514 SUMMARY OF CUBJRENT RESEARCHES RELATING TO 



incut how the brightness of diffracted light may be estimated, and on 

 what view of the nature of light-propagation it is possible to explain the 

 appearance of diffracted light in the region of the geometrical shadow, 

 the lecturer gave a short review of the history of perioptrics. Grimaldi, 

 in the middle of the seventeenth century, was the first writer on the 

 subject, but his results were of no particular value, because he did not 

 succeed in determining the essential nature of diffraction. Newton, in 

 his " Opticks," was aware of the incompleteness of his own researches, but 

 the " queries " which he propounded for others to solve were so worded 

 as to suggest that he thought gravitation was responsible for the bend- 

 ing of light-rays round bodies, especially when in close proximity. 

 Newton's influence in this department of physics was predominant for 

 150 years, although Huyghens had laid the foundation for the next 

 step in advance by explaining that the propagation of light is due to 

 the interference of wave-impulses starting from the surface of a wave- 

 front. In 1816 Fresnel contributed to the French Academy his cele- 

 brated exposition of the law determining the form of the diffraction 

 pattern. As he dealt only with unfocused light, the diffraction pattern 

 deducible by FresnePs own method is that at infinity. The first writer 

 to explore the phenomena of diffraction in the focal plane was Fraunhofer, 

 whose paper on the subject was contributed to the Berlin Academy 

 about the year 1830. Curiously enough, although Fraunhofer was 

 writing ten years after Fresnel's great paper, he seems to have been 

 unaware of it. The work of Fresnel and Fraunhofer in a manner, 

 somewhat unsystematically, covered the whole field of diffraction 

 phenomena, but they left one very important region of it undeveloped, 

 viz. the diffraction pattern of a circular aperture. This practical 

 problem was simultaneously solved, in 1835, by Airy in our own country 

 and by Schwerd in Germany. In 1873 Helmholtz, by a very bold and 

 elegant generalization, brought the Fresnel and Fraunhofer phenomena 

 into a mutual inter-dependent relationship by proving that the diffrac- 

 tion image in a focal plane is simply the conjugate to that image at 

 infinity. If, then, we know what is the image at infinity which any 

 given aperture will yield, we have only to apply the law of optical pro- 

 jection, and thereby determine its image in a given focal plane. .Strangely 

 enough, Helmholtz' demonstration has not yet found its way into the 

 text-books, and notwithstanding the value and elegance of the theorem 

 it is still practically unknown to writers on the subject of perioptrics. 



Although the theory of the diffraction image is now in a sense com- 

 plete, it still lacks practical handiness. The mathematical difficulties of 

 integration are very considerable, but the lecturer suggested a method 

 whereby, if the enveloping surface of the aplanatic cone were taken as 

 the radiant surface, the process of integration coiild be much simplified ; 

 and in the most important case, that of a circular aperture, nothing more 

 abstruse than trigonometrical functions would be required. 



Accurate Measurement of the Refractive Indices of Minute 

 Crystal Grains under the Petrographic Microscope.* — F. E. Wright 

 discusses this subject, and the following is his summary of his remarks. 



* Washington Acad. Sci., v. (1915) pp. 101-8. 



