852 



MR HENRY BR1GGS ON 



An inspection of the figure shows that 



S - T = ± (a, + a.,) 



(2) 



Draw Oa bisecting the angle T. The position of the point N is conveniently referred 

 to the line Oa. Let the angle aON be x. 



Fig. 2. 



Then, OM and OQ being drawn at right angles to P r N and P 2 iV respectively, we 



have : 



OM r . / T \ 



or, since u 1 is always very small, 



a-]=T^- sin \n+x 



In like manner, 

 Therefore 



'"Lj — Va 



•> 



a2 = E; sill (2" x } 



(S - T) = j- sin (2" + -^J + J7 sin f f ~ *) 



(3) 



The equation is quite general for all positions of N on the circle. At E or F, 

 (S—T) = 0; therefore at either of these points : 



or 



• . /T \ /• . /T \ 



- sin ^ + x J = - j- sin (j - a J, 



^tan| 



(4) 



