reason for bisecting the angle between the vertical and the angle of repose of the material, when he undertakes to determine the thickness of key, is not obvious.  This assumption is shown to be absurd when carried to either limit, for when the angle of repose equals zero, as is the case with water, this, method would give a definite thickness of key, while there can be absolutely no arch action possible in such a case; and, when the angle of repose is 90 deg., as may be assumed in the case of rock, this method would give an infinite thickness of key, which is again seen to be absurd.  It would seem as if altogether too many unknowable conditions had been assumed.  In any case, no arch action can be brought into play until a certain amount of settlement has taken place so as to bring the particles into closer contact, and in such a way that the internal stresses are practically those only of compression, and the shearing stresses are within the limits possible for the material in question.

The author has repeatedly made assumptions which are not borne out by the application of his mathematical formulas to actual extreme conditions.  This method of application to limiting conditions is concededly sometimes faulty; but the writer believes that no earth pressure theory, or one concerning arch action, can be considered as satisfactory which does not apply equally well to hydraulic pressure problems when the proper assumptions are made as to the factors for friction, cohesion, etc.  For example, when the angle of repose is considered as zero, in the author’s first formula for W{1}_, the value becomes 1/2 W{1}_, whereas it should depend solely on the depth, which does not enter the formula, and not at all on the width of opening, l, which is thus included.

The author has given no experiments to prove his statement that “the arch thrust is greater in dryer sand,” and the accuracy of the statement is questioned.  Again, no reason is apparent for assuming the direction of the “rakers” in Fig. 3 as that of the angle of repose.  The writer cannot see why that particular angle is repeatedly used, when almost any other would give results of a similar kind.  The author has made no experiments which show any connection between the angle of repose, as he interprets it, and the lines of arch action which he assumes to exist.

With regard to the illustration of the condition which is thought to exist when the “material is composed of large bowling balls,” supposedly all of the same size, the writer believes the conclusion to be erroneous, and that this can be readily seen by inspection of a diagram in which such balls are represented as forming a pile similar to the well-known “pile of shells” of the algebras, in the diagram of which a pile of three shells, resting on the base, has been omitted.  It is then seen that unless the pressures at an angle of 60 deg. with the horizontal are sufficient to produce frictional resistance of a very large amount, the balls will roll and instantly break the arch action suggested by the author.  Consequently, an almost infinitesimal settlement of the “centering” may cause the complete destruction of an arch of earth.