Square threaded external screws are cut in a similar manner; they are usually about twice the pitch of the angular threads, the original cylindrical surface of the blank left to form the top of the thread, being generally of the same width as the interval; the depth of the thread is also usually about equal to its width. A single square ended tool or blade in fig. 523. at the appropriate angle, cutting only upon the end, and a series of shallow cuts, usually produces both the sides and the bottom of the square groove forming the thread, at the same time. The groove required to receive the tool at the end of the trip, as before, is turned in square threaded screws of moderate dimensions; larger screws, usually have a shallow, radial hole drilled at the termination of the thread, for the same purpose. The hole, rather exceeds the interval of the thread in diameter and it is drilled, its center upon that of the screw line, to a depth slightly beyond that of the intended thread.

External screws are usually fitted to their internal screws or nuts, occasionally the reverse; either operation is readily effected with angular threads, by simple reduction or enlargement in diameter. With square threads it is less easy, for besides the fitting in depth between the top and bottom of the respective threads, obtained by turning the external and boring the internal screws to their appropriate diameters, the square thread on the external screw must also fit that in the nut in width, or by the sides of the thread, and cutting the one to accurately fit the other in both particulars is rather difficult. It is perhaps most readily effected by making the tools to the exact dimensions of one half of the pitch, the width of the groove, and then very slightly reducing this width, to the extent of about 1/2000 of an inch, by carefully applying one side of the blade upon a fine revolving lap. It is far safer that the tools should thus be rather below than above their true width; for it is obvious that in the latter case, the interval of the thread of the external screw would be too great, and therefore beyond correction or service, except by cutting the internal thread by a correspondingly thinned tool.

The tools for cutting internal threads, are very generally made with a single point standing at right angles to their stems, which are clamped in the slide rest parallel with the mandrel. The late Charles Holtzapffel's Cutter bar for internal threads fig. 524, carries separate blades with single angular or square points, that should agree in dimensions with the corresponding blades of the external cutter bar, fig. 523. The stem is held at right angles to the mandrel, presenting the shafts of the blades parallel with it, a position giving greater freedom of management than when the stem of the tool itself is parallel with the mandrel. The point of the inside screw tool, or the blade of the cutter bar, should receive a similar inclination to that of the external tool, but this entails difficulty from the smallness of the space within which it has to work, and its unfavorable position compared with that of the external tool. The want of inclination occasions a marked difference between the form of the thread in the nut and that on the screw, and this, although unimportant for some purposes with the angular threads, renders it constantly necessary to make special tools with the cutting portion filed to the inclination required; indeed the inclination of many internal screws of both angular and square threads, is too great for them to be cut in any other manner.

When accuracy or many copies are required, it is usual if possible to employ taps for producing both forms of internal threads. The nut is cut by a tap or taps made from a portion of a screw similar to that upon which it is to be used, the external screw thus becoming the tool to impart its proportions to the internal. The construction of these taps and the entire subject, has been treated at length in the second volume. When the screw and the nut are required to fit absolutely, the former is made of slightly larger diameter than the tap, but only just sufficiently so, as to render it difficult to get the screw into the nut; the screw is then partially eased at one end and worked in, by employing as much force as the strength of the screw will safely permit. The external square threaded screw, is usually previously equalized by a very smooth flat file, carefully applied while the screw is revolving in the lathe ; and in some cases, a grinder is used to ensure still further accuracy in the parallelism of the diameter.

The nut varies in thickness with its purpose. Thus for fixing or holding, a thickness equal to one diameter of the screw is found to present the maximum of advantages. Screws cut in the slide lathe however, are more usually required for moving slides and similar purposes; when to increase its durability or wear, the nut is seldom less than from one and a half to two diameters in length, and except when it interferes with the traverse it may sometimes be even longer with advantage. The nut is tapped prior to its reduction to external size, and the parallelism of its faces may be ensured, by partially turning them when the nut is in its place on the screw mounted between centers; the surfaces being finished by turning, filing, or planing under the guidance thus obtained.

Producing the internal screw by the tap, very frequently entails the additional labour of making a set of taps, expressly for one screwed hole, which also may be of exceptional dimensions; the proportions of the screw to be cut may also render the use of a tap quite unavailable; many internal screws therefore, have to be cut in the lathe, either on the question of suitability of means, or that of economy. The thickness of the nut or piece for these latter, usually varies from about one and a half to sometimes three diameters of the external screw. It is surfaced and bored with a parallel hole, carried in a chuck with fixing screws, or bolted on a surface chuck. Lifting pieces may be placed between the work and the latter, to afford a space for the tool to cut out free of the thread at the termination of the traverse. Or, the nut is made of greater length, and the parallel hole is enlarged by a groove turned towards the back end to receive the head of the tool; the enlarged portion, which has no thread, being subsequently cut off if required.