The Circular Locus. 



9 



the origin formed by the two vectors x-f' " and x— ?•. Simi- 

 larly, the principle of vector-addition is to be borne in 

 mind in uniting the result with the term x. The ordinary 

 geometric constructions of a bisectrix and a mean propor- 

 tional may be combined with a fair degree of convenience 

 as follows: Let the two axes, OJ and 01, 



and the circle of radius r about the origin be first drawn, in 

 ink, or so as to remain permanently through the construc- 

 tion. If the a"-coniitant /j- is to be drawn, where ."■ is a given 

 quantity, let a point M be taken on the axis of imaginaries, 

 at a distance //. above the origin; also a point S midway 

 between O and M ; and let lines MN and ST be drawn par- 

 allel to the real axis to an indefinite length. These two 

 lines will remain during the construction of a single comi- 

 tant, but all that follow must be erased and drawn anew 

 for each point constructed. On MN take any point X, 

 and on the same line two points, H and K, at distances 

 equal to r, on opposite sides of X. Of these, let H be on 

 the side of X opposite M. Draw OH. With center O and 

 radius OK describe an arc intersecting OH at G, and at G 

 erect a perpendicular to OH. From center I^ (the point 

 where OH meets ST) with radius UH, describe an arc cut- 

 ting this perpendicular at Q. From K and G, with equal 



