414 Mr. R. T. GUazebrook on 



The conclusion may be drawn from figs. III. and IV., that 

 both in water and in the saponine solution the effect of the 

 surface disappears when the edge of the disk is about a milli- 

 metre and a half below it. 



We cannot conclude without expressing our sincere thanks 

 to Prof. Eucker for his kind assistance in our experiments. 



LXII. On Curved Diffraction-gratings. By R. T. Glaze- 

 bkook, M.A., F.R.S., Fellow and Lecturer of Trinity Col- 

 lege, Demonstrator at the Cavendish Laboratory, Cambridge* . 



PROF. ROWLAND has described the appearances pre- 

 sented when a beam of light, after passing through a 

 slit, falls on a grating ruled on a cylindrical surface, and has 

 given a very elegant construction for determining the position 

 of the diffracted foci in the case in which the principal section 

 of the grating is a circle and the source of light is placed at 

 its centre of curvature. The mathematics of the subject have 

 been dealt with still more recently by M. Mascart (Journal de 

 Physique, January 1883) and Mr! W. Baily (Phil. Mag. 

 March 1883). The object of the present paper is to carry the 

 discussion somewhat further. 



Prof. Rowland claims for his gratings that they enable him 

 to form a pure spectrum without the use of lenses, and hence 

 have an immense advantage over those hitherto employed. It 

 must, however, be remembered that the formulae obtained to 

 give the position of the diffracted spectra are only true to a 

 first approximation, that the spectra formed and the source of 

 light are to one another in the relation of the conjugate geo- 

 metrical foci of a lens or mirror. All the waves which arrive 

 at any one point of the spectrum are not in exactly the same 

 phase. Aberration effects are produced, and have to be con- 

 sidered just as in the ordinary theory of lenses or mirrors. Now, 

 if a plane wave of light fall on a plane grating, and the effects 

 be observed on a screen at an infinite distance behind the gra- 

 ting, the spectrum formed is perfectly pure ; all the red light, 

 after passing the grating, is definitely brought to a focus at 

 one point ; there is no aberration, so far at least as the gra- 

 ting is concerned. Of course the difficulty is to obtain the 

 plane wave and the screen at an infinite distance. If the 

 source of light be placed at the principal focus of a col- 

 limating lens, the emergent wave differs from a plane by 

 quantities depending on the aberration of the lens ; while if 

 the diffracted beam is received on a second lens and a screen 



* Communicated "by the Physical Society ; read April 14, 1883. 



