An elementary idea of the form of the screw, or helix, is obtained by considering it as a continuous circular wedge; and it is readily modelled by wrapping a wedge-formed piece of paper around a cylinder; the edge of the paper then represents the line of the screw, and which preserves one constant angle to the axis of the contained cylinder, namely, that of the wedge.

The ordinary wedge, or the diagonal, may be produced by the composition of two uniform rectilinear motions, which, if equal, produce the angle of 45°, or if unequal, various angles more or less acute; and in an analogous manner, the circular wedge or the screw, nay be produced of every angle or coarseness, by the composition of an uniform circular motion, with an uniform rectilinear motion. And as either the rectilinear or the circular motion may be given to the work or to the tool indifferently, there are four distinct modes of producing screws, and which are all variously modified in practice.

The screw admits of great diversity; it may possess any diameter; it may also have any angle, that is, the interval between the threads may be either coarse or fine, according to the angle of the wedge, or the ratio of the two motions; and the wedge may be wound upon the cylinder to the right hand or to the left, so as to produce Other right or left-hand screws.

The idea of double, triple, or quadruple screws, will be conveyed by considering two, three, or four black lines drawn on the uncovered edge of the wedge-formed paper, or likewise by two, three, or four strings or wires placed in contact, and coiled as a flat band around the cylinder, the angle remains unaltered, it is only a multiplication of the furrows or threads; and lastly, the screw may have any section, that is, the section of the worm or thread may be angular, square, round, or of any arbitrary form. Thus far as to the variety in screws.

The importance of this mechanical element, the screw, in all works in the constructive arts, is almost immeasurable. For instance, great numbers of screws are employed merely for connecting together the different parts of which various objects are composed, no other attachment is so compact, powerful, or generally available; these binding or attachment screws require, by comparison, the least degree of excellence. Other screws are used as regulating screws, for the guidance of the slides and the moving parts of machinery, for the screws of presses and the like; these kinds should possess a much greater degree of excellence than the last. But the most exact screws that can be produced, are quite essential to the good performance of the engines employed in the graduation of right lines and circles and of astronomical and mathematical instruments; in these delicate micrometrical screws, our wants ever appear to outstrip the most refined methods of execution.

The attempt to collect and describe all the ingenious contrivances which have been devised for the construction of screws, would be in itself a work of no ordinary labour or extent: I must, therefore, principally restrict myself to those varied processes now commonly used in the workshops, for producing with comparative facility, screws abundantly exact for the great majority of purposes. It has been found rather difficult to arrange these extremely different processes in tolerable order, but that which seems to be the natural order has been adopted, thus:

There appears to be no doubt, but that in the earliest production of the apparatus for cutting screws, the external screw was the first piece made; this plain circular metal screw was serrated and thus converted into the tap, or cutting tool, by which internal screws of corresponding size and form were next produced; and one of these hollow screws, or dies, became in its turn the means of regenerating, with increased truth and much greater facility, any number of copies of the original external screw. In these several stages there is a progressive advance towards perfection, as will be hereafter adverted to.

These hand processes are mostly used for screws, which are at least as long, if not longer than their diameters. The rotatory and rectilinear guides, and the one or several series of points, are then usually combined within the tool. This first group will be considered in three sections, namely: II. On originating screws.

III. On cutting internal screws, with screw-taps.

IV. On cutting external screws, with screw-dies.

Subsequent improvements have led to the employment of the lathe, in producing from the above, and in a variety of ways, still more accurate screws. These methods arc sometimes used for screws which possess only a portion of a turn, at other times for screws twenty or thirty feet long and upwards. The rotatory guide is always given by the mandrel, the rectilinear guide is variously obtained, and the detached screw-tool or cutter, may have one single point, or one series of points which touch the circle at only one place at a time. This second group will be also considered in three sections, namely:

V. On cutting screws, in the common lathe by hand. VI. On cutting screws, in lathes with traversing mandrels.

VII. On cutting screws, in lathes with traversing tools.

It may be further observed that the modes described in the six sections are in general applied to very different purposes, and arc only to a limited extent capable of substitution one for the other; it is to be also remarked that it has been considered convenient, in a great measure to abandon, or rather to modify, the usual distinction between the tools respectively used for wood and for metal. The eighth and concluding section of this chapter describes some refinements in the production of screws which are not commonly practised, and it is in some measure a sequel to the second section.