Tangent screws are occasionally double, triple, or quadruple, in order that 2, 3, or 4 teeth of the wheel may be moved during each revolution of the screw. In the Piedmont silk-mills, this principle is carried to the extreme, as the screw and wheel become alike, and revolve turn for turn; the teeth supposing them to be 20, are then identical with those of a 20 thread screw, the angular coils of which cross the axis at the angle of 45°, that is when the shafts lie at right angles to each other; other proportions and angles may be adopted. In reality they fulfil the office of bevel wheels, or rather of skew-bevel wheels, in which latter also the axes, from being in different planes, may cross each other; so that the skew-bevel wheels may be in the center of long shafts, but which cannot be the case in ordinary bevel wheels, the teeth of which lie in the same plane as the axis of the wheel. The Piedmont wheels act with a very reduced extent of bearing or contact surface, and a considerable amount of the sliding action of screws, which is disadvantageous in the teeth of wheels, although inseparable from all those with inclined teeth, and which are indeed more or less distant modifications of the screw.*

* When the obliquity of the teeth of worm-wheels is small, it gives a very or railway depot, should contain sets of screwing tackle, corresponding with those used by every different manufacturer whose works have to be dealt with: otherwise, both the delay and expense are from necessity aggravated.

Having treated somewhat in detail the different forms of screws, and the circumstances which adapt them to their several purposes, I have now to consider some of the inconveniences which have unavoidably arisen from the indefinite choice of proportions in ordinary screws, and also some of the means that have been proposed for their correction. The slight discussion of the more important of these topics will permit the introduction of various additional points of information on this almost inexhaustible subject, the screw.

No inconvenience is felt from the dissimilarities of screws, so long as the same screwing tools are always employed in effecting repairs in, or additions to, the same works. But when it is considered, how small a difference in either of the measures will mar the correspondence of the screw and nut; and further the very arbitrary and accidental manner, in which the proportions of screwing apparatus have been determined by a variety of individuals, to suit their particular wants, and without any attempt at uniformity of practice (sometimes on the contrary, with an express desire to be peculiar), it is perhaps some matter of surprise when the screws made in different establishments properly agree. Indeed their agreement can be hardly expected, unless they are derived from the same source, and that some considerable pains are taken not to depart from the respective proportions first adopted.

In a few isolated cases this inconvenience has been partially remedied by common consent and adoption, as in the so-called air-pump thread, which is pretty generally used by the makers of pneumatic apparatus; and to a certain degree also in some of the screws used in gas-fittings and in gun-work. But the non-existence of any common standard or scale, enhances both the delay and expense of repairs in general mechanism, and leads to the occasional necessity for making additional sizes of tools to match particular works, however extensive the supply of screw apparatus.

This perplexity is felt in a degree especially severe and costly, as regards marine and locomotive engines, which from necessity, have to be repaired in localities far distant from those in which they were made; and therefore require that the packet station, smooth action, but at the expense of friction; but in ordinary toothed wheels, the teeth are exactly square across or in the plane of the axis, and the aim is to employ rolling contact, with the greatest possible exclusion of sliding, from amongst the tooth.

Mr. Whitworth has suggested that for steam machinery and for the purposes of engineering in general, "an uniform system of screw threads" should be adopted, and after having used some prior scales, he has proposed the following table, which may be justly considered as a mean between the different kinds of threads used by the leading engineers.

Mr. Whitworths Table for Angular Thread Screws*

Diameters in inches . . .

1/4

5/16

3/8

7/16

1/2

5/8

3/4

7/8

1"

1 1/8

1 1/4

1 3/8

1 1/2

1 5/8

1 3/4

1 7/8

2"

Nos. of threads to the inch

20

18

16

14

12

11

10

9

8

7

7

6

6

5

5

4 1/2

4 1/2

Diameters in inches . . .

2 1/4

2 1/2

2 3/4

3"

3 1/4

3 1/2

3 3/4

4"

4 1/4

4 1/2

4 3/4

5"

5 1/4

5 1/2

5 3/4

6"

Nos. of threads to the inch

4

4

3 1/2

3 1/2

3 1/4

3 1/4

3

3

2 7/8

2 7/8

2 3/4

2 3/4

2 5/8

2 1/2

2 1/2

As regards the smaller mechanism, made principally in brass and steel, such as mathematical instruments and many others, the screws in the above scale below half an inch diameter are admitted to be too coarse; and the acute angular threads which arc not rounded, are decidedly to be preferred from their greater delicacy and durability, that is when their strengths arc proportioned to the resistance to which they are exposed. In these respects the following table may be considered preferable.

* In selecting this scale, the following judicious course was adopted: - An extensive collection was made of screw-bolts from the principal workshops throughout England, and the average thread was carefully observed for different diameters. The 1/4 inch, 1/2 inch, 1 and 1 1/2 inch, were particularly selected, and taken as the fixed points of a scale by which the intermediate sizes were regulated, avoiding small fractional parts in the number of threads to the inch. The scale was afterwards extended to 6 inches. The pitches thus obtained for angular threads were as above:

"Above the diameter of 1 inch the same pitch is used for two sizes, to avoid small fractional parts. The proportion between the pitch and the diameter varies throughout the entire scale.

"Thus the pitch of the 1/4 inch screw is 1/5th of the diameter; that of the 1/2 inch 1/6th, of the 1 inch 1/8th, of the 4 inches 1/12th, and of the 6 inches 1/15th.

"The depth of the thread in the various specimens is then alluded to. In this respect the variation was greater than in the pitch. The angle made by the sides of the thread being taken as an expression for the depth, the mean of the angle in 1 inch screws was found to be about 55°, which was also nearly the mean in screws of different diameters. Hence it was adopted throughout the scale, and a constant proportion was thus established between the depth and the pitch of the thread. In calculating the former, a deduction must bo made for the quantity rounded off, amounting to 1/3rd of the whole depth, i.e., 1/6th from the top, and 1/6th from the bottom of the thread. Making this deduction, the angle of 55° gives for the actual depth rather more than 3/5ths, and less than 2/3rds of the pitch." Quoted from the Abstract of Mr. Whilworth's Paper, given in the Proceedings of the Institution of Civil Engineers, 1841, p. 157-160. The entire paper is also printed separately.