Researches in Circular Solar Spectra. 183 



of the cone of rays radiant from the illuminated particle mounted 

 in balsam, a much larger pencil reaching the objective via water 

 than can possibly be effected via air. The " critical angles " of 

 total internal reflexion which determine the form of the caustic 

 being so much larger in passing from glass into water than into 

 air. I have shown elsewhere that the volume of the cone of rays 

 transmitted from a radiant particle placed in balsam and sur- 

 mounted with a thin glass cover, is about four times greater via 

 water than via air ; that result is explanatory of the greater 

 brightness of the immersion lens.] 



The question of the spherical and chromatic aberrations of eye- 

 pieces has occupied the attention of the most distinguished mathe- 

 maticians, and may theoretically be considered nearly exhausted, 

 yet the practical detection of its existence is known to few, as it is 

 liable to be mixed up with the objective aberration. The methods 

 described are equally applicable to eye-pieces as to objectives.* 



The construction of a compound compensating eye-piece which 

 should almost be perfectly free from this residuum next engaged 

 my attention. 



From the discovery that the advance of an eye- piece towards 

 the objective caused a violent under-correction in the refocussed 

 ohjective, it became evident that a shortened microscope could be 

 employed as a compound eye-piece nearly free from the usual aber- 

 rations, provided its object-glass were properly over-corrected, as 

 compared with its performance at the usual standard distance of 

 10 inches. 



The new eye-piece is finally corrected on the circular solar 

 spectrum (herein described), being regarded and treated as a real 

 microscope. Its object-glass, considering the exceedingly small 

 pencil engaging it, may conveniently be formed of slightly over- 

 corrected achromatic lenses, compensated by a variable interval. I 

 have found an inch focal length sufficiently deep, mounted with a 

 low eye-piece. The substitution of this compensating eye-piece for 

 the ordinary deep Huyghenians afforded that degi'ee of comfort in 

 observation corresponding to enlarged pencils. 



After adjustment it is quite as applicable to examine the per- 

 formance of telescopes as microscopes. The adjustment is thus 

 accomplished : — 



1. The instrument, mounted as a complete microscope, was 

 adjusted for the most perfect definition on an uncovered object; 

 and supposing the glasses A, B (adjustable by a variable interval) 

 defined perfectly with the usual length of tube, 10 inches, they 

 require over-correction t or separation for a shorter tube of 6 inches. 



* Appendix B. 



t Considering the small angular aperture, a single set of achromatic leEses 

 might be constructed and employed ; but their correction is much more tediously 

 attained than by separable sets of lenses. 



