traced upon the Surface of the Sphere. 



407 



equations is sufficiently obvious. We shall, therefore, here only add the 

 equations of the tangent and normal of a polar plane curve in terras of the 

 differential coefficients and the co-ordinates of the points concerned. 



5. To find the tangent to a polar curve. 



The equation of EC is 



r == a sec 6 / 

 Now the angle OFE is denoted by 



_] T I UV I , 



tan : , and 



dr, 



OE = r, sin tan" 1 '- - = a 



(19.) 



(20.) 



Again 



7T 



EOC = 



or 



= -5 -- tan 



-i 



rp.+0, , 



dr. 



Expanding (19) we have 



a 



= cos Q cos /3 + sin 6 sin 



( r d v X /' 



tan" 1 - - 6, \ + sin & cos f tan' 

 dr t / \ 



(81.) 



^-r,de, 





