502 



Mr. A. Ferguson on certain Small 



minor axes o£ the ellipse be measured on the vertical scale, 

 then, as the figure shows, 



Fio-. 1. 



tail i ^= 



ah 

 cd 



if toe assume that the rings are truly circular, and concentric 

 with the point of contact of the surfaces between which they are 

 formed, so that ab may be assumed to be given by the 

 measurement of the major axis of the ellipse. 



Such a method is probably more satisfactory than those 

 which depend on the measurement of the inclination either 

 of microscope or collimating system, but its use obviously 

 depends on the correctness of the assumption italicised 

 above. 



This assumption again depends on the manner in which 

 the equations of the ring-curves are formed. It is a re- 

 markable fact that, even in the definitive treatises on the 

 subject, it is tacitly — or, as for example in the case of 

 Airy's " Undulatory Theory/' overtly — assumed that the 

 parallel-plate formulae can be used without modification, and 

 this, despite the fact that there is a somewhat extensive litera- 

 ture dealing with the subject *. The papers cited below deal 

 fairly exhaustively with a variety of points of importance — 

 e. g. the exact shape of the interference surfaces, and the 

 plane in which the fringes are formed — but the expressions 

 arrived at are somewhat cumbrous in form, and not well 

 adapted for practical use. 



The variety and importance of the measurements of 

 physical quantities which depend on the production of in- 

 terference systems, are such as render it desirable to put 



* See e. g., Wangerin, Pogg. Ann. cxxxi. p. 497 (1867) ; Feussuer, 

 Wied. Ann. xiv. p. 564 (1881) ; Sohncke and Wangerin, VVied. Ann. 

 xii. pp. 1 & 207 (1881), and Wied. Ann. xx. pp. 177 & 391 (1883) ; 

 Mascart, Trait 6 d'Optique, i. pp. 439 scqq. 



