338 



Mr DAVIES on Equations of the. Loci 



6 = 



RESULTS. 



INFERENCES. (Fig. 25.) 



1 



"o 



m 







.. tan 5 (f> =0 



:<p = primary 

 (f) = IT secondary 



log tan (f) = 





.-. tan i ^: 1 ; 



, ^. 



<f> -^ -^- secondary 



log tan ^ (f) = 

 .-. tan ^ (p = 1, 



<p = primary 



^ 37T 



= secondary 



r. 2 j- 



log tan ^ (b = _ 

 in 



.. tan J <f> -^- 1 ; and 



1 



2 TT ^ (f) ^ secondary I 



log tan (p = + - 



.-. tan ^ = + 1 



= TT primary 

 (f) = 27T secondary 



The primary branch of negative revolution passes through P, 

 and there meets the secondary branch of positive revolution. 



The secondary branch of negative revolution passes through P', 

 and there meets the primary branch of positive revolution. 



The primary branch of negative revolution is in the first quad- 

 rant of polar distance. 



The secondary branch of negative revolution is in the third 

 quadrant of polar distance. 



The primary branch of negative revolution has arrived at the 

 origin of revolution, and the tracing point is in the equator. 



The secondary branch of negative revolution has arrived at the 

 opposite meridian, and the tracing point is in the equator. 



The primary branch of positive revolution is in the second 

 quadrant of polar distance ; and 



The secondary branch of positive revolution is in the fourth 

 quadrant of polar distance. 



The primary branch of positive revolution has arrived at the 

 opposite pole P', where it unites with the secondary branch 

 of negative revolution. 



The secondary branch of positive revolution has arrived at the 

 upper pole P, where it unites with the primary branch of 

 negative revolution. 



