810 THE EQUIANGULAR SPIRAL [ch. 



PP'/PR' = dsjdr = sec a, and therefore sec a = sjr, or the ratio of 

 arc to radius vector. 



Fig. 394. 



Accordingly, the ratio of I, the total length, to r, the radius 

 vector up to which the total length is to be measured, is expressed 

 by a simple table of secants ; as follows : 



Putting the same table inversely, so as to shew the total length 

 in terms of the radius, we have as follows : 



