Quetelet's Hingis and other Allied Phenomena. 829 



the methods of observation here described, several interesting 

 results have been obtained which will now be detailed. 



3. The Configuration of the Rings. 



There is a noteworthy difference between the configuration 

 o£ the rings as seen with the air-film and with the sheet of 

 mica. As is well known, the diameters of Quetelet's rings 

 are given by the formula 



2fit(cos r — cos #) = + n\, (I) 



where t is the thickness of the plate, X the wave-length of 

 the light, r and 6 are the angles which the regularly trans- 

 mitted and diffracted rays inside the plate make with the 

 normal to its surface, and /j, is the refractive index of the 

 substance of the plate. The achromatic ring for which r=6 

 passes through the reflected image of the source. The 

 spacing of the rings depends on the variation only of 0, and 

 is thus practically the same as for Haidinger's rings or the 

 " interference-curves of equal inclination " as they are called, 

 observed by reflexion at the surfaces of the plate of an 

 extended source of monochromatic light. The positions of 

 the latter are given by the formula 



2/jitcosr— ±n\ (2) 



r in this case being also the direction within the plate of the 

 regularly emergent rays. The corresponding angle of 

 emergence % from the plate is given by the relation 



sin z = //, sin r (3) 



The angular width di of a ring is given by the relation 



,. ll\ cos r ,n 



t sin 2i 



From (4) it is seen that when /x^l, the rings are broad both 

 for normal and grazing emergence, and the width of the 

 rings is a minimum for some intermediate direction, whereas 

 if //, = 1, the width decreases continually from normal to 

 grazing emergence. These features in the spacing of the 

 rings are also easily observable with the Quetelet's rings. 

 With the air-film, fju ~1, and the rings decrease continually 

 in width from normal to grazing emergence as indicated by 

 the theory. With the mica however, /x=^=l, and the rings 

 seen with white light are seen first to become narrower and 



