H. S. Uhler — Deviation Produced by Prisms. 389 



Art. XXXIY. — On the Deviation Produced hy Prisms ; by 



H. S. Uhler. 



By consulting all available standard reference books and 

 scientific journals, the writer has been unable to find a discus- 

 sion of the general case of refraction of oblique rays by a single 

 prism which will enable the reader to form a clear or adequate 

 conception of the dependence of the total deviation upon the 

 angles defining the direction of the incident ray. The refer- 

 ence books give but little more than a formula connecting the 

 deviation (D) of the oblique ray with the deviation (E) of the 

 projection of the ray on a principal section of the prism, and 

 with the angle (77/; which the incident ray makes with such a 

 section. Furthermore, the formulae to be found in the books 

 are not equivalent, most authors write 



cos \D = cos %Ecos t) x * 



(apparently following Heath), and one author, at least, writes 



sin \D = sin \E cos rj x .\ 



Neither equation throws much light on the subject because E 

 is a function of rj 1 and of another angle, so that I) is an implicit 

 function of two independent variables. On the other hand, 

 the journal articles treat, in a fragmentary manner, of certain 

 special problems connected with the general case of the devia- 

 tion of oblique rays, consequently it requires a disproportionate 

 amount of time to find out what has already been done. 

 Unfortunately not all of these articles are trustworthy. Since 

 this state of affairs exists, and since the question is not without 

 interest to students of geometrical optics, it seems desirable to 

 collect in one place the correct results hitherto obtained, to 

 supplement these results by original investigation, when neces- 

 sary, and to present in graphical form all the facts amenable 

 to such treatment. In other words, the endeavor will be made 

 in the present paper to treat the problem of prismatic devia- 

 tion in as complete and thorough a manner as possible. 



The entire discussion will have reference to the case of a 

 single prism with unlimited plane faces, and surrounded by 

 one medium whose absolute index of refraction is less than the 



* S. Czapski : Winkelmann's "Handbuch der Physik," vol. vi, p. 189, 

 1906; E. S. Heath : ''Geometrical Optics," p. 32, 1887 ; H. Konen : Kayser's 

 "Handbuch. der Spectroscopic," vol. i, p. 262, 1900; F. Lowe: M. von 

 Rohr's "Die Theorie der optischen Instrumente," vol. i, p. 428, 1904 ; J. P. C. 

 Southall : "The Principles and Methods of Geometrical Optics," p. 126, 

 1910. 



f J. Walker : "The Analytical Theory of Light, 



