33G FOURTH REPORT — 1834. 



sion of I'lchly coloured diffracted images, which increase in 

 breadth and diminish in brightness, as they recede from the 

 centre. The firot pair of spectra are separated from the central 

 image by a space absolutely black, and a similar interval occurs 

 between the first and second pair. Fraunhofer observed, under 

 favourable circumstances, 13 such spectra on either side of the 

 central image. He has measured with great accuracy the an- 

 gular deviations of the rays of each colour from the axis ; and 

 he has found that the experimental laws thus deduced agree in 

 the most complete manner with the results of the principle of 

 interference*. The results ai-e the same, both by theory and 

 experiment, in the case of reflexion from ruled surfacesf . 



The optical phenomena of gratings are interet^ting in many 

 points of view. The appearance of lateral spectra, produced by 

 simply intercepting a part of the tight, proves that the light 

 actually diverges in all directions from the front of the grand 

 wave whei'e it meets the lens, and that it is to the interference 

 of this light with that intercepted by the grating that we are 

 to ascribe its want of sensible effect under ordinary circum- 

 stances %. Another very remarkable circumstance of these pheno- 

 mena is the purity of the light of each simple colour, which is 

 such that the fixed lines may be discerned in the spectra. The 

 distances of these lines, in the diffracted spectrum, are always 

 proportional, whatever be the diffracting substance ; while the 

 ratio of their intervals, or the breadths of the coloured spaces, 

 in the spectra formed by refraction, vary with the nature of the 



* The angular deviation, 6„ of any ray from the axis is expressed by the 

 formula 



sin 6„ = "Ll^ 

 t 

 in which n denotes the order of the spectrum, "K the length of an undulation, 

 and i the intei-val of the axes of the wires. The value of £ is obtained with 

 great precision, so that the measurement of the angular deviations of the rays 

 of each simple colour affords the most exact data for the determination of the 

 length of their waves. Fraunhofer has in this manner computed the lengths of 

 the waves, corresponding to the seven principal fixed lines in the spectrum ; 

 and the resulting values are perhaps the most exact optical constants we possess. 

 It Js a remarkable consequence of the expression above given, that when £ is less 

 than A, the angle d^ will be imaginary. In this case, then, there can be no coloured 

 spectra; and it follows that scratches or inequalities on any polished surface, 

 whose interval is less than the length of a wave, do not distiirb the regularity 

 of reflexion and refraction. 



t Fraunhofer's researches on diffraction are published in the Memoirs of the 

 Bavarian Academy of Sciences, vol. viii. A very full analysis of them is given 

 in the Edinburgh Encyclopcedia, art. Optics ; and in Sir J. Herschcl's " Essay 

 on Light," Encyc. Metrop. 



X Airy's Math. Tracts, p. 331. 



