optical Alen-atio/tfi-om Pignri. ft 



ind N, from the convex and concave lenfes, be required to be the fame as reprefcnted in 

 the figures, then muft the objea be placed much nearer to the convex. Hence the image 

 of the near objeft S is reprcfented at the fame diftance from the convex lens in Fig. 3, 

 as the virtual focus-of the concave in Fig. 4, where it is reprefcnted as receiving parallel 

 rays which are fuppofed to come from an infi-nitcly diibnt objedl. 



Now when the diftance between K and N, which is the point from which parallel rays 

 are made to diverge by the concave lens, is equal to the diftance between T and F, which 

 is the point to which rays ifluing from S are made to converge by the convex, and when 

 the aberrations DF and PN are alfo equal ; it will follow in this cafe, that if the two lenfes 

 be placed contiguous, in the manner reprefcnted in the twelfth figure, parallel rays incident 

 on thefe lenfes will be converged to the point S, without any aberration of the external ray. 



For it is an axiom in optics, that if a ray of light after refraction be returned diredly 

 back to the point of incidence, it will be refradcd in the line which was before defcribcd 

 by the incident ray. 



If, therefore, we conceive the whole of the light emitted from the point S (Fig. 3.) and 

 converged by the convex lens towards the points D and F, to be returned direftly back 

 from thefe points, it will be accurately converged to the point S, whence it iiTued. Nowr 

 the parallel rays SH, RK (Fig. 4.) after their emergence from the concave lens in the 

 lines HX, KV, are precifely in the fame relative fituation as the rays fuppofed to be re- 

 turned dire£Hy back from F and D are in at their incidence on the convex ; and therefore 

 when thefe lenfes are placed contiguous in the manner reprefcnted in the twelfth figure, 

 parallel rays incident on the concave lens, and immediately after their emergence from 

 It, entering the convex lens, will be accurately converged to the point S without any 

 aberration. 



This, whicli is the moft fimple cafe, will fuffice to explain the nature of that aberration 

 \yhich arifes from the fphetical figures of lenfes, and a method of obviating it, by com- 

 bining a convex and concave. 



The demonfti-ation is perfect as far as regards the external ray, which is here reprefcnted 

 pairing from the external part of the concave into the external part of the convex, in 

 immediate contaft with it ; and if the furfaces of the two lenfes, which refpeft each other, 

 were either in contaQ or parallel, it would be true with regard to all the rays. But as 

 this is not the cafe, there arifes a fmall fecondary aberration, the effed of which only be- 

 comes fenfible in large apertures. 



Hence may be underftood the reafon why the indiftindncfs arifing from the fpherical 

 figures of lenfes, may, in the common Achromatic Telefcope, be more nearly removed in 

 thofe conftruclions of objea-glafTes in which three lenfes are employed, than in thofc 

 compofed only of two ; and alfo the advantages in this rcfped which may be derived from 

 introducing fluid mediums which differ from glafs in their mean refraftive denfity, and in 

 the quantity of aberration produced by their refradions. For it will be found upon com- 

 putation, that when the fluid medium is rarer than glafs, the aberration from the fpherical 

 figure is increafed, and becomes greater in proportion as its dcnfity diminiflies. Now, by 

 making the denfity of the fluid medium approach nearer and nearer to the denfity of tlic 

 glafs with which it is in contaa, we may incrcafc the rarity of our refrafting medium, or. 

 Vol.. I.-Ai-RiL 1797. C which 



