258 M. Fraunliofer on the Laws 



any two intermediate spaces, namely s ; and that if the spectra 

 are to be homogeneous these spaces £ must be perfectly equal 

 throughout the system of lines. If these distances are une- 

 qual, the larger g will produce smaller spectra, and, on the con- 

 trary, the smaller s large spectra, which, according to the de- 

 gree of irregularity, will mingle with each other with great 

 irregularity ; heterogeneous colours can be no longer seen ; and 

 the light in the white room must be white, as is confirmed by 

 experience. It is, however, interesting to know what pheno- 

 mena would arise if the magnitudes of the intervals were re- 

 gularly unequal, that is, if the inequality of the distances, 

 whatever it may be, is regularly repeated in equal parts. For 

 this purpose I have etched parallel lines in various ways regu- 

 larly unequal upon several plates of glass covered with gold 

 leaf. I can in this place only mention briefly some of the re- 

 sults of these experiments, which must be further prosecuted. 

 The spectra which are seen through this system of lines by 

 means of a telescope, consist of homogeneous light, and their 

 fixed lines are most clearly perceived, so that their distances 

 or divergences from the axis can be most accurately measured. 

 If the distances between the centres of the intervals of regu- 

 larly uneven systems of lines are expressed by s', s" and so forth, 

 and if one of the equal parts which consist of unequal s ^s, is 

 expressed by s' -|- s" -|- g"' . . . . -|- g" then, according to the re- 

 sults of the experiments with light incident vertically, the dis- 

 tances of the various spectra from the axis will be represented 

 by the following equation : 



sin ^ ^"^ = 



g:_l_ g" + s'" ^ g-^ 



The spaces g, however, in the division consisting of unequal 

 parts, which is represented by the divisor of the equation, may 

 succeed each other, even if some among them are equal, still the 

 equation remains always the same, but only when this division 

 cannot again be divided into smaller ones, in which the spaces 

 £ succeed each other exactly in the same order. This pheno- 

 menon produced by irregularly unequal lines is remarkable 

 on account of the proportional intensity of the various spectra, 

 upon which, however, nothing general can be deduced in this 



