430 Transactions of the Society. 



same, but in No. I. it is 7' 1", and in No. IV. 6' 55" ; in t his las 

 Microscope there is also an error in the ver. sin of 0-00239. 



Dr. Smith's angle of aperture, tan J-, is common to all the four 

 Microscopes. 



Under these circumstances, it seemed better to make an in- 

 dependent examination of the Microscope, No. III. being selected for 

 that purpose. Two sets of calculations were made, one analytical, 

 the other trigonometrical — the results being that the final aber- 

 ration by the trigonometrical method* is +0-0017, by the 

 analytical + ■ 0005, while that by Dr. Smith is - • 001. No. III. 

 Microscope is, therefore, aplanatic as well as achromatic. We 

 are now in a position to see what this Microscope was really like. 

 Its objective, which consisted of two mirrors, had J an equivalent 

 focus of 0-604 (a little higher than a §), and the very large optical 

 index of 19-0. The tube-length was so short that the effectual 

 power of the objective was reduced to 5 • 3 ; the eye-piece was 

 very deep, its power being 71 ; the combined power was there- 

 fore 375, or, in Dr. Smith's terminology, 300, as he used an 8-in. 

 eye-point. 



This Microscope is quite unique, inasmuch as the object was 

 kept at a fixed distance from the objective, the focusing being per- 

 formed by the eye-piece alone. The mechanical arrangement was 

 that of a direct-acting screw, as was usual in Microscopes of that 

 date, but herein lies the ingenuity of the device, because the objec- 

 tive forms an optical lever to slow down the effect. In the modern 

 Microscope a levgr of some sort is placed between a direct-acting 

 screw and the objective to slow down the motion, because its effect 

 is multiplied by the optical action of the objective ; in Dr. Smith's 

 the optical action of the objective is in the contrary direction, and 

 so the effect of the movement of the eye-piece is reduced. It was 

 not considered necessary to work out any of the other three Micro- 

 scopes, as this one proved so satisfactory. We may therefore pass 

 at once to the compound dioptric Microscope. 



The optical efficiency of this instrument reached its zenith in 

 the hands of Benjamin Martin. After Martin's death Adams copied 

 Martin's optical parts, and his successor, Jones, carried on the same 

 form right up to the introduction of achromatism. Martin's Micro- 

 scope had an eye-piece with a double eye-lens and a field lens ; at 

 the top of the " pipe," or, as we should say, '' nose-piece," there was 

 a biconvex f lens of 5^-in. focus to do duty as a back lens to the 

 six non-achromatic single equiconvex object-glasses. These old 

 opticians had found out precisely the largest aperture that might 

 be given to a single biconvex lens before the fog and chromatic 

 fringes became too pronounced. The following list gives the 



* Calculated to the first decimal place of a single second of arc. 

 t That in my Microscope is not equiconvex. 



