4 Set off such other points upon the copy, by means of the compasses, as may be desirable, and draw the curved lines upon tracing paper placed over the drawing. 5. Fill in the lines indicated by the points set off by the compasses, and transfer the curved lines from the tracing paper to the copy, by rubbing the back of the tracing paper with powdered black lead, placing it in its correct situation upon the copy, and passing a blunt tracing point* over the lines drawn upon it.

Second Method.-A sheet of tracing paper having the under side rubbed over with powdered black lead may be placed upon the paper intended for the copy. The original being then placed over this, the tracing point may be carefully and steadily passed over all the lines of the drawing with a pressure proportioned to the thickness of the paper; and the paper beneath will receive corresponding marks, forming an exact copy, which is afterwards to be inked in.

Third Method. The drawing is placed upon a large sheet of plate glass called a copying glass, and the paper to receive the copy placed over the drawing. The glass is then fixed in such a position as to have a strong light fall upon it from behind, and shine through it. By this means the original drawing becomes visible through the paper placed over it, and a copy can be made with precision and ease, without any risk of soiling or injuring the original.

To copy with nicety upon a reduced or enlarged Scale.For this purpose we may have recourse to the method of squares, by which, with the aid of the proportional compasses, the most minute detail may be copied with great accuracy This may, perhaps, be best shown by an example.

Let figure 1 in the following engraving represent a plan of an estate, which it is required to copy upon a reduced scale of one half. The copy will therefore be half the length and half the breadth, and, consequently, will occupy but one-fourth of the space of the original. Our subject is a map of an estate, but the process would be precisely the same if it were an architectural, mechanical, or any other drawing.

1. Draw the lines FI and F G at right angles to each other. 2. From the point F towards I and G, set off any number of equal parts, as F a, a b, b c, &c., on the line FI, and F i, i k, kl, &c., on the line F G. 3. From the points on the line FI draw lines parallel to the other line FG, as a a, b b, c c, &c.,

*The eye end of the pricking needle, or the fine point of a porcupine's quill, may be used for this purpose.

and from the points on F G draw lines parallel to F I, as i i kk, ll, &c., which being sufficiently extended towards G and I, the whole of the original drawing will be covered with a reticule of small but equally-sized squares.

This done, draw upon the paper intended for the copy a similar set of squares, but having each side only one-half the length of the former, as is represented in figure 2. It will now be evident that, if the lines of the plan A B, B C, C D, &c., figure 1, be drawn in the corresponding squares of figure 2, a correct copy of the original will be produced, and of half the original scale. Commencing then at A, observe where, in the original, the angle a falls, which is towards the bottom of the square marked on the top d e. In the corresponding square, therefore, of the copy, and in the same proportion towards the left-hand side of it, which should be determined by the use of the proportional compasses, described at page 4, place the same point in the copy. From thence, finding by the proportional compasses the point on the bottom line of that square, where the curved line AF crosses, which is about twofifths from the left-hand corner towards the right, cross it similarly in the copy. Again, as it crosses the right-hand bottom corner of the second square below de, describe it so in the copy; and by means of the proportional compasses find the points where it crosses the lines fƒ and g g, above the line ll, by taking the distances of such crossings from the nearest corner of a square in the original, between the large points of the proportional compasses, and with the small points at their opposite end, setting off the required crossing on the correspond ing lines on the copy. Lastly, determine the place of the

point B, in the third square below g h on the top line, and a line drawn from A in the copy, through these several points to B, will be a correct reduced copy of the original line. Proceed in like manner with every other line on the plan, and its various details, and you will have the plot or drawing, laid down to a small scale, yet bearing all the proportions in itself exactly as the original.

It may appear almost superfluous to remark, that the process of enlarging drawings by means of squares is a similar operation to the above, except that the points are to be determined in the smaller squares of the original, and transferred to the larger squares of the copy. The process of enlarging, under any circumstances, does not, however, admit of the same accuracy as that of reducing.

Having now completed the description of those instruments, applicable to the purposes of geometrical drawing, to the consideration of which we propose for the present to limit our selves, in accordance with the plan of our little work, we now propose to add thereto a description of Coggeshall's Sliding Rule, and then to conclude this part of our subject with some practical hints*, which we think may prove acceptable to the commencing student.

COGGESHALL'S SLIDING RULE. (Plate II. Fig. 4.)

Coggeshall's, or the Carpenter's Sliding Rule, is the instrument most commonly used for taking the dimensions and finding the contents of timber. It consists of a rule one foot long, having on its face a groove throughout its entire length, in which a second rule of the same length slides smoothly. On the face of the rule are four logarithmic lines marked at one end A, B, C, and D. The three lines A, B, C, are called double lines, because the figures from 1 to 10 are contained twice in the length of the rule, and are, in fact, repetitions of the logarithmic line of numbers already described (p. 25). The fourth line, D, is a single line numbered from 4 to 40, and is called the Girt Line, because the girt dimensions are estimated upon it in computing the contents of trees and timber. The lengths upon this line denote the logarithms of the squares of the numbers, from 4 to 40, placed against the several divisions; and enable us, as will be seen, to obtain approximately the contents of a solid by a single operation.

*Extracted from a treatise on drawing instruments, by F. W. Simms, Civil Engineer and Surveyor.