TRACING OF POLAE CURVES. 



879 



increases from to Sir, r is negative, and -v~ is positive so 

 that r numerically diminishes. 



To draw the asymptote we proceed thus: since, when 



BTT 

 6 = , r is infinite, and the polar subtangent is 3a, the eye 



A 



must be supposed at looking along OF, and a distance 

 OGr = 3a must be measured to the right of OF and at right 

 angles to it ; a straight line drawn through G parallel to OF 

 is the required asymptote. 



As 6 changes from to - - the branch AB CD is traced 



2 



out, cutting OA at right angles at A since tan <j> = oo when 



6 = 0. When becomes greater than - , r is negative, and 



J> 



according to the usual conventions with respect to sign, must 

 be measured in a direction opposite to that which it would 

 have if it were positive. For example, if the angle AOQ 



