Chap. XI.

MECHANICS.

927

Divers forms of the wedge are given to workmen’s tools, and great loss of labour is oc-casioned by those most constantly in use, which have not always the prismatic fohn : whenthey are pyramidal, having three or four faces, the equilibrium between the power andthe resistance is analogous to those of the prism; the first is equal and opposed to theresultant of three or four forces, which depend on the length of each face, and the sideswhich form the head.

The wedge is also a truncated prism, and often nothing more than a cone with acylindrical head ; but the condition of its equilibrium is the same as that of the isosceleswedge, viz. the power is to the resistance, as the diameter of the head, is to the length ofthe side of the cone.

Chisels, knives, nails, files, &c. are half flat prisms, the surfaces of which are striated orcut into furrows at a certain angle, and crossed at another, so as to form smallpyramids or wedges, the points of which carry off the particles to be filed. Saws arean assemblage of wedges, the lower face of which is slightly inclined towards thecutting edges and in the thickness of the blade; one tooth also inclines differently to theother, viz. one to the right, the other to the left, that the saw may clear itself, and workmore freely. All wedges act on their cutting side, or on their pointed extremities, andthere is a proper angle for every tool according to its use, which practice can alone de-termine. The chief matter for the workman to consider, when he is setting a cutting instru-ment to act upon any surface, should be that he endeavour to make its end form the leastpossible angle with the face to be cut; it should, therefore, be kept nearly parallel with thesurface it is employed upon, and should it be required to he made very sharp, the acute-ness given to it must be obtained by taking away from the front part of the cuttinginstrument against which the shavings slide. The carpenter’s axe has the bevelled surfaceoutwards, and the flat side is that which is placed against the wood to he cut, so that theangle between the face of the tool next the wood and its surface forms the least angle possible.

The Screw depends for its action on the same principles as those of the inclined plane,and to have an idea of the form of the square thread screw, suppose a cylinder BCE D

Fig. 1244.

Fig. 1243.

Fig. 1244.

Fig. 1245.

drawn with the axis at A vertical. If there be attached to the surface of this cylinderor newel a rectangle, as abed, and which represents the profile of the thread of the screw,when the cylinder turns on its. axis, this rect-angle will form an annulus or ring, as long asit remains in a horizontal position : but sup-posing when it turns, the rectangle is madeto descend, and for each quarter of a revolutionit descends a fourth of the vertical height, asquare thread will be projected on the newel,called a helix ; when this has passed entirelyround its height, it is termed the step of thescrew, and is measured by the interval a a', be-tween the upper surfaces of two consecutivethreads; the inclination or stiffness of the helixdiminishes towards the external edge of thethread. When this has been formed, anotherbody, cut in an opposite manner, and called thenut is applied to it; these together have a doublemovement of rotation, and act as on an in-clined plane.

Fig. 1246.

v -- d

The screw is nothing more than a cylinder, b, having a rectangular or triangular prism,as ad, wrapped or coiled round it, in such a manner that one of the faces of the prism is