According as these factors are varied in a sense favorable or unfavorable to their proper action, we obtain variations in the final erosion. Thus, in rubbing together two bodies of different hardness and nature of surface, we obtain a wear inversely proportional to the hardness and state of polish of their surfaces. Through the interposition of a pulverized hard body we can still further accelerate such wear, as a consequence of the rapid renewal of the disintegrating element. The gradual wear effected over the entire surface of a body brings about a polish, while that effected along a line or at some one point determines a cleavage or an aperture. The process usually employed in quarries or stone-yards for sawing consists in slowly moving a stone-saw backward and forward, either by hand or machinery, and with scarcely any pressure. Mr. P. Gray has, however, devised a new process, which is based upon the theoretical considerations given above. His _helicoidal saw_ is, in reality, an endless cable formed by twisting together three steel wires in such a way as to give the spirals quite an elongated pitch. The apparatus in its form for cutting blocks of stone into large slabs (Figs. 1, 2, and 3) consists of two frames, A A, five feet apart, each formed of two iron columns, 7½ feet in height and one foot apart, fixed to cast iron bases resting upon masonry. At the upper part, a frame, B B, formed of double T-irons cross-braced here and there, supports a transmission composed of gearwheels, R R, and a pitch-chain, G G. Along the columns of the frame, which serve as guides, move two kinds of pulley-carriers, C C. The pulleys, D D, are channeled, and receive the cable, a a, which serves as a helicoidal saw. The direction of the saw's motion is indicated by the arrow. The carriages, C C, are traversed by screws, V V, which are fixed between the columns. The extremity, v, of the axle of the pulley to the right is threaded, and actuates a helicoidal wheel, E, which transmits motion to the wheel, R, through the intermedium of the vertical shaft, F. This transmission, completed by the wheels, R R, and the pitch-chains, G G, is designed to move the saw vertically, through the simultaneous shifting of the carriages, C C. A tension weight, P, through the intermedium of pulleys, D_{1} D_{1}, permits of keeping the saw taut. A reservoir, H, at the upper part of the frame, B B, contains the water and sand necessary for sawing. The feeding is effected by means of a rubber tube, I, terminating in a flattened rose, J, which is situated over the aperture made by the saw. A small pump, L. over the reservoir takes water from K, and raises it to H. The sand is put in by hand.