352 FERGUSON'S LECTURES. 



LECT. Perhaps it may not be unacceptable to explain the 

 v^-v~%_; method of constructing the dialing lines, and some 

 others ; which is as follows. 



With any opening of the compasses, as E A, (fig. 1. pi. 

 6.) according to the intended length of the scale, describe 

 the circle A D C B, and cross it at right angles by the 

 DiaKng- diameters C E A and DEB. Divide the quadrant A B 

 construct^ ^ rs * * n * ^ e( l ua l P ar *s, and then each part into 10 ; so shall 

 ed. the quadrant be divided into 90 equal parts or degrees. 



Draw the right line A F B for the chord of this quad- 

 rant, and setting one foot of the compasses in the point 

 A } extend the other to the several divisions of the quad- 

 rant, and transfer these divisions to the line A F B by 

 the arcs 10 10, 20 20, &c. and this will be a line of 

 chords, divided into 90 unequal parts : which, if trans- 

 ferred from the line back again to the quadrant, will 

 divide it equally. It is plain by the figure, that the dis- 

 tance from A to 60 in the line of chords is just equal to 

 A E, the radius of the circle from which that line is 

 made : for if the arc 60 60 be continued, of which A is 

 the center, it goes exactly through the center E of the 

 arc A B. 



And therefore, in laying down any number of degrees 

 on a circle, by the line of chords, you must first open 

 the compasses so, as to take in just 60 degrees upon 

 that line, as from A to 60 : and then, with that extent, as 

 a radius, describe a circle which will be exactly of the 

 same size with that from which the line was divided : 

 which done, set one foot of the compasses in the be- 

 ginning of the chord line, as at A, and extend the other 

 to the number of degrees you want upon the line, which 

 extent, applied to the circle, will include the like num- 

 ber of degrees upon it. 



Divide the quadrant C D into SO equal parts, and 

 from each point of division draw right lines, as i, k, /, 

 &c. to the line C E ; all perpendicular to that line, and 

 parallel to D E, which will divide E C into a line of 



