474 Transactions of the Society. 



VIII. — On the Theory of Optical Images, with special reference 



to the Microscope. 



(SuPPLEMENTABY PaPEB.) 



By Loed Eayleigh. 



{Bead June 17th, 1903.) 



In the memoir, above reprinted from the Philosophical Magazine, 

 I discussed the theories of Abbe and Helmholtz, and endeavoured 

 to show their correlation. It appeared that the method of the 

 former, while ingenious and capable of giving interesting results 

 in certain directions, was inapplicable to many of the problems 

 which it is necessary to attack. As an example of this, it may 

 suffice to mention the case of a self-luminous object. 



The work of Helmholtz, to which attention has recently been 

 recalled by Mr. J. W. Gordon in a lively criticism (p. 381), was 

 founded upon the processes already developed by Airy, Verdet, 

 and others for the performance of the telescope. The theories 

 both of Abbe and Helmholtz pointed to a tolerably definite limit 

 to the powers of the Microscope, dependent, however, upon the 

 wave-length of the light employed and upon the medium in 

 which the object is imbedded. It appeared that two neighbours, 

 whether constituting a single pair of points or forming part of an 

 extended series of equidistant points, could not be properly dis- 

 tinguished if the distance were less than half the wave-length of 

 the light employed. The importance of this conclusion, as im- 

 posing a limit upon our powers of direct observation, can hardly 

 be overestimated ; but there has been in some quarters a tendency 

 to ascribe to it a more precise character than it can bear, or even 

 to mistake its meaning altogether. A few words upon this subject 

 may not be out of place. 



The first point to be emphasised is that nothing whatever is 

 said as to the smallness of a single object that may be made 

 visible. The eye, whether unaided or armed with a telescope, is 

 able to see as points of light stars subtending no sensible angle. 

 The visibility of the star is a question of brightness simply, and 

 has nothing to do with resolving power. The latter element enters 

 only when it is a question of recognising the duplicity of a double 

 star, or of distinguishing detail upon the surface of a planet. So 

 in the Microscope there is nothing except lack of light to hinder 

 the visibility of an object however small. But if its dimensions 

 be much less than the half wave-length, it can only be seen as a 

 whole, and its parts cannot be distinctly separated, although in 

 cases near the border line some inference may be possible founded 

 upon experience of what appearances are presented in various 



