2(j4 Transactions of the Soeietrj. 



'9 mm., and even with the y'^" (1 '2 mm. focal length) the smallest 

 radius (O'O mm.) is very httle less than that of Tolles's ^", whilst 

 an objective of equal power would require, according to Tolles's 

 formula, the abnormally small radius of " 22 mm. 



For the advantageous application of the duplex front in ob- 

 taining larger angular aperture, the more favourable ratio between 

 the radius of the front lens and the focal length which is here 

 attained will be of some importance, because it provides the only 

 possible means of producing objectives of great magnifying power, 

 without having too much recourse to the tube and eye-j)iece for 

 amplification. By Tolles's construction it would be practically 

 impossible to make an objective such as Zeiss's xV"> ^ot to mention 

 the ~i\", with an angle of aperture of any considerable extent, to 

 say nothing of the intolerable limitation of the working distance of 

 lenses so abnormally small. 



As far as the mere observation of diatoms and similar test- 

 objects is concerned, an objective of 4 mm., if thoroughly well made 

 and possessing a good large angle of aperture, would indeed leave 

 scarcely anything to be desired, especially as the small front lens of 

 Tolles's consl ruction involves relatively favourable conditions for 

 the employment of deep eye-pieces. But when we take into con- 

 sideration the much more complicated structures of the difficult 

 objects of biological research, it cannot be doubted that systems 

 which give considerably higher objective amplification will remain 

 a real necessity until in practical optics more perfect methods of 

 getting rid of the aberration than at present known are discovered. 

 In my opinion, therefore, looking to general scientific requirements, 

 the end to be kej)t in view at present is the production of objectives 

 of sufficiently short focal length, which do not present too much 

 difficulty in ordinary use, and this has been the principle which 

 has guided me in my labours in this particular case. 



A decidedly unfavourable feature in the formula which I have 

 produced is the technical difficulty of construction, in which require- 

 ments are made such as were scarcely ever demanded and satisfied 

 in the manufacture of Microscopes. In this construction the 

 spherical surface of the front lens must be utilized to an extreme 

 extent, and must bear angles of incidence which for the marginal 

 rays (on the air side) exceed 45°. The manufacturing optician 

 has therefore to produce spherical surfaces of the small dimensions 

 of the front lens, which shall be strictly true in form to the extent 

 of a full hemisphere, and afterwards to mount these lenses in such 

 a manner that without affecting tiie firmness of their setting they 

 shall freely admit rays of light nearly up to the equator. The 

 difficulty of this work and the extreme sensitiveness to the least 

 defect of form and centering of the lenses, in a system of so great 

 an angular aperture, make the production of such objectives an 



