Letters used to give a description of a drawing, or for the purpose of reference to a written explanation, may be put in very expeditiously by means of stencil plates. These are thin plates of metal having the letters very neatly cut out from them; by laying them on the paper, and brushing the ink over them with a hard brush, it is painted on the paper through the openings, forming a very elegant typography.

CHAPTER II.

INSTRUMENTS FOR DRAWING STRAIGHT LINES.

A STRAIGHT-EDGE.

ALL instruments used for drawing straight lines must be provided with straight edges, and long flat rulers, intended solely for this purpose, are termed straight-edges. They are made of plain mahogany, pear wood, mahogany edged with ebony, or of the very best of steel. It is important in the first place to test the accuracy of such edges. This may be done by placing two such edges in contact and sliding them along each other, while held up between the eye and the light if the edges fit close in some parts, so as to exclude the light, but admit it to pass between them at other parts, the edges are not true: if, however, the edges appear, as far as the test has now proceeded, to be true, still this may arise from a curvature in one edge fitting into an opposite curvature in the other; the final step then is to take a third edge, and try it in the same manner with each of the other two, and if in each case the contact be close throughout the whole extent of the edges, then they are all three good.*

"To draw a straight line between two points upon a plane, we lay a rule so that the straight edge thereof may just pass by the two points; then moving a fine-pointed needle, or drawing-pen, along this edge, we draw a line from one point to the other, which, for common purposes, is sufficiently exact; but, where great accuracy is required, it will be found extremely difficult to lay the rule equally with respect to both the points, so as not to be nearer to one point than the other. It is difficult also so to carry the needle, or pen, that it shall *Euclid bk. i. axiom 10. Peacock's Algebra, let edition, art. 532. p. 429.

incline neither towards the rule nor from it; and third it, is very difficult to find a rule that shall be perfec straight."

A right line should never be obtained by the prolongati of a very short one, unless some point in that prolongation first found by some other means, especially in any essenti part of a problem.

All lines, perpendicular or parallel to another, should 1 drawn long enough at first.

Whenever a line is required to be drawn to a point, order to insure the coincidence of them, it is better to com mence the line from the point; and if the line is to pas through two points, before drawing it the pencil should b moved along the rule, so as to ascertain whether the lin will, when drawn, pass through them both. If severa radii to a circle are required to pass through any number o points respectively, the lines should be begun from the centr of the circle; any error being more obvious when several lines meet in a point.

"If the two points be very far distant, it is almost impossible to draw the line with accuracy and exactness; a circular line may be described more easily, and more exactly, than a straight or any other line, though even then many difficulties occur, when the circle is required to be of a large radius.

"And let no one consider these reflections as the effect of too scrupulous exactness, or as an unnecessary aim at precision; for, as the foundation of all our knowledge in geography, navigation, and astronomy, is built on observations, and all observations are made with instruments, it follows that the truth of the observations, and the accuracy of the deductions therefrom, will principally depend on the exactness with which the instruments are made and divided, and that those sciences will advance in proportion as these are less difficult in their use, and more perfect in the performance of their respective operations."

BOW LINE.

This is merely a slip of wood which has a small piece of hard wood fastened upon one side of it at each end, across which a fine wire is drawn; a plain key at the back of the

* Geometrical and Graphical Essays, by George Adams, jun., edited by William Jores.

lath, similar to the key of a violin, will tighten the wire to any degree. It is used when a line considerably longer than the straight-edge is required. To produce a long line with it, marks must be made exactly under the line at distances apart that a straight edge will reach; the bow line is then removed, and the straight edge is used to produce the line.

PARALLEL RULES.

Lines are drawn parallel to each other with the greatest facility and accuracy, either by means of a triangle and straight-edge, or by the T-square; but rolling parallel rules are also much used by professional draughtsmen. They will produce parallel lines in any direction; they move freely and admit of rapid use. The accuracy of the work can also be readily tested by running the rule back to the original line, and again by turning the rule round end for end and repeating the operation.

THE T-SQUARE.

This instrument consists of a blade A, which forms the straight-edge, and the stock B, which guides its motion and has its guiding edge set accurately at right angles to the straight edge of the blade. The following are the two most useful forms of this instrument.

d d

In Fig. (1) the stock is on one side flush with the blade, and on the other projects beyond it, forming a rabbet which passes over the edge of the drawing board, and being gently pressed against it, guides the straight-edge, and enables us to draw lines c, c, d, d, throughout the whole extent of the paper, at right angles, to the edges of the drawing board, and consequently parallel and perpendicular to each other.

Fig. 1.

In the absence of a good drawing board, this T-square may be turned over and worked against a straight-edge clamped to a drawing board or a table.

In Fig. (2) the square is merely a blade screwed upon a stock without being either sunk or mortised into it. This form can be used only with a good drawing board; but it

allows the set square to pass over the head, so as to be us for drawing lines close up to the edge of the drawing boar The instrument makers also supply movable head squares

Fig. 2

form bevels for drawing oblique parallel lines. One of these has a graduated arm attached to the blade, for setting the stock at any desired angle with it.

THE TRIANGLE OR SET SQUARE.

For drawing parallel lines of short lengths, and in any directions the best instrument is a triangle worked against a straight edge. They are made with angles of various sizes, but the most useful are those with angles of 45° and 30°,

and the triangle of the Marquois's scales. The angle of 30° enables us at once to draw all the principal lines in an isometrical drawing.

THE CENTROLINEAD.

In the perspective representation of objects, all parallel lines in the object represented, which are not at the same time parallel to the plane of the picture, upon which they are to be represented, must be so drawn as to meet in a point, which is denominated the vanishing point. This point is generally so distant as to require a very long straight-edge and drawing board to produce the lines, and often to render even this mode impracticable, and necessitate a troublesome geometrical construction for each line to be drawn. A convenient instrument for drawing lines which shall all converge to the same point, no matter how distant, is, therefore, a very great desideratum, and in the centrolinead we have an instru

ment of very simple construction, which perfectly accomplishes this object. It consists of a rule A, with a straight edge, to which a circular head в is so fitted that the prolongation of the straight edge would pass exactly through its centre. To this head two arms, c c, of equal length are

B

A

jointed so as to have their working edges, which are the edges farthest from the rule, also each in line with the centre of the head. These arms can be moved into any desired position, and then securely clamped. They work against two studs, s s, which are to be fixed to the drawing board.

Now if AB and CD be two lines at right angles to each other, intersecting in E, and if the instrument be set so that its straight edge BF may coincide with AB, while the arms lie

B ?