CHAP, v.] PLOTTING 119 



Before describing in detail the different methods in plotting, plotting 

 it is necessary to understand the system of laying down angles ^yCioid? 

 by chords, and why this is done. 



It will easily be seen that, where lines are to be drawn of 

 considerable length, a protractor whose radius will be much 

 shorter than the desired line, can hardly give the angle exact 

 enough to ensure the extremity of the Une being precisely 

 placed ; for the straight-edge, perhaps 6 feet in length, by 

 which the required line is to be drawn, will only be directed 

 by two pricks in the paper, which, with the largest protractor, 

 will not be more than 18 inches apart. However exactly the 

 protractor has been placed, and the pricks made, the mere 

 laying of the straight-edge so that the line drawn will pass 

 'precisely through the centre of the two pricks near together, 

 is almost an impossibility, and an error, quite imperceptible 

 at the pricks, will be very appreciable at the end of the straight- 

 edge. 



For this reason, we want our directing prick as far along 

 the straight-edge as we can get it. 



We accomplish this by using chords. 



If two radii of a circle of given length of radius, containing 

 between them a given angle 0, be drawn to cut the circum- 

 ference of the circle, the chord to the arc of the circumference 



thus cut off is 2 radius sin .* 



2 



Thus, by reversing this and describing from the centre A, 

 Fig. 20, an arc of a circle of any radius, drawing the line A C, 

 and measuring the chord C B (which will be done in practice 



Fig. 20, 



by describing a short arc of a circle with the required chord 

 as radius, from the centre C), the point B, where the chord 

 cuts the circumference (or the two arcs intersect) joined to A, 

 will give the required angle Q. 



* Vide proof of this rule in Appendix C. 



