

oaching it. List never quite reaching it, i.e., p - only 



iiuinlM i 4 have been deacribed. 



The locus of equation (1) U ahown in Fig. 138 ; the heavy 



fm W 



being the part of the locus obtained from the positive 

 of p, while the dotted part belongs to the negative 

 of p. 



NOTE. The four spiral* Jut discussed, and w! 



1S5 to 188, are all included under the 

 by the equation 



forma are giren In 

 of the 





1, thw in the spiral of Archimedes; if n = 1, it Is the hyperbolic 

 i, it is the parabolic spiral; while if n = - J, "it is the 



19a The logarithmic spiral.* TliU curve is traced by a 

 whii -li moves around a fixed point in a plane in K 



Tills oorte might hmre been defined by aayiag that the 



In a 9 om*tric ratio while the rectorial angle tncreaec* In an 

 nulo. An important property of this rurre Is (see McMahon and 

 Differential Calcuhw. Art, ISO) that tt cats all the radii rcclores 

 same angle, and the unp-nt of this angle It the modulus of the systos* 

 logarithms which the particular spiral 



