478 PROCEEDINGS OF THE AMERICAN ACADEMY 



Five Hundred and ninety-second Meeting. 



March 10, 1868. — Adjourned Statute Meeting. 



The President in the chair. 



The President called the attention of the Academy to the 

 recent decease of Sir David Brewster of the Foreign Honorary 

 Members, and of Hon. Daniel Lord, of New York, of the As- 

 sociate Fellows. 



Five Hundred and ninety-third Meeting. 



April 14, 1868. — Monthly Meeting. 



The President in the chair. 



The President called the attention of the Academy to the 

 recent decease of Dr. Samuel L. Dana, of the Resident Fel- 

 lows, and of Professor William Smyth, of the Associate Fel- 

 lows. 



The following paper was presented : — 



Dispersion of a Ray of Light refracted at any number of 

 Plane Surfaces* By Edward C. Pickering. 



Let a 1 a 2 a s , &c, be the angles included between the surfaces, n x n 2 n 3 

 their indices of refraction, i± i 2 i s the angles of incidence, r x r 2 r 3 the 

 angle of refraction ; sin i± = n x sin r x and in general 



sin i m = r m sin r m (1) 



also i m = a m _ 1 -\-r m _ 1 (2) 



As the dispersion of any portion of the spectrum is always propor- 

 tional to the angular divergence of two rays of nearly equal refran- 

 gibility, if we vary % n 2 , &c, dr m will measure the dispersion. Differ- 

 entiating (1) 



cos i m di m = r m cos r m dr m -f sin r m dn m 



* Since presenting this communication to the Academy, I have learned that a 

 portion of this subject was studied by Sir David Brewster in 1812. I have, there- 

 fore, modified my paper, omitting what was not new, except when necessary to 

 preserve the context. 



