completely water-tight. The machine is fixed in an inclined position, with its lower extremity iunnenexl in the water which is to be raised. While it is at rest the water occupies the lower part between two of the threads or bends of the spiral, at bottom ; but, when turned on its axis, this part of the machine being made to ascend, the water will by its gravity be caused to descend into the lower part between the next bends of the spiral, while in reality it rises, with respect to its former position, in con.