126 PROCEEDINGS OF THE SOCIETY. 



Mr. Gordon, by a succession of mysterious operations, succeeds in 

 arriving at the finite result which he covets. 



The proofs offered in support of the new ideas being thus found to 

 be absolutely worthless and absurd, all the conclusions drawn from 

 assumptions proved to be false necessarily fall to the ground. It may 

 only be added that the black and white dot phenomenon which Mr. 

 CJordon tries to claim as an experimental proof of his strange proposition 

 does not at all call for " conical wave-fronts " and " polyphasal anti- 

 points " in explanation. For on the basis of the usual theory it follows 

 at once, that when we go either within or beyond the true focus, the 

 wavelets from different zones of the object-glass will arrive with a 

 difference of phase in the new image plane, and will therefore interfere ; 

 and there must be a point on either side of the true focus where this 

 interference is complete, and results in a dark centre of the spurious. 



disc. . . 



Unfortunately, there are many statements in this paper which cannot 

 be allowed to pass unchallenged. 



First of all, we find a repetition of the absolutely unfounded assertion 

 that Professor Abbe had disavowed the theory of microscopical images 

 which bears his name,* and the reiteration is the more disingenuous 

 because Professor Abbe is unfortunately now unable to defend himself ; 

 and it is rendered more offensive than before by being advanced in the 

 form of a protest against an alleged misuse of Professor Abbe's name in 

 connection with his world-famous theory. 



The few statements by which Mr. Gordon tries to discredit the Abbe 

 theory only prove once more how completely he has misunderstood that 

 theory which apparently he has not studied in the only full and authentic 

 account, viz. that in Dippel's handbook. Incidentally, Mr. Gordon 

 refers to his " proof of the sine condition," which, as a matter of fact, is 

 no proof at all ; a postulate is put forward which, far from being " almost 

 axiomatic," is indeed manifestly absurd ; a wholly arbitrary diagram— 

 which has no ostensible relation to any lens system— is then drawn which, 

 by construction, implies a sine relation, and having thus drawn this 

 diagram, Mr. Gordon proves that it does indeed follow a sine law. Any- 

 thing whatever may be prqved by this method. 



As a matter of fact, neither this alleged proof, nor the claim that 

 the sine condition secured an extended and flat field, can be substantiated ; 

 all the valid proofs imply, directly or indirectly, the principle of the 

 minimum optical path (this was, I believe, first pointed out by Lord 

 Rayleigh), and are in consequence limited to an element of surface m the 

 optical axis. That objectives which fulfil the sine condition generally 

 have a sufficiently large field within which the definition is satisfactory, 



* The following sentence from the passage in Carpenter-Dallinger (pp. 64-G5. 

 of the eighth edition), on which Mr. Gordon relies, should alone sufiice to show 

 that Abbe, far from disavowing bis theory, claimed it as universally applicable :- 

 >• Theoretical considerations have led me to the conclusion that there must always be 

 the same conditions of delineation as long as the objects are depicted by means of trans- 

 mitted or reflected light, whether the objects are of coarse or of very fine structure. 

 Further experiments . . . have enabled me to observe the diffraction-effect and its 

 influence on the ima?e, viewing gratings of not more than forty lines per inch. 

 (The italics are taken from the original.) 



