1W-11*.] /// l.AHX CURVES 



same ratio M the reciprocal* of the angle* which they form 



initial 1 



ilriiniuoii ii follows that the equa 



where k is a constant . 



iioxv* that the curve begins at infinity 

 n and winds mm. I the center, always 



: Caching it, i.nt n.-\ n .jnii.- reaching it ; i.e., p only 

 after an infinite nnmU-: s have been described. 



nation (1) also shows that the constant k i* the 

 en inference of the measuring eh ' . 1 | the 



measuring circle (Art. l'.:l) is the radius vector of the gener- 

 ating point of tin- mrve at tl- end of the first revolution, 

 when 2 ir; but, from equation ( 1), this radius vector 

 is , and u inference of the circle of whi.-h this is 



the radius is k. 



A pi in, if P m (p, ff) be any point on the locus of equa* 

 i(l), then 



circumference of measuring circle ; 



but p0 equals the length of the circu- 

 lar arc descriU-d with radius p and 

 subtending an angle 0, therefore the 

 length of any circular arc as HP, 

 described about 0, with radius p, and 



:uling from the initial line to 



-urve, is equal to the circum- 

 ference of the measurin 



locus of equation (1), for ]>ositive values of 0, is 



