Regarding his criticism of the lack of arching action in balls or marbles, he seems to reason that the movement of the marbles would destroy the arch action.  It is very difficult for the writer to conceive how it would be possible for balls or marbles to move when confined as they would be confined if the earth were composed of them instead of its present ingredients, and under the same conditions otherwise.  Mr. Goodrich can demonstrate the correctness of the writer’s theories, however, if he will repeat the writer’s Experiment No. 3, with marbles, with buckshot, and with dry sand.  He is also advised to make the experiment with sand and water, described by the writer, and is assured that, if he will see that the washers are absolutely tight before putting the water into the box, he can do this without bringing about the collapse of the arch; the only essential condition is that the bottom shall be keyed up tightly, so as not to allow the escape of any sand.  He is also referred to the two photographs, Plate XXIV, illustrating the writer’s first experiment, showing how increases in the loading resulted in compacting the material of the arch and in the consequent lowering of the false bottom.  As long as the exposed sand above this false bottom had cohesion enough to prevent the collapse of the “centering,” this arch could have been loaded with safety up to the limits of the compressive strength of the sand.

To quote again from Mr. Goodrich: 

“Furthermore, the author’s 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.”

Mr. Goodrich assumes that water or liquid has an angle of repose equal to zero, which is true, but the writer’s assumptions applied only to solid material, and the liquid gives an essentially different condition of pressure, as shown by a careful reading of the paper.  In solid rock Mr. Goodrich assumes an angle of repose equal to 90 deg., for which there is no authority; that is, solid rock has no known angle of repose.  In order to carry these assumptions to a definite conclusion, we must assume for that material with an angle of repose of 90 deg. some solid material which has weight but no thrust, such as blocks of ice piled vertically.  In this case Mr. Goodrich can readily see that there will be no arching action over the structure, and that the required thickness of key would be infinite.  As to the other case, it is somewhat difficult to conceive of a solid with an angle of