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# APPENDIX

NOTE 1. — Enlarging a sketch on the same proportions.

To Chapter 1, "square up." A small sketch (Fig. 383) can more easily be re-drawn on a larger canvas (Fig. 384) if both of them are divided into sections of equal proportions. These sections can either be in divisions of half with further subdivisions of quarters, etc., or the guiding lines can be drawn through prominent features of the sketch. Either method, or others that will present themselves, will answer, provided that the canvases are of similar proportions. Cotton threads stretched across the face of the sketch and attached to its sides by drawing-pins will save it from the disfigurement of drawn lines. Small working sketches can be drawn on " sectional paper " (paper ruled with faint blue squares used by mechanical draughtsmen), and the squares then repeated to scale on the canvas selected.

NOTE 2. — How to divide a line into a number of given proportions.

(A) To mark off on a line of indefinite length a certain number of divisions of a given length. The first division will be marked off and repeated as often as necessary by compasses, or by a piece of folded paper with that length marked on its folded edge.

(B) If, however, the length of the line is fixed and we have to divide it into a stated number of divisions we shall not know beforehand the length of those divisions (as in A).

Suppose the line 1-2 (Fig. 385) has to be divided into five divisions. From one end (Fig. 386) draw another line at a convenient angle and indefinitely long 2-3. On it mark off five equal divisions (of any length). Join the last division with end of the given line (1). From each division draw lines parallel to 5-1. These will eut the given line 1-2 into five divisions of equal length. Unequal divisions could in similar fashion be marked off on the measuring line 2-3, and would be repeated in the same proportion on the given line (Fig. 387).

To subdivide a rectangular form. — The base line of a rectangular form (Fig. 388) can be divided into any number of even figures (2, 4, B, etc.) by using diagonals to find the half of the whole form, and successively the half of each division.

NOTE 3. — How to transfer in the same proportion the divisions of a line on to another of greater or lesser length.

Problem (Fig. 389). — The short line 3-4 is to be divided in the same proportions as the long line 1-2.

Practice (Fig. 390). — Draw 1-2 parallel to 3-4. Join the ends 1-3 and 2-4, continue these connections till they meet (at A). Join each division with A, and then the line 3-4 will be divided proportionally to the line 1-2.

The proportions of a short line can be transferred to a larger line in the same way. Call 3-4 the short divided line, and 1-2 the long line to be divided. Join their ends and continue the connections till they meet (at A). Join A with each division on line 3-4 and continue the joining lines till they cut the line 1-2 into similar proportions.

NOTE 4. — How to estimate the measurements of a canvas that is to be proportionately larger than another.

We have often to transfer a sketch on to a larger canvas and wish it to bear the same proportions.

Practice (Fig. 391). — Continue the side of the small canvas A until it is the required length. (say B–C). Take a diagonal from B of indefinite length. From C draw line at right angles to B–C and continue it till it meets the diagonal. The line thus obtained C–D will be the width of the larger canvas. This workman's practice arises out of the method of drawing concentric squares. If absolute exactness is necessary " proportion " in arithmetic might be employed instead.

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