6o4 



NATURE 



[January 30, 1913 



he applied his system to practical computations have 

 not been made known. 



A further valuable contribution to practical optics 

 was made by Helmholtz and Abbe, who, by discover- 

 ing the sine condition, sliowed the means by which 

 an object and its image can be made geometrically 

 similar. It is, however, a great mistake to suppose 

 that these achievements in the mathematical equip- 

 ment of the microscope inaugurated a brilliant epoch 

 in the history of the microscope, and that enormous 

 progress was made henceforth. In the first place, 

 it was found that by a carefully developed trial-and- 

 error system opticians had succeeded in producing 

 objectives which in a high degree satisfied the con- 

 ditions postulated by mathematical theory. Thus it 

 was found that all objectives tested by Abbe com- 

 pletely satisfied the sine condition, although until 

 then this had been unknown in principle. 



The investigations of Helmholtz and Abbe (1873-4) 



showed bv the formula of the former, 6= — , — , and 



2 sin a 



Abbe's formula, «= , that the optical perform- 



2« sin <i 

 anc-c of the microscope is confined within definite 

 limits. In these formulse e denotes the smallest dis- 

 tance separating two successive particles of an object 

 which can be differentiated under a microscope ; ^ is 

 the wave length of any given ray of light, as defined 

 bv Helmholtz, in air or any other medium intervening 

 between the object and the front lens ; a is the semi- 

 apertural angle of the objective, and n the refractive 

 index of the medium between the objective and the 

 cover glass. In drv lenses the value of n is accordingly 

 I'o, in water-immersion it is i'33, and in oil-immersion 

 lenses n=i'52. The denominator in Abbe's formula, 

 n sin a, has been named by him the numerical aper- 

 ture of the lens; it furnishes the principal criterion 

 of the optical capacity of the microscope. When these 

 factors, which determine the optical resources of the 

 microscope, were discovered, the microscope liad 

 already been brought to a very high degree of perfec- 

 tion by purely empirical means, and in practical re- 

 spects the formula had already been satisfied to a 

 very considerable extent, and but little scope was 

 left to the investigator and computer. The apertural 

 angle had already attained very considerable mag- 

 nitudes ; water-immersion and oil-immersion lenses 

 were already in existence, and accordingly the 

 element n in Abbe's formula had already received 

 practical consideration, whilst in the formula enun- 

 ciated by Helmholtz the wave length of a ray in air 



had become reduced to a quotient -. by which the 



wave length was shortened in proportion to the re- 

 fractive index of the medium. 



Amici in Italy, Spencer in America, Fraunhofer, 

 Kellner, Oberhauser, and Hartnack in Germany, 

 Chevalier in France, and Ross and Powell and Lea- 

 land in England had all done a great deal to perfect 

 the microscope objective. In medical research a new 

 era had been inaugurated by the achievements of 

 microscopic observations ; histology and pathology had 

 been placed upon a firm basis ; and Pasteur had 

 alreadv planted the beginnings of bacteriology and 

 identified a number of pathogenic germs. In the face 

 of the difficulties and limited nossibilities with which 

 the optician had to contend, it would be interesting 

 to form an estimate of the results which opticians 

 had been able to achieve from the time that they 

 commenced to annlv the resources of scientific re- 

 search. The formula given above made it clear that 

 there was no possibility of ' extendintr the capacity of 

 the microscope bv increasing without limit its mag- 

 nifying power. Means had indeed been found to 



NO. 2257, vol,, go] 



increase the angular aperture a in a measure as the 

 magnification rose higher and higher, but there was 

 a limit beyond which it was impossible to increase 

 the magnifying power of a lens without reducing the 

 free distance between the object and the front lens 

 to an impracticably small amount, which did not even 

 provide room for a thin cover glass. Continued 

 attempts were made to extend the power of the micro- 

 scope by increasing its magnifying power. It was 

 soon found that lenses having such extremely short 

 focal lengths as 1/20 in. 1/50 in., and even 1/75 in., in 

 which there was no corresponding increase of the 

 angle of aperture, were in no wise superior in their 

 optical capacity to lenses of lower power, and the 

 trouble expended upon them was clearly wasted. 

 These extremely high powers, of which many 

 examples were produced by the opticians of fifty or 

 forty years ago, have now been entirely discarded, 

 and one rarely meets now objectives having a shorter 

 focus than 1/16 in. 



Opticians then proceeded to concentrate their efforts 

 upon increasing the numerical aperture. Dry lenses 

 had alreadv I hen been made with apertures of o'go, 

 and this value has not been exceeded even in these 

 days. Water-immersion and oil-immersion lenses, 

 with their theoretical apertural limits of i'32 and 

 i'52, were, however, still far removed from what 

 was practically attainable ; in fact, they did not 

 exceed I'o in water-immersion and i'2 in oil-immersion 

 lenses. To carry the aperture further it was neces- 

 sary to endow the lenses with a greatly improved 

 spherical correction, and much higher demands were 

 made upon the skill of the optician, both in the 

 matter of lens grinding and mounting. By the exer- 

 cise of an extraordinary degree of skill in the mount- 

 ing of the front lenses and by clamping them by their 

 extreme ridge, the practical optician has come very 

 near to the theoretical limits, and has been able to 

 realise apertures up to i"2 in water-immersion lenses 

 and i'4 in oil-immersion lenses. These were momen- 

 tous achievements, and it is to lenses of high aperture 

 that bacteriological research owes the greater part 

 of its success. When the limit had been thus reached 

 in both types it was thought to increase the power 

 of the lens by introducing a medium of higher re- 

 fractive power. Since the transition of light from 

 air (n=i) to w-ater (n=r33), and that from air to 

 oil (n=r52) had furnished such striking results, it 

 was expected that the transition to a more highly 

 refracting medium having a refractive index of r66 

 would furnish a means of increasing the aperture 

 still further. 



An objective of this kind, in which the immersion 

 medium was monebrome naphthalin, was computed 

 by Prof. Abbe and made by Carl Zeiss in 1889. Its 

 numerical aperture was i'6o. To secure the full 

 advantage of this large aperture it became, however, 

 necessary to satisfy an extensive range of conditions. 

 The condenser must have a similar aperture, both it 

 and object slide required to be joined by a stratum of 

 monebrome naphthalin, and the slide as well as the 

 cover glass had to be made of glass having the same 

 refractive index ;is the immersion medium, and the 

 obiect itself had to be mounted in a powerfully 

 refracting medium. 



Dr. Van Hcurck (Van Heurck, " Le Microscope," 

 i8qi, p. 63), who used this objective for a consider- 

 able time, and obtained with it many remarkable 

 photoeraphs, including striking photographs of 

 Aniphipleiira pelhicida. whilst praising the great re- 

 solving power of the objective, described it as scarcely 

 adapted for regular practical use, both on account 

 of the enormous difficulties which its use entails and 

 its inordinatelv hiyh price. Of the chief causes which 

 militate against the use of the objective, and indeed 



