The Hclmlwltz Theory of the Microscope. By J. W. Gordon. 389 



importance. This problem Helmholtz attacks, and his solution of 

 it constitutes, as I venture to think, the real merit and the very 

 great merit of his paper. Yet the law disclosed by him appears to 

 be still unknown to those whose business it is to explain these 

 things, and you will look in vain in the text-books for any exposi- 

 tion of the fundamentally important propositions in which he 

 embodies it. Of the practical importance of the conclusions which 

 Helmholtz reached you will this evening have the opportunity 

 of judging for yourselves. 



In order to lay the foundation for his theory, Helmholz com- 

 mences by giving two proofs of what is now known in optics as 

 "the sine condition." He first formulates it thus, subsequently 

 modifying the formula by substituting the sine of the divergence 

 angle for the divergence angle itself. As it stands here the pro- 

 position is due to Lagrange ; as modified by substituting the sine 

 for the angle it is due to Helmholtz.* 



"The product of the divergence angle of a given ray, the 



Fig. 80. 



refractive index of the medium in which it lies and the magnitude 

 of the image formed in that medium in which it comes to focus 

 remains constant in a centred system of spherical refracting 

 or reflecting surfaces after any number of refractions or reflec- 

 tions, provided that the conditions of correct image-formation are 

 satisfied." 



" It follows that this function has the same value when the 

 ray has left the system as before its entry into the system." 



This is rather a formidable enunciation of a law which may be 

 very simply expressed in symbols and easily understood by the 

 aid of the diagram fig. 80. 



Here we have four successive images formed one from another 



* It is said that Prof. Abbe announced the sine law — withholding the proof 

 of it — some few weeks before the appearance of Helmholtz' paper. I have no 

 personal knowledge of this, having sought in vain for the announcement, and mention 

 the claim only lest it should be thought — as has indeed been suggested by some 

 of Prof. Abbe's friends — that I am doing an injustice to the Professor by not 

 importing the discussion of this matter into the preoent paper. 



