206 ON THE THEORY OF THE MICROSCOPE. 



without introducing various questions into the theory of the 

 microscope which at present form no part of it. 



To develope such a theory more fully in the directions here 

 indicated, was mainly a mathematical task involving problems to 

 be solved by the aid of established principles of Dioptrics. Experi- 

 ment and experience v^^ere concerned in the enquiry only so far as 

 it was necessary to become acquainted with the actual form in 

 which each separate source of error, as indicated by theory, might 

 be recognised in the microscope when finished, and also to 

 estimate rightly their veiy unequal significance in the practical 

 use of the instrument. On the other hand, a fresh deficiency in our 

 present theoretical knowledge revealed itself, which could only be 

 supplied by fresh experience. The nature of this deficiency is 

 indicated in the uncertain, and often contradictory, views held 

 respecting the significance of angular aperture and the so-called 

 ** defining" and '* resolving " powers of an objective. To remove 

 all uncertainty, and to obtain clear insight into the conditions 

 which operate here was a conditio sine qua non for any successful 

 attempt to develope a theory in the sense above mentioned ; for 

 upon the eff'ect supposed to be obtained by angular aperture 

 depends the whole direction and solution of the problems. Each 

 single proportion in the construction will diff'er altogether, accord- 

 ing as it is calculated for an objective — say, of 40^, 90°, or 150*^ 

 aperture. But what kind of effect was to be expected remained 

 wholly doubtful, so long as no accurate account of the real signifi- 

 cance of these factors (*' definition," and ''resolution,") could 

 be given. 



III. The result of investigations which were undertaken 

 independently, in order to bring these questions to some issue, was 

 the discovery that an important feature in the optical functions 

 of the microscope had been hitherto overlooked, for in all previous 

 explanations or interpretations it has been accepted as a self- 

 understood proposition that the formation of an image of an object 

 in the microscope takes place in every particular, according to 

 the same dioptric laws by which images are formed in the tele- 



