We shall close the present article by the description of a beautiful invention, by Mr. John Anderson, a member of the London Mechanics' Institution, to whom was awarded, in 1830, the annual prize, "for the best machine, or im provement of a machine ;" and of whom Dr. Birkbeck (in • public address on the distribution of the prizes,) elegantly and justly observed, that be had "ele vated himself in society, by becoming its benefactor;" that, " though now a work ing millwright, Mr. Anderson had evinced a genius that pointed him out for a distinguished engineer—probably a Smeaton or a Watt; neither of whom, at his age, possessed so much knowledge of algebra, or of geometry, and neither of them bad am given such decided proofs of genius." After the Doctor had explained the construction and use of the instrument, which was an improved slide-rest for lathes, Mr. Anderson gave a practical illustration of its utility by turning a convex and a concave roller, which were completed with great expedition, and fitted each other with mathematical exactness. In this improved slide-rest the object proposed, was to turn the surfaces of the bodies circular in the longitudinal direction : the curved surface in such direction being either convex or concave to the axis of rotation. And i it was more evecially intended to apply when the degree of curvature required was very sma% or, which is the same thing, when the radius of the required curve was very great, as, by the present mode of turning, the greatest difficulty is found in such cases. The improved rest is also found to be equally appli cable to the turning of bodies in the form of lenses, whether convex or concave ; and in each of these cases the facility of operation, and accuracy of perform ance, is equal to that of the common slide-rest in turning straight or fiat surfaces.
The principle of the improvement or circle-turning appendage depends upon two geometrical propositions : 1st, that all angles in the same segment of a circle are equal ; and 2d, that a straight line of any length, being made to move always parallel to itself with one end touching a circle, the other end will describe a circle equal in every respect to the first.
Now in the improved slide-rest, shown in the annexed figure, the triangle de f is made to slide against the fixed pins at d and f; whence the vertex c will describe a portion of a circle greater or less in diameter, according as the angle def is made more or less obtuse ; and further, the centre of the circle thus described, will be on the one side or the other of a straight line joining d according as the vertex c of the triangle is on the opposite side.
The sliding triangle del consists of three pieces ; viz. of two sides d c, and c f, with a slit or opening in each for the pins d and f to slide in ; and they are movable round a centre at c, by which means they can be made to form any angle with eaoh other. The third piece, or base of the triangle, is the
connecting-bar a b, by means of which the two sides are held fast in any required position.
The sliding-plate e e is similar to that of a common slide-rest, and it is moved backward or forward by a screw and handle b, in the same manner. Upon this plate, and at right angles to the direction in which it moves, a box a is made to slide; within this box there is another sliding piece 1, carrying the tool or cutter S. The interior sliding-piece 1 is made to move within the box by means of a screw turned by the a; and by this means the cutter I can be made to advance or recede, as in a common slide•rest. The sliding-box a is connected with, and movable round the centre c, at the vertex of the sliding triangle ; and hence if the box * move in any direction, the vertex c of the triangle must move along with it in the same direction.
Now it were required to turn a body of the form Pin the figure. Set the sides d c and c f to the proper angle ; then screw the three nuts a a b tight, which will retain them in that position. By means of the screw and handle a, make the sliding piece and cutter t advance as near the body p as is necessary to turn it of the required diameter. Then by the screw and handle b move along the sliding-plate e e, which plate will carry along with it the slidin piece, carrying the cutter I, the sliding-box *, and the sliding triangle d But it will be readily perceived, that as the triangle d e f moves along, tthhqq vertex c will describe a portion of a circle ; and as the end of the sliding-box is connected with the centre a, the box will move along always parallel to itse14 with that end touching the circle described by the vertex of the triangle. But the box s, and the sliding-piece carrying the cutter, may be considered as forming only one piece, as they always retain the same relative position to each other, except when altered by turning the screw and handle a. And hence the joint of the cutter t, and centre c, may be considered as the two ends of a straight line, which always moves parallel to itself; and as the one end e always touches the circle described by the vertex of the sliding triangle, the other end will (according to the geometrical proposition,) describe the portion of a circle equal to it in every respect; and will thus, by the revolution of the body p, turn It of the form required.
The separate 1Rg. re, represents a concave roller, produced by shifting the vertex of the triangle, or centre c, to the opposite side of the connecting bar a &