The proportions given to screws employed for attaching together the different parts of works are in nearly every case arbitrary, or, in other words, they are determined almost by experience alone rather than by rule, and with little or no aid from calculation, as will be shown.

In addition to the ordinary binding screws, which, although arbitrary, assume proportions not far distant from a general average, many screws, either much coarser or finer than usual, are continually required for specific purposes; as are likewise other screws of some definite number of turns per inch - As 2, 10, 12, 20, Etc. - in order to effect some adjustment or movement having an immediate reference to ordinary lineal measure. But all these must be considered as still more distant than common binding screws from any fixed proportions, and not to be amenable to any rules beyond those of general expediency.

Neither the pitch, diameter, nor depth of thread, can be adopted as the basis from which to calculate the two other measures, on account of the different modes in which the three influence the effectiveness of the screw; nor can the proportions suitable to the ordinary J inch binding screw be doubled for the 1 1/2 inch screw, or halved for that of 3/8 inch, as every diameter requires its individual scale to be determined in great measure by experiment in order to produce something like a mean proportion between the dissimilar conditions, which will be separately explained in various points of view.

The reasons for the uncertainty of measure in the various fixing screws required in the constructive arts are sufficiently manifest; as first, the force or strain to which a screw is exposed, either in the act of fixing or in the office it has afterward to perform, can rarely be told by calculation; and secondly, a knowledge of the strain the screw itself will safely endure without breaking in two, or without drawing out of the nut, is equally difficult of attainment; nor thirdly, can the deduction for friction be truly made from that force the screw should otherwise possess from its angle or pitch when viewed as a mechanical power, or as a continuous circular wedge.

The force required in the fixing of screws takes a very wide range, and is faintly indicative of the strain exerted on each. The watchmaker, in fixing his binding screws, employs with great delicacy a screw-driver the handle of which is smaller than an ordinary drawing pencil; while for screws, say of five inches diameter, a lever of six or seven feet long must be employed by the engineer, with the united exertions of as many men. But in neither case do we arrive at any available conclusion, as to the precise force exerted upon, or by each screw; nor of the greatest strain that each will safely endure.

The absolute measures of the strength of any individual screw being therefore nearly or quite unattainable, all that can be done to assist the judgment, is to explain the relative or comparative measures of strength in different screws, as determined by the three conditions which occur in every screw; whether it be right or left-handed, of single or of multiplex thread, or of any section whatever; and which three conditions follow different laws, and conjointly, yet oppositely determine the fitness of the screw for its particular purpose, and therefore tend to perplex the choice.

The three relative or comparative measures of strength in different screws are: first, the mechanical power of the thread, which is derived from its pitch; secondly, the cohesive strength of the holt, which is derived from its transverse section; thirdly, the cohesive strength of the hold, which is derived from the interplacement of the threads of the screw and nut.

These conditions will be first considered, principally as regards ordinary binding screws, and screw bolts and nuts, of angular threads, and which indeed constitute by far the largest number of all the screws employed; screws of angular and square threads will be then compared.

The comparative sections, Figs. 514 to 517, represent screws of the same diameters, and in all of which the depth of the thread is equal to the width of the groove; Figs. 515 and 517 show the ordi-dinary proportions of 3/4 inch angular and square thread screws; 514 and 516 are respectively as fine and as coarse again as 515.

Various measures of the screws which require little further explanation are subjoined in a tabular form; and the relative degrees of strength possessed by each screw under three different points of view, are added.

Square thread screws, have about twice the pitch of angular threads of similar diameters, and Fig. 517 estimated in the same manner as the angular, will stand by comparison as follows. The square thread, Fig. 517, will be found to be equal in power to Fig. 516, the pitch being alike in each. In strength of bolt to be equal to Fig. 515, their transverse areas being alike. And in strength of hold, to possess the half of that of Fig. 515, because the square thread will from necessity break through the bottom of the threads, or an interrupted line exactly like the dotted line in Fig. 516, that denotes just half the area or extent of base, of the thread of Fig. 515; which latter covers the entire surface of the contained cylinder, and not the half only.

* The angles of the threads of screws are calculated trigonometrically, the circumference of the bolt being considered as the base of aright-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.