scent along the arc A A'. This admits of easy demonstration. The angle BC 1' is half of 2' C D, and consequently, when the point B has arrived at 1', the radius C D, then coinciding with C B, will have passed through an angle equal to 1' C B, and again, at the next point in the revolution, will coincide with C 2'. Therefore the portion B D of the curve will impel the given point through the arc 1' 2', in the same time and with the same velocity, as the part A B will have raised it from A to 1'. By a similar process of reasoning it will be manifest, that the angle 1' CB being just one-third of 3′ C I, the point A will also traverse the space 2' 3' with a uniform motion.

By a glance at the figure it will be seen that this curve is not symmetrical; in other words, that the part A FE is not equal or similar to ADE. This may be accounted for by observing, that the arc b 1', for instance, is equal to 1' B, and consequently the point b (which is determined by the intersection of the circle passing through 1' with the arc described from the centre 15) cannot be situated in the same position in relation to A as the point B, since the radius C A does not pass through 1'; the same remark applies to all the other arcs, d 2', &c. It is not the less certain, however, that the part A F E of the eccentric will cause the given point to descend through the arc A' A in the same uniform manner as it had been elevated by the part A D E.

In the two preceding examples of eccentrics it has been shown, that the point A moves through equal spaces in equal times, both in ascending and descending. In some cases, however, this is by no means desirable ; thus, if the eccentric is destined to give motion to a mass of matter which offers considerable resistance, such a form would give rise to injurious and destructive shocks. In such cases, it is necessary so to regulate the curvature of the eccentric, that the point A shall move at the beginning and end of its stroke with diminished velocity; and that for this purpose, the space A A should be unequally divided, as in the example which comes next under notice.

Fig. 3.-To draw a double and symmetrical eccentric curve, such as to cause the point A to move in a straight line, and with an unequal motion; the velocity of ascent being accelerated in a given ratio from the starting point to the vertex of the curve, and the velocity of descent being retarded in the same ratio.

Upon A A' as a diameter describe a semicircle, and divide it into any number of equal parts; draw from each point of division 1', 2', 3', &c., perpendiculars upon CA'; and through the points of intersection 12, 22, 32, &c., draw circles having for their common centre the point C, which is to

be joined, as before, to all the points of division on the circle (A' 48.) The points of intersection of the concentric circles with the radii C 1, C2, C 3, &c., are points in the curve required.

Fig. 4. To construct a double and symmetrical eccentric, which shall produce a uniform rectilinear motion, with periods of rest at the points nearest to, and farthest from, the axis of rotation.

The lines in the figure above referred to indicate sufficiently plainly, without the aid of further description, the construction of the curve in question, which is simply a modification of the eccentric represented at Fig. 1. In the present example, the eccentric is adapted to allow the movable point A to remain in a state of rest during the first quarter of a revolution B D; then, during the second quarter, to cause it to traverse, with a uniform motion, a given straight line A A', by means of the curve DG; again, during the next quarter E F G, to render it stationary at the elevation of the point A'; and finally, to allow it to subside along the curve BE, with the same uniform motion as it was elevated, to its original position, after having performed the entire revolution.

Fig. 5 represents an edge view of this eccentric, and fig. 6 a vertical

section of it.

Figs. 7, 8, and 9, a Circular Eccentric.-These figures represent a model of a variety of the circular eccentric, which is the contrivance usually adopted in steam-engines for giving motion to the valves regulating the action of the steam upon the piston. The circular eccentric is simply a species of disc or pulley fixed upon the crank-shaft, or other rotating axis of an engine, in such a manner that the centre or axis of the shaft shall be at a given distance from the centre of the pulley. A ring or hoop, either formed entirely of, or lined with brass or gun metal, for the purpose of diminishing friction, is accurately fitted within projecting ledges on the outer circumference of the eccentric, so that the latter may revolve freely within it; this ring is connected by an inflexible rod with a system of levers, by which the valve is moved. It is evident, that as the shaft to which the eccentric is fixed revolves, an alternating rectilinear motion will be impressed upon the rod, its amount being determined by the eccentricity, or distance between the centre of the shaft and that of the exterior circle. The throw of the eccentric is twice the eccentricity CE; or it may be expressed as the diameter of the circle described by the point E. The nature of the alternating motion generated by the circular eccentric is identical with that of the crank, which might in many cases be advantageously substituted for it.

Fig. 8 is the edge view, fig. 9 the section of the eccentric, in this par

ticular example, formed in a single piece, and which can be applied only when the shaft to which it is to be attached is straight and uninterrupted by cranks, &c. The mode of representing the arm in fig. 9, which is a section on the line D F, is not strictly accurate, but is a license frequently practised in similar cases, and which is attended with obvious advantage.

In many machines, the eccentric is used for the raising of a weight a certain height and then letting it fall, as in the case of ore stampers, cloth beetles, trip hammers, and the valve rod of some steam engines. In these cases the eccentric may be considered as merely a single long tooth geer, in which commonly, on account of the uniformity of action, the wiping or rubbing surface is an involute curve, the boss of the eccentric being the generating circle.

In practice, the term eccentric is generally confined to the circular eccentric; all others, with exception of that last described, or wypers, being called cams.

DRAWING OF SCREWS.

The screw is a cylindrical piece of wood or metal, in the surface of which one or more helical grooves are formed. The thread of the screw

is the solid portion left between the grooves; and the pitch of the screw is the distance, measured on a line parallel to the axis of the cylinder, between the two contiguous centres of the same thread.

Projections of a triangular-threaded screw and nut, plate XVIII., fig. 1. -Having drawn the ground line A B, and the centre lines C C' of the figures, from O as a centre, with a radius equal to that of the exterior cylinders, describe the semicircle a 3 6; describe in like manner the semicircle bee with the radius of the interior cylinder. Now draw the perpendiculars a a" and 6 6′′, b b′′ and e c", which will represent the vertical projections of the exterior and interior cylinders. Then divide the semicircle a 3 6 first described into any number of equal parts, say 6, and through each point draw radii, which will divide the interior semicircle similarly. On the line a' a" set off the length of the pitch as many times as may be required; and through the points of division draw straight lines parallel to the ground line A B. Then divide each distance or pitch into twice the number of equal parts that the semicircles have been divided into, and following instructions already laid down (page 100), construct the helix a' 3' 6 both in the screw and nut.

Having obtained the point b' by the intersection of the horizontal line passing through the middle division of a' a with the perpendicular 6 b", de