It is impossible to deduce a precise rule for the threads of screws from mechanical principles or from any number of experiments. On the other hand, the nature of the case is such that mere approximation would be unimportant, absolute identity of thread for a given diameter being indispensable. There are three essential characters belonging to the screw thread, namely, pitch, depth and form. Each of these may be indefinitely modified independently of the others, and any change will more or less affect the several conditions of power, strength and durability. The selection of the thread is also affected by the mutual relation subsisting between the three constituent characters of pitch, depth and form. Each of these may be separately modified; but practically no one character can be determined irrespective of the others. We find instead of that uniformity which is so desirable, a diversity so great as almost to discourage any hope of its removal. The only mode in which this could be attempted with any probability of success would be by a sort of compromise, all parties consenting to adopt a medium for the sake of common advantage. The average pitch and depth of the various threads used by the leading engineers would thus become the common standard, which would not only have the advantage of conciliating general concurrence, but would, in all probability, be nearer the true standard for practical purposes than any other. An extensive collection was made of screw bolts from the principal workshops throughout England, and the average thread was carefully observed for different diameters. (Then follows the well-known table showing the number of threads per inch.) It will be remembered that the threads, of which the preceding table shows the average, are used in cast iron as well as wrought; and this circumstance has had its effect in rendering them coarser than they would have been if restricted to wrought-iron. The variation in depth among the different specimens was found to be greater proportionately than in pitch. The angle made by the sides of the thread will afford a convenient expression for the depth. The mean of the variations of this angle in 1-in. screws was found to be about 55 deg., and this was also pretty nearly the mean of the angle in screws of different diameters. As it is for various reasons desirable that the angle should be constant, more especially with reference to general uniformity of system, the angle of 55 deg. has been adopted throughout the entire scale. A constant proportion is thus established between the depth and the pitch of the thread.