ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 501 



terior face of the objective. It can be shown that <f> p = d — *L and 



y 



<£„ = - — d. These relationships can also be obtained by graphic con- 

 structions. The notation is thus established by means of two figures, 

 without complicated formulas or special apparatus — merely by help of 

 ordinary microscopic auxiliaries. A number of interesting facts regard- 

 ing a lens may be easily deduced from y and <f>, including a graphic 

 diagram. Again, the first of the two figures would be the ordinary title 

 of the lens, the second (<£) could be engraved on the mount. Thus 

 objectives would be known by figures giving their magnifying power at 

 the same distance, viz. 1 decimetre from their posterior face. The 

 author suggests that makers should, in anticipation of the universal 

 adoption of his scheme, supplement their ordinary descriptions of objec- 

 tives by two columns recording the new notation. This is now actually 

 being done by one maker, Stiassnie, of Paris, who has materially helped 

 the author with the necessary information and apparatus for drawing up 

 the lists and tables in the treatise. 



Theory of Symmetrical Optical Objectives.* — S. D. Chalmers, as 

 the result of his investigation, concludes that, subject to the errors 

 introduced by the want of correspondence of the stop and its image, the 

 combined system is completely corrected for astigmatism, curvature of 

 field, and spherical aberration, provided the back component is so 

 corrected. This want of correspondence, however, introduces some 

 slight errors, but in practical systems these are almost negligible. 



Construction of Aplanatic Combinations of Lenses with or 

 without Achromatism. f — " H " discusses this subject in a series of 

 four letters to the " English Mechanic," illustrated by very clear dia- 

 grams. He takes, as his model, the lens figured by Engel in plate xi. of 

 Schellbach's " Geometrical Optics." The writer's design is to simplify 

 the subject as much as possible, and his method is a combination of 

 graphics with calculations from Halley's formulas. These classic 

 formulas have the advantages of (1) great simplicity and clearness ; 

 (2) absence of all error from incomplete recognition of the effect of 

 " thickness " ; (3) the comparatively small number of figures needed in 

 working out the details ; (4) the accurate way in which they may be got 

 to supplement a partly graphic method, as both deal with one surface at 

 a time. The formulas are — 



f m dr f m d r 



(m - n) d - nr (m - n) d + nr 



, m f m d 



J3 m-n n 



where — = ratio of refraction, d = distance of radiant, r = radius of 

 a 



curvature of surface. 



* Proc. Roy. Soc, lxxiv., No. 482, pp. 267-72 ; No. 504, pp. 396-9 (3 figs.). 

 t English Mechanic, Nos.2068, pp. 321-2 ; 2069, p. 340 ; 2072, pp. 406-8 ; 2080, 

 pp. 595-6. 



