Fig. 614 Fig. 615 Fig. 616 Fig. 617 External diameters in hundredths of an inch... •75 •75 •75 •75 Internal diameters in hundredths of an inch . . •65 •55 •35 •55 Number of threads per inch, or rates of the screws 20. 10. 5. 5. Depths and widths of the threads in hundredths •05 .10 •20 •10 Angles of the threads on the external diameters* 1° 16' 2° 33' 5° 5' 5° 5' Angles of the threads on the internal diameters* 1o 28' 3o 28' 10o 47' 6° 55' Relative mechanical powers of the threads . . 20 10 5 5 Relative cohesive strengths of the bolts . . . 4 8 1 8 Relative cohesive strengths of hold of the screws 65 55 35 27 1/2 Relative cohesive strengths of hold of the nuts . 75 75 75 37 1/2

* The angles 'of the threads of screws are calculated trigonomotrically, the circumference of the bolt being considered as the base of a right-angled triangle, and the pitch as the height of the same.

The author has adopted the following mode, which will be found to require the fewest figures; namely, to divide the pitch by the circumference, and to seek the product in the table of tangents; decimal numbers are to be used, and it is sufficiently near to consider the circumference as exactly three times the diameter.

For the external angle of fig. 616 say 20÷ 2.25 = .0888, and this quotient by Mutton's Tables gives 5 deg. 5 min.

For the internal angle of fig. 614 say. 05 ÷1. 95=0. 2564, and by Hutton's Tables, 1 deg. 28 min. In this method the pitch is considered as the tangent to the angle, and the division effects the change of the two aides of the given right-angled triangle, for two others, the larger of which is 1 or unity, for the convenience of using the tables.

Square thread screws, have about twice the pitch of angular threads of similar diameters, and 617 estimated in the same manner as the angular, will stand by comparison as follows. The square thread, 617, will be found to be equal in power to 61G, the pitch being alike in each. In strength of bolt to be equal to 615, their transverse areas being alike. And in strength of hold, to possess the half of that of 615, because the square thread will from necessity break through the bottom of the threads, or an interrupted line exactly like the dotted line in 616, that denotes just half the area or extent of base, of the thread of 615; which latter covers the entire surface of the contained cylinder, and not the half only.

The mechanical power of the thread, is derived from its pitch. The power, or the force of compression, is directly as the number of threads per inch, or as the rate; so that neglecting the friction in both cases, fig. 614 grasps with four times the power of 616, because its wedge or angle is four times as acute.

When however the angle is very great, as in the screws of fly-presses which sometimes exceed the obliquity of 45 degrees, the screw will not retain its grasp at all; neither will a wedge of 45 degrees stick fast in a cleft. Such coarse screws act by impact; they give a violent blow on the die from the momentum of the fly, (namely, the loaded lever, or the wheel fixed on the press-screw,) being suddenly arrested; they do not wedge fast, but on the contrary, the reaction upwards, unwinds and raises the screw for the succeeding stroke of the fly-press.

Binding screws which are disproportionately coarse, from leaning towards this condition, and also from presenting less surface-friction, are liable to become loosened if exposed to a jarring action. But when, on the contrary, the pitch is very fine, or the wedge is very acute, the surface friction against the thread of the screw is such, as occasionally to prevent their separation when the screw-bolt has remained long in the hole or nut, from the adhesion caused by the thickening of the oil, or by a slight formation of rust.

The cohesive strength of the bolt, is derived from its transverse section. The screw may be thus compared with a cylindrical rod of the same diameter as the bottom of the thread, and employed in sustaining a load; that is, neglecting torsion, which if in excess may twist the screw in two. The relative strengths are represented by the squares of the smaller diameters: in the screws of 20, 10, and 5 angular threads, the smaller diameters are 65, 55, and 35; the squares of these numbers are 4225, 3025, and 1225, which may be expressed in round numbers as 4, 3, 1; and therefore, the coarsest screw 616, has transversely only one-fourth the area, and consequently one-fourth the strength of the finest, represented in the three diagrams.

The cohesive strength of the hold, is derived from the helical ridge of the external screw, being situated within the helical groove of the internal screw. The two helices become locked together with a degree of firmness, approaching to that by means of which the different particles of solid bodies are united into a mass; as one or both of the ridges must be in a great measure torn off in the removal of the screw, unless it be unwouud or twisted out.

A slight difference in the diameter or the section of a screw and nut, is less objectionable than any variation in the coarseness or pitch; as the latter difference, even when very minute, will prevent the screw from entering the hole, unless the screw is made considerably smaller than it ought to be, and even then it Mill bear very imperfectly, or only on a few places of the nut.

To attempt to alter a screwed hole by the use of a tap of a different pitch, is equally fatal, as will be seen by the annexed diagram fig. 618. For instance, the upper line a, contains exactly 4 threads per inch, and the middle line or b, has 4 1/3 threads; they only agree at distant intervals. The lowest line c, shows that which would result from forcing a tap of 4 threads such as a, into a hole which had been previously tapped with the 4 1/3 thread screw b, the threads would be said to cross, and would nearly destroy each other; the same result would of course occur from eemploying 4 or 5 thread dies on a screw of 4 1/3 threads per inch. Therefore, unless the screw tackle exactly agree in pitch with the previous thread, it is needful to remove every vestige of the former thread from the screw or hole; otherwise the result drawn at c, must ensue in a degree proportionate to the difference of the threads, and a large portion of the bearing surface, and consequently, of the strength and the durability of the contact, would each be lost. Some idea may thence be formed of the real and irremediable drawback frequently experienced from the dissimilarity of screwing apparatus; nearly to agree will not suffice, as the pitch should be identical.