In the above formula Z = a coefficient which depends on the condition of the surface against which the hydraulic pressure or resistance works, in this case a sphere; g = the acceleration of gravity equivalent to 9.81 meter; and S = the specific gravity of the particle. This expression signifies that in a given case, the velocity of the current in the apparatus is just sufficient to counteract the tendency of a given particle to sink. All particles of a smaller diameter, in such a case, will be carried on by the current, while all of a greater diameter would separate by sedimentation. These theoretical conditions are not met with in practice where silt particles of all shapes and degrees of aggregation abound. These particles, whatever their shape, may be said to have the same hydraulic value when carried by the same current. It is necessary, therefore, to secure some uniform standard of expression to assume a normal form of particle and a normal specific gravity. For the form, a sphere is evidently the normal which must be considered and for specific gravity that of quartz is taken; _viz._, 2.65. The mean coefficient for Z may also be placed at 0.55, although slightly different values are ascribed to it. Substituting these values in the formula, it is reduced to the expression; d = v² × 0.0000255 millimeters. It can, therefore, be said that by this or that velocity of the current, silt particles will be removed of this or that diameter, it being understood that all particles of equal hydraulic value to spherules of quartz of the given diameter are included in each class. In order to have the theoretical formula agree with the results of analysis it is necessary to modify it empirically to read d = v^{⁷⁄₁₁} × 0.0314 millimeters. This formula is found to agree well with the results obtained for all velocities between 0.1 millimeter and twelve millimeters per second, the ordinary limits of silt separation. _The Apparatus._—The conic-cylindrical elutriating vessel A, B, C, D, E, F, G, Fig. 31, is of glass. The part B, C, is cylindrical, ten centimeters in length and as nearly as possible five centimeters in diameter. The conical part C, D, is fifty centimeters in length. Its inner diameter at D must not be greater than five centimeters nor smaller than four centimeters. The bend, D, E, F, should have the same diameter; _viz._, four to five centimeters. The part A, B, C, D, and D, E, F, G, may be made of separate parts and joined by a rubber tube.