444 Transactions of the Society. 



Now if that plane be occupied by focal light compared to which all 

 neighbouring light must be feeble, we may be sure that the image pro- 

 duced by the focal light will not be greatly disturbed by the diffraction 

 from unfocussed wave-fronts. 



Note IV. — De. Fkipp's Teanslation of Helmholtz' Papee. 



Readers of Dr. Fripp's translation of Helmholtz' paper, referred to 

 in the headnote under the titles of the Monthly Microscopical Journal 

 and the Proceedings of the Bristol Naturalists' Society, should be warned 

 that the diagram which appears as the second diagram in that paper — 

 to illustrate equation (6) — is not in the original paper and is entirely 

 incorrect. Helmholtz postulates a small plane area for his object dS 

 and its plane image ds. Dr. Fripp has fallen into the error of trans- 

 lating the word Field lenelement used by Helmholtz by the word " point," 

 with the result that the entire passage relating to equation (6) is unin- 

 telligible in his translation. But as I am compelled to publish this 

 criticism of Dr. Fripp's work I trust that I may be allowed to add that 

 this one is, so far as I know, the only serious blot on a piece of trans- 

 lation which is otherwise admirable, both for accuracy of rendering and 

 for felicity of style. 



Note V. — Note to Page 419. 



A diffraction grating produces not one only but three diffraction 

 fringes on three different scales of magnitude. The broadest, which 

 may be called No. 1, is due to the single bright line of the ruling, and 

 its breadth is inversely proportional to the breadth of that line — the 

 luminous component of the grating. But this diffraction fringe is so 

 masked by the other two as to be scarcely discernible. Fringe No. 2 

 is the most conspicuous of the three. It is proportional inversely to 

 the breadth of the grating element consisting of one bright and one 

 dark component, and it passes from maximum to minimum brightness 

 in an angular breadth comprising one half set of phase values. In the 

 common case, therefore, of a grating with bright and dark lines of equal 

 breadth, the breadth of fringe No. 2 is one-fourth part of the breadth of 

 fringe No. 1. It is a comparatively brilliant object, and is commonly 

 spoken of as the fringe formed by its grating. Fringe No. 3 is formed 

 by the entire surface occupied by the grating operating as a single 

 aperture. It is inversely proportional to the whole diameter of the 

 grating, therefore, and its breadth has no definite relation to the dimen- 

 sions of the other two fringes. But, as a rule, it is microscopically 

 small, and for that reason it is usually ignored altogether. But when 

 the question is one of testing by experiment the resolving power of a 

 given antipoint the presence of this minute diffraction fringe cannot be 

 ignored, if it be present, for it will itself be the principal factor in 

 determining the state of resolution of the resulting image. 



