repose of zero; aqueous material does not fulfill this condition, as it is either a liquid or a combination of water and solid material.  The best illustration, perhaps, would be to assume a material composed of iron filings, into which had been driven a powerful magnet, so that the iron filings would be drawn horizontally in one direction.  It is easy to conceive, then, that in tunneling through this material there would be no necessity for holding up the roof; the definite thickness of key given, as being at the point of intersection of two 45 deg. angles, would be merely a precautionary measure, and would not be required in practice.

It is thus seen that both these conditions can be fulfilled with practical illustrations; that is, for an angle of repose of 90 deg., that material which has weight and no thrust, and for an angle of repose of zero, that solid material which has thrust but no weight.

Mr. Goodrich says the author has given no experiments to prove his statement that the arch thrust is greater in dryer sand.  If Mr. Goodrich will make the experiment partially described as Experiment No. 3, with absolutely dry sand, and with moist sand, and on a scale large enough to eliminate cohesion, he will probably find enough to convince him that in this assumption the writer is correct.  At the same time, the writer has based his theory in this regard on facts which are not entirely conclusive, and his mind is open as to what future experiments on a large scale may develop.  It is very probable, however, that an analytical and practical examination of the English experiments noted on pages 379 and 380, will be sufficient to develop this fact conclusively.

The writer is forced to conclude that some of the criticisms by Mr. Goodrich result from a not too careful reading of the paper.  For instance, he states: 

     “‘It is conceded’ (line 2, p. 357, for example) when the writer,
     for one, has not even conceded the accuracy of the assumptions.”

A more careful reading would have shown Mr. Goodrich that this concession was one of the writer’s as to certain pressures against or on tunnels, and, if Mr. Goodrich does not concede this, he is even more radical than the writer.

And again: 

     “’Nor can anyone * * * doubt that the top timbers are stressed more
     heavily than those at the bottom’ is emphatically doubted and
     earnestly denied by the writer.”

It is unfortunate that Mr. Goodrich failed to make the complete quotation, which reads: 

     “Nor can anyone, looking at Fig. 5, doubt,” etc.

A glance at Fig. 5 will demonstrate that, under conditions there set forth, the writer is probably correct in his assertion as relating to that particular instance.  Further: