Note Return to text — DISCUSSION.

The pressures given in Columns 5 and 7 are intended to apply to a long section of a tunnel, those in Columns 4 and 6 refer to a short section about the heading. The values for are intended to apply to what Mr. Meem styles “soft normally dry ground,” and it is hoped that he may approve the figures, as they are somewhere near his own. The coefficient, , refers to hard consolidated ground. Here the pressure is 0 at the working faces of the 15-ft. tunnel. Fig. 27 shows the variation in for , , , for some of the larger values of , as obtained by the revised formula given in the foot-note. It will be observed that the above demonstration for finding the limiting value of , is perfectly independent of Janssen’s formula. In it the relation, , is only assumed to be true for this one value of , and need be determined by experiment only for this value. The result is thus general, no matter how varies for other values of . A glance at all the diagrams,[Footnote 31] giving the experimental values of and for various depths, will show that is far from being a constant for varying depths, though the assumption is found to lead to practical results, as obtained from Janssen’s formula. The experiments of Jamieson on 12 by 13½ by 67½-ft. wheat bins, and of Bovey on 12 by 14 by 44 ft. 10-in. bins, both of wood, indicate that the maximum pressure, , is realized, practically, for heights of about four diameters. Pleissner’s experiments on a wooden bin, 11.51 by 8.20 ft., show four and a half diameters, and Luft, for a concrete bin, 23 ft. in diameter, gives, say, three diameters, for the height corresponding to maximum .