The sides of solid bodies, whatever be the degree of hardness, and however fine the texture, possess surfaces formed of a succession of projections and depressions.  When two bodies are in contact, these projections and indentations fit into one another, and the adherence that results is proportional to the degree of roughness of the surfaces.  If, by a more or less energetic mechanical action, we move one of the bodies with respect to the other, we shall produce, according as the action overcomes cohesion, more or less disintegration of the bodies.  The resulting wear in each of them will evidently be inversely proportional to its hardness and the nature of its surface; and it will vary, besides, with the pressure exerted between the surfaces and the velocity of the mechanical action.  We may say, then, that the wear resulting from rubbing two bodies against each other is a function of their degree of hardness, of the extent and state of their surface, of the pressure, of the velocity, and of the time.

[Illustration:  FIGS. 1, 2 and 3.—­APPARATUS FOR SAWING STONE.]

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, 71/2 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,