Resistance of Tubes to Internal Pressure. During the investigation on the comparative resisting powers of tubes to collapse, a question arose as to the relative powers of cylindrical tubes to resist an internal force acting uniformly over their surface. It has already been demonstrated that the resistance of cylindrical vessels to internal pressure varies inversely as the diameters, but what effect the length may have upon the strength has yet to be determined. We have already seen that a cylindrical tube, when subjected to external pressure, loses one-half its strength when the length is doubled, and so on in other cases; hence arose the inquiry, what effect, if any, will an increase of length have upon a tube exposed to internal pressure? To solve this problem, three tubes of precisely the same diameter and thickness of plates, but of different lengths, were prepared and submitted to experiment as seen in Table XI. Considerable discrepancies occur in the experiments on internal pressure, as in each case the tube gave way at the riveted joint. Every precaution was taken, by carefully brazing them, to render them as nearly uniform in strength as possible. The weakness of these joints was, however, very apparent, and the results are in accordance with those arrived at several years previously, when it was found that the strengths of riveted plates were as the numbers 100, for the solid plate; 70, for the double-riveted joint; This constant failure at the joints renders the experiments on internal pressure very unsatisfactory, as they do not exhibit the ultimate strength of the plate, but only the strength of the joint; and as boilers invariably present joints, these facts are probably of some significance when applied to them. On a careful examination of the fractures, that of the tube Ff appeared the most perfect. Ee was not so well soldered, and burst by tearing off the rivet-heads, and Dd was torn partly through the plates and partly through the rivets; the plate of which this tube was composed was, however, exceedingly brittle, and broke like cast-iron. Tube Gg was ruptured in the same way and in the same direction as the others; the rivets were torn through the plates, and the soldering (not very sound) was ripped up for 10 inches along the joint: this tube, as also the others, would have borne a greater pressure had the joints been more perfect and of sounder workmanship. Comparing the tube Cc, 1 foot long, with the tube Ff, 4 feet long, and assuming the joints to be equally perfect in each, it would appear that there is a slight loss of strength when the length is increased; and this again suggests the question, do the rigid ends in short tubes increase the strength of the unsupported portion in proportion to the length of the tube? For example, let us take two tubes of any given diameter, the one 10 feet and the other 20 feet long; it would appear, primâ facie, that a 2 it was much easier to force the long tube into the form of a barrel, as at a, than it would be to produce the same form in the shorter tube, as at b; in an elastic material, such as an indian-rubber tube, the extension would certainly take place at the centre, where the particles possess diminished resistance, arising from their respective distances from the ends or points of support. To ascertain how far this view is correct, two leaden pipes were prepared of 3 inches diameter, and of the lengths of 1 foot 2 inches, and 2 feet 7 inches respectively, and these were submitted to the experimental tests in Table XII., :— The tube Hh ruptured at the thin part of the metal, the water bursting through a narrow slit; Jj ruptured similarly; and on measuring the expanded circumferences at the broadest part, it was found that the metal of the former had elongated 14 inch, and that of the latter 1 inch. These experiments seem to show pretty conclusively, that the length has very slight influence on the resisting powers of tubes of wrought iron to internal pressure. Beyond the limit of one or two feet in length, it appears to affect the strength so slightly, that it may be almost entirely disregarded in practice. GENERALISATION OF THE RESULTS OF THE EXPERI MENTS. In the reduction of the experiments, I have, as on former occasions, been ably assisted by my friend Mr. Tate, whose sound philosophical views and high mathematical attainments are, from his numerous publications, so well known to the public. To that gentleman I am indebted for many services, and among others for an elaborate inquiry into the specific gravity and properties of steam, which I hope will be shortly forthcoming as a new addition to our knowledge, and that more particularly in |