60 VISION WITH THE COMPOUND MICROSCOPE 



demonstrate for himself that immersion lenses not only possess an 

 excess of aperture over dry lenses, but that the rays so in excess are 

 image - for ming . 



The refractive indices of (cedar) oil, water, and air are respec- 

 tively 1*52, 1'33, and I'O. 'Angular aperture' claimed that the 

 angles of the admitted pencils to lenses of these three constructions 

 expressed equal ' apertures.' But this is a fallacy, now so palpable, 

 but which has exerted an influence so deterrent on the progress 

 of the construction of our higher object-glasses and condensers, 

 that its final disappearance as an unjustified assumption which had 

 crept into the area of theoretical and practical optics, unverified by 

 facts and devoid of the wedding garment of deduction, is a triumph 

 which will make the name of Abbe long and gratefully remem- 

 bered. 



The principle upon which increase of numerical aperture gives 

 increased advantage to an object-glass manifestly needs careful 

 study and elucidation. We have but to refer to the best work done 

 by those who have employed the microscope to any scientific purpose 

 for the past fifty years to discover that there has been an admission, 

 which has steadily strengthened, that by enlargement of aperture an 

 increase in the efficiency of the objective, when well made, was 

 inevitable. During the last thirty-five years this has been especially 

 manifest. To increase the aperture of an objective under the name 

 of greater * angle ' has been the special aim of the optician and the 

 constant and increasing desire of all workers with moderate and 

 high powers. 



The true explanation of this is quite independent of any con- 

 sideration of apertures in excess of the maximum in air, and indeed 

 of the whole question of immersion objectives. The old view that 

 all high and excellent results depended on the angle at which the 

 light emerged from the object, involving some assumed property of 

 a special kind in the obliquity as such, has been most tenaciously 

 held ; but it is an x in the problem which has not only never been 

 demonstrated, but the scientific explanations of all the optical 

 properties of lens combinations in the formation of images by means 

 of numerical aperture, prove that it is hopeless to attempt to attach 

 any value to angle as angle. 



About thirty years ago it presented itself to Professor Abbe as 

 a problem worthy of most careful inquiry as to w r hy great ' angle ' 

 or obliquity as such gave to objectives an enhanced capacity in the 

 disclosure of obscure structure. The first step was a consideration 

 of the grounds on which the theory of the value of angle of aperture 

 rested. But no such basis was found to exist ; no investigation of 

 the question had been made. It was demonstrated that a pencil of 

 170 would show minuter structure than one of 80 in the same 

 medium ; and from this a generalisation had been made that upon 

 the obliquity of the * angle ' of light depended the delineating power. 

 It was taken as a self-evident proposition that the formation of the 

 image in the microscope took place in every particular according to 

 the same dioptric laws by ivhich images are formed in the telescope, 

 and it was tacitly taken for granted that every function of the 



