1898.J MICROSCOPICAL JOURNAL. 95 



6. But considering now microscopic objectives, many 

 such have been made as short in focus as 1-50 of an inch. 

 It is impossible to regard light emitted from an object, 

 as consisting of uniform plane waves on arriving at the 

 surface of such a lens, after a path of, perhaps, 1-200 of 

 an inch ; except in the case of plane-wave illumination of 

 the object, as in the Abbe theory. 



H. Consider next the supposed dynamical system. 

 This is by hypothesis set up, not by the object alone, or 

 in ordinary method : " We begin by positing repetitions 

 of the objective lield." Then it is assumed that all these 

 replicas emit light from their similar points "the same 

 in direction, intensity, phase, and position of trans- 

 versal." This postulate seems altogether illegitimate in 

 a theory purporting to represent actual phenomena ; we 

 know that it is not true in physical reality. It, too, 

 depends for the qualified truth which it does possess, 

 upon plane-wave illumination; then it is true, so far as 

 that when approximately plane waves fall upon a grating 

 the width or number of lines does not affect the image 

 of the ruling, as ruling. But it seems to push the result 

 of certain mathematical expressions to an extent which 

 can hardly be justified. The ground of the immense pos- 

 tulate here objected to, lies in the fact that resolution 

 into plane waves of ether-disturbances set up by an 

 object, is represented by expressions which equally 

 represent replicas of the disturbances; the nature of cir- 

 cular functions involving this necessity. Mathematical 

 expressions are but tools, and often have the usual 

 defects of tools ; in particular that of not being sharp 

 enough. Ask these functions to express a given disturb- 

 ance and many surrounding replicas, and they will do it. 

 But ask them next to express an actual limited disturb- 

 ance resolved in this manner, and no more, and they 

 fail ; their edge at present is not sharp enough to do that. 

 Such failure, however, is in this case an imperfection ; 



