408 LIMITS OF OPTICAL CAPACITY OF THE MICEOSCOPE. 



The theoretical grounds taken by these two authors are identical, and 

 their results, so far as the researches were directed to the same points 

 also agree. Eut in each essay the mode of treatment is thoroughly 

 independent, and the experimental proof of the conclusions 

 respectively obtained is conducted by each writer in a separate and 

 original method. The mathematical demonstrations omitted in 

 Professor Abbe's article are fortunately supplied by Professor 

 Helmholtz, and the two essays are confirmatory and supplementary 

 to each other in several other respects, whilst in both we recognise 

 that clearness of thought and precise knowledge of the subject 

 treated, which justifies entire confidence in the conclusions. It 

 seems therefore to me that Professor Helmholtz's essay should 

 naturally follow in this number of our Proceedings. Por, taken 

 together, these two essays form the most complete and authoritative 

 exposition of the optical principles involved in the action of 

 microscope objectives, and the most trustworthy interpretation of 

 that action, and consequently of the capacity of performance of 

 such objectives, that have as yet been made public. 



In introducing the first of these essays to the notice of our Society, 

 I expressed my strong conviction of its high value as a contribution 

 of really scientific character to the theory of the microscope. The 

 essay of Professor Helmholtz deals somewhat more fully with that 

 aspect of optical science which is known as physiological optics, 

 and of which no physicist of our times has a more profound 

 knowledge. This point of view had not been neglected by 

 Dr. Abbe, but in my translation two short sections of his essay, 

 which referred to brightness of image, and to certain enquiries 

 connected with illamination of the image, were, for reasons 

 mentioned in the preface, omitted. It is therefore so much the 

 more satisfactory that Professor Helmholtz's essay enters fully into 

 the subject. The peculiar conditions under which objects are seen 

 when magnified by the microscope, can only be understood by 

 studying both aspects, physical and physiological, in connection 

 ■with each other. The laws of formation of optical images (when 

 amplified by interposition of lenses,) and the laws of dispersion of 



