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Transactions of the Society. 



meters proves that differences of phase of tens of thousands and in 

 some cases even of millions of wave-lengths do not prevent regular 

 interference ; and as in microscopical optics the differences of 

 phase that have to be reckoned with amount at most to a few 

 hundred wave-lengths, we need have no fears in that direction. 

 These were the considerations which led Professor Abbe to drop * 

 the restriction of his diffraction theory to small objects which he 

 had mentioned in his paper of 1873, and to claim instead that his 

 theory really applied to all objects which were seen by borrowed 

 light, in his own words : " even to fencepoles." 



We now proceed to deduce the resultant of the combination of 

 different portions of the light from a common source when there 

 are differences of phase between them, on the principle stated 



Fig. 75. 



above — that the resulting disturbance is the algebraical sum of 

 all the contributing portions. It is evident that if we can combine 

 two disturbances, we have the means of combining any desired 

 number by repeating the process the necessary number of times. 

 Hence the case of two combining waves is of especial interest. 



The easiest solution is a graphical one. In fig. 75 let X and Y 

 be the two waves to be combined, the difference of phase being 



* The " disclaimer" here referred to was first published by Professor Abbe in a 

 paper of 1S80, which is reprinted in " Ernst Abbe, Gesammeltc Abhandungen, Jena 

 19(14." Hero, on page 290, we read : " Froin my present standpoint I must there- 

 fore abandon the distinction of two modes of microscopical imape-formation existing 

 side by side, and also the assumption of any kind of direct image-formation except in 

 the case of self-luminous object*. Even fencepoles have their images formed by a 

 secondary process after the same manner as bacteria and the most delicate diatom- 

 structures." And there is a footnote which states : " But this is the only point on 

 which I have to correct my former explanations." The italics are Abbe's, and the 

 translation is as nearly literal as is possible. 



