110 M. Fraunhofer on the Laws 



The aggregate observations with both systems of lines are 

 very nearly represented by the following equation : 



(II.)sin.aW=^. 



With rays falling vertically the sines of the deviation of a 

 coloured ray from the axis in the different succeeding spectra 

 are as the numbers 0, 1 , 2, 3, &c. * 



The system e = 0,0005919 has the peculiar property, that 

 all the spectra produced by it on one side of the axis have more 

 than double the intensity of those which lie on the other side 

 of the axis. The lines of this system are indeed visible with 

 a microscope, but no particular form can be distinguished. 

 I therefore suppose the reason may be, that, in etching, the 

 diamond point might have had such a position in respect to 

 the plate of glass, that one edge of each line must have be- 

 come sharp, and the other less defined ; and I believe that this 



• If the sines, and not the angles of deviation of a coloured ray in the 

 different spectra had not been in the proportion in question, then through 

 the finer systems of lines on glass, where D'= 10° 14' 31", D" = 20° 29' 2", 

 but, according to the experiment D" = 20° 49' 44", consequently by 20 

 minutes more, the sines of the angles have on the other hand this pro- 

 portion. In the seconds we still meet in the calculation with a small dif- 

 ference, which is, however, too great to be attributed to an error in the 

 observation. Whether this difference is to be looked for in a small imper- 

 fection of the lines, or lies in the nature of these phenomena, may be de- 

 termined by a greater number of experiments with different very fine sys- 

 tems of lines. I do not here, however, give the angles quite faithfully, as 

 I obtained them by the experiments without allowing a correction. I 

 had repeatedly determined these angles, and each time by six repetitions ; 

 and in the lighter colours I obtained almost constantly the same angle ac- 

 curate to a second ; nevertheless, small constant errors might produce the 

 above difference. 



