Figure 15.—The rolling parallel rule.
The drawing pen is used in making ink lines by the edge of a ruler ; the cavity between the plates receives the ink, which is supplied from a common quill-pen. or a camel-hair pencil ; or, what is perhaps better than either, by wetting the inside of the nibs, and taking up the ink or colour with the point of the pen, by which means the ink will rise with out difficulty, and free from sediment. In performing this operation, the plane of the inside of the plate should he parallel to the edge of the rule, and in a plane perpendicular to the surface of the paper.
The use of the dividers is to take the extent of any line or surface from one point to another, in order to transfer it to some other line ; to repeat any extension upon a straight line in an equimultiple ; tet livide a straight line, or the circum ference of a circle, or any arc thereof, into equal parts ; to proportion the parts of a drawing by a scale, in any desired ratio to each other ; to construct a drawing similar to one already drawn, either greater or less, by an appropriate scale to each ; to construct an angle of any number of degrees ; to measure the quantity of any given angle in degrees.
The drawing compasses are used either in describing tem porary arcs, or whole circumferences, with black-lead pencil, or permanently in ink. If the diagram or drawing consist of many circles, and is to be finished in ink, the circumfer ences must be first drawn with a pencil, and when after wards inked must be cleaned with Indian rubber.
The bow compasses are used in the description of small circles, in which the legs of the larger kind would be apt to vibrate, and thereby make the arc or circumference ragged.
The triangular compasses are used in transferring a given angle from one place to another ; or in taking the three points of a triangle at once, and transferring them to any required place, where the figure may be completed by joining the points. These compasses, though exceedingly useful, are but little known : they are serviceable in copying all kinds of drawings, as from two fixed points the position of a third may always be ascertained.
The proportional compasses are used in making one draw ing similar to another, without the use of scales or lines ; in graduating the radii of spirals ; in dividing circles into any number of parts between two limits, generally from six to twenty ; in dividing a straight line into any of equal parts, from two to a certain other limit, which is generally about ten.
Some general uses of the proportional compasses may he obtained from the following examples, which, though made to particular numbers in the cases of the planes and solids, will show the application of the principle to any other num ber contained in the margin of the instrument.
To divide a straight line into any number of equal parts. —Set the index marked upon the centre to the number on the line of lines ; then take the extent of the given line with the longer points of the instrument, and the shorter points will divide the line as required. Thus, let it be required to divide three inches, or any distance within the reach of the compasses. into five equal parts : set the index to five on the line of lines: then take three inches, or the distance required by the longer points of the compass, and the shorter points will divide the line into five equal parts.
To divide a circle into any number of equal parts, from six to twenty, that the length of the compasses will admit of —Set the index upon the number in the line of circles, and with the longer points take the radius of the circle; then the distance between the shorter ends being repeated as chords round the circumference, the circle will be divided as required. Should it be required to divide the circle into ten parts, set the index to ten on the scale of circles, and with the longer points of the compasses take the radius of the circle, and the shorter points will divide the circumference into ten equal parts. And thus any regular polygon, from six to twenty sides, may be inscribed in a circle.