Dr. G. J. Stoney on Microscopic Vision. 333 



by microscopes ; and has usually been called the Diffraction 

 Theory, because it gives a special prominence to the fact that 

 when we pass beyond the meagre hypotheses of geometrical 

 optics, we find that diffracted light* is " the machinery by 

 which good definition is brought about. " It was undoubtedly 

 desirable to emphasise this fact, because an error prevailed 

 and is not yet extinct that diffracted light intervenes only to 

 impair the image ; and it can scarcely be made any objection 

 to the name that it runs counter to this error. As, however, 

 both processes are only methods of investigation, it would 

 perhaps be desirable to avoid calling either of them a theory. 

 On this account, and to avoid cavilling about mere names, 

 the two methods of investigation are in the present memoir 

 distinguished as the Airy and the Abbe modes of pro- 

 cedure f. 



3. In a recent paper by Lord Rayleigh the generality of 

 Abbe's method seems not to have been appreciated (see Phil. 

 Mag. for last August, p. 167); and the main object of the 

 present communication is to offer a fuller account of this 

 generality than the writer has elsewhere given (see " On the 

 Foundation of the Diffraction Theory " ; ' English Mechanic ' 

 for December 13, 1895, p. 380), and to trace its consequences. 



4. Two terms have been used above in the first paragraph 

 which need to be defined. 



(a) By a physical point is to be understood an element of 

 the volume of the object (if the object be translucent), or of 

 its superficial layer (if it be opaque), which element of volume 

 is small enough to justify us in substituting for it in our 

 investigation a mathematical point regarded as a centre of 

 an undulation of hemispherical waves. The physical point is 

 small enough for this use of it, if its linear dimensions are in 

 any considerable degree less than X/4, where A. is the wave- 

 length of the light employed. To give definite form to our 

 conceptions we may suppose its dimensions to be comparable 

 with X/10. This is a convenient size ; since if an opening of 

 this size were made in a thin opaque screen, and if a pencil 

 of light were incident from any direction upon it, the hole is 

 small enough to ensure that the light which gets through 

 shall spread on the other side of the screen in the form of 



* Light which advances in other directions than those prescribed by 

 geometrical optics is called diffracted light. 



t Lord Rayleigh suggests the name Spectrum Theory for the method 

 of investigation which proceeds by resolving the light into plane waves ; 

 but will perhaps not press this name on the acceptance of scientific men 

 when he finds that the limitation which the name implies has no existence. 



