below, the lines of which are obtained by continuing those of the upper figure, as in the drawing. .

Example 25, fig. 26, represents the front elevation of the cover for a gas retort. The centre of the parts b} c, and d is at a on the line de; the centre of the curve joining op at m, on the line nm.

Example 26, fig. 27, represents the 4 transverse vertical section9 of a boiler a ft, and its brick ( setting.' From a with ab describe the circle ab; from a measure to c; draw cd, and from d, de. From d measure to g, from which point a line drawn parallel to c d marks the point /, where the curve fo terminates at the boiler. The point»' is the centre of the curve fo'; transfer this part from/to n, and describe o'f. From a measure to the lines o*, nnt, and draw lines through these parallel to cd; measure from d to r and g. The centre of the curve oh is at s, and that of the curve hr at m.

Example 27, fig. 28, represents an 1 angular-threaded screw.' To copy. ^ it proceed as follows: Measure from a to d, and from d to e, 1, 2, 3, &c..

These are the points through which the centre-lines of each thread are drawn. From a measure to /, and draw fg; and from a to b and c, and

distance between them; the line from g is the line of the inside of the screw, the line / the outside line of the threads. The last example shews the method of copying this.

Example 29, fig. 30, represents a ' helix' of wire, ad being centreline, de being half die thickness of the coil, the lines from c, b} intersecting fig. 27.

draw bn. From/on the line bf measure to g, and from b to n; through' d draw ndg, and parallel to this, through e, 1, 2, 3, &c., draw lines. Next, from d measure on each side of dg, equal to half the breadth of each thread, to o and n'. These lines terminate at the perpendicular bn; join the angles as in the drawing.

Example 28, fig. 29, represents a 4 square-threaded screw.' From e measure to a; ab, be, cd, represent the thickness of each thread and the fig. 29.

those drawn parallel to d, giving the centre of the circles forming the termination of coils.

Example 30, fig. 31, represents another form of screw.

Example 31, fig. 32, represents the Archimedean, or endless screw; and another form is given in

Example 32, fig. 33, where ab is the central shaft round ^which the helix or thread ee is coiled, according to a determined pitch. »-4»*»**-

Example 33, fig. 34, shews the method of drawing-in the teeth of wheels. Let cx be the diameter of wheel from centre] to outside of teeth.

The circle, of which part is shewn, and of which cb is the radius, is termed the 1 pitch-circle or line.' It is on this line that the number of teeth are marked off. Having ascertained the diameter of pitch-line, the depth of teeth, and the number of them, divide the pitch-circle into as many equal parts as there are to be teeth in the wheel, and proceed as follows: Let a, by 4, 5, &c., be the divisions on the pitch-circle representing the centres of teeth; ditide the distances between them into two eqtud parts, as at d* From d as 4 centre, with db on both sides of one point d, describe arcs of circles as fb, joining the pitch-circle and the outer circle, giving the termination of the teeth as the circle xl. Proceed in this way till all the arcs are made to jcdn the circle 38, giving the bottom of the teeth by-radial lines to the centre cc as in the diagram. The forms of teeth are various (see treatise on Mechanics in this series). For the method of describing different curves, and of setting out teeth of wheels and pinions, see treatise on Mechanical and Civil Engineering. The method of drawing the side elevations of toothed wheels may be seen in

Example 34, fig. 35. The small dotted circles shew another method of describing the form of teeth. The manner of delineating bevil-wheels

(for the nature and operation of these see treatise on Mechanics in this series, at pp. 51, 52,) may be gathered from the two following figures.

Example 35, fig. 36. Let ab represent the centre-line of the wheel, cd the line of its greatest diameter or ' pitch-line,'/the line giving termination of teeth, cd being the breadth of the teeth The teeth on the part between cv, dm converge to the point b; those between hd, cn to the point a, on the line ahg, efb. It is foreign to the purpose of this work to go into the subject of the teeth of wheels, belonging, as it does, to a strictly technical department; we cordially recommend, however, the pupil anxious to study this interesting and important department, to Buchanan's work on Mills and Mill Gearing, edited by Sir John Rennie, and published by Weale of Holborn; and the Engineers9 and Machinists' Assistant, by Blackie of London and Glasgow. Both of these works, although somewhat high-priced, abound in valuable information. We may possibly, at some future time, publish a cheap work, which may serve as a guide or introduction to the sciences of Civil and Mechanical Engineering, useful to those who may contemplate devoting themselves to either of these branches as a profession« To proceed, however, with our explanation. The method of copying the teeth ofbevil-wheels may be seen in

Example 36, fig. 37, where ab is the centre-line of wheel, eg the pitch-line, eh the line terminating the teeth on the back part of the wheel eg.

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