///./// sa HI 



- definition ;" th- lunar.. n. as well aa the equation 



u issymuietrir.il \\ith regard to 

 intial line, an* I that it hit* t . shown i 129. 



t r . The rectangular aquation of the limaoon for which k m a te 

 eauily derived from equation (.1). Choosing UM initial line and a perpen. 



ir t.. it through O as rectangular axes, to that x = pcos& and 

 9 pain 0, equation (3) becomes 



nationalising equation (4) gives 



which U the usual form for the rectangular equation of the limaooo. 

 189/'. The cardioid. The canlioid may be defined M 



special case of the lim.i<;>: it is a limayon in 



the constant (-. which is added to eiuh <>f the radii vectorea, 

 niken equal t<> the (li.im.-t.-r ,,f tin- ftuulamental t-i 

 i the .-.jii.iti.n ,,f tli.- lmi.i.;..M [ A tt. 189o, equation 

 constant A: be taken equal to 2 a, that equation become* 



p = -Ja(l -f cos^), . . (1) 



- the polar equation <>f iii.- . 

 The more usual form in \vhi.-h the equation of the 



-, . . 

 but this am. units merely to turning the figure through 180 



111 its \vn plane. 



NOTB 1. The rectangular equation of the 

 eardioid is obtained an in Art l*9o. 



(* + f" + 2 r) = 4 (** -r O 

 curve represented by equa 

 and (3) has the form shown in Fig. 130. 



I is usually defined as the 



traced by a joint on a piven circle 



i A i,/.. which i- Us on an equal but fixed 



t ion also leads to 



aqua .uid (!) already derived. 



