JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. 9 APRIL 4, 1919 No. 7 



OPTICS. — Trigonometric computation formulae for meridian 

 rays. P. V. Wells, Bureau of Standards. (Communicated 

 by S. W. Stratton.) 



The design of optical instruments is notoriously so laborious 

 and complicated that any simplification of notation, or shortening 

 of labor, is important. By far the largest amount of labor is 

 spent in tracing the actual path of selected rays through the 

 tentative system by means of the trigonometric formulae. 

 These formulae are simplest for logarithmic computation when 

 referred to the center of curvature of the refracting surface 

 instead of to its vertex. This is doubtless known to many 

 designers but as I have not seen it in the literature, it may be 

 useful to others. 



The resulting formulae, using the notation defined in figure i , 

 where the subscript k refers to the k'th surface are: 



sin ^K = 7~ sin a^ (i) 



Where Ck = Tk 



