Form of Newton's Rings. 



237 



Fier. 6 





x , —m x n x ; 



The direction -cosines will be similar to those used in 

 Sect. II. Part L, so far as the two cases coincide, viz.: — 



The direction-cosines 



of LA, L'A', BO, B'C are -I, -m, n; 



of AB,A'B' are -Z', -7 



of BiC are l x , m l} nj ; of B^i are 



&c. &c. 



of BfyCk-ij are h, m k , n k ; of Bk, C*are — l k , — m k ,n k . 



Also we shall take as direction-cosines of 



C*D, -Zfc+i, -w*+i, w*+i; CD', -a', -/3', 7'; 



FD, —4+2, —m k+2 , n k+2 ; FD', —a, — /3, 7. 



The rectangular and spherical coordinates of 



C are f 1? ??,, &, and (j),f; 



C 2 are f 2 , %, f 2 , and <£, ^ ; 



&c. 



0* are f fc+1 , 77^+1, & +1 , and </>*, ^ ; 



C are £', 1/, ?', and (/>', f ; 



while F is ?, *7, f. 



The thickness of the lens at its centre will be denoted by d, 

 while r is the radius of its convex surface. The direction- 





