964 Transactions of the Society. 



and of the object itself produces what I called the " actual ampli- 

 fication," this amplification is necessarily no fixed number for any 

 given system, but varies with the distance of the image and 

 depends upon the conditions of the observing eye. 



The case is quite different with the " linear amplification." 

 This value is constant for any given optical system and inde- 

 pendent of the actual amplification in a particular case. That in 

 general the " linear" and the "actual " amplification do not coincide 

 is of no consequence whatever, for a change in the position of the 

 virtual image formed by the instrument does not produce any real 

 change for the observer's eye ; for the image varies very nearly in 

 the same proportion as the distance at which it is formed, so that 

 (at least very nearly again) the diameter of the retinal image may 

 be regarded as remaining the same. 



2. Our idea of the diameter of objects with which we are not 

 acquainted by experience, the diameter in which we " see " them, 

 depends upon the dimensions of the image on the retina, and on 

 the distance at which we estimate the object in question to be 

 placed. 



Now the idea is somewhat frequently met with that the linear 

 amphfication is in accordance with the dimensions in which we 

 " see " the image, whilst these again are regarded as agreeing with 

 the actual amplification. 



It is not necessary to explain any further that these factors 

 are quite independent of one another. The linear amplification 

 vpill only agree with the subjective dimensions of the image, if 

 we " see " the object at a distance for which the linear amplifica- 

 tion is determined ; whilst concordance with the actual amplification 

 will only exist, if the virtual image lies exactly at the distance at 

 which it is seen, which in microscopy will not very often be the case. 

 For the image is seen in general at about the distance at which we 

 know the object to be placed, independent of the refractive con- 

 ditions of the eye, whereas its real place entirely depends upon the 

 latter. 



Prof Abbe, in the above-named article, calls the generally 

 adopted notion of " linear amplification at a certain distance " a 

 "very awkward and irrational way of defining the amplifying 

 power of a lens or a lens-system," and wishes to change it for 

 another one. Accordingly he defines the amplifying power as the 

 tangent of the visual angle, under which the unit of length is 

 shown through the optical system. 



As far as I can see, however, there is no great advantage in 

 this way of defining the " power " in question, or rather, I think, 

 the old way is preferable. 



First, I must point out that according to my view the definition 



