120 STUDIES IN THE DIFFRACTION SPECTRUM. [MEMOIR VII. 



Selecting one of the fixed lines, that in the yellow 

 space, the sodium line D, for example, in the successive 

 spectra, it will be found that the distance which inter- 

 venes between it and the middle of the white image A' 

 is in the second double, in the third triple, etc., the dis- 

 tance it is in the first. These angular distances are des- 

 ignated as the deviations of the ray under examination. 

 Fraunhofer proved that 



(1) The deviation of the same ray, e. g., D, depends on 

 the sum of the width of a groove in the grating and of a 

 transparent interval, being in the inverse ratio of that 

 sum. 



(2) The deviation of any one of the colors of the spec- 

 trum of the first order, multiplied by the sum of a trans- 

 parent interval and a groove, gives the length of a wave 

 of light of that color. 



(3) The deviations of the same color in the successive 

 spectra increase as the whole numbers 1, 2, 3, 4, etc. 



(4) The deviations of two colors in the same spectrum 

 are to each other as the length of their undulations. 

 Hence in all the violet is nearest to A', and the red the 

 most distant. 



The undulatory theory gives a rigorous explanation 

 of all these facts. The lengths of the waves of light 

 have hence been most critically and accurately deter- 

 mined. 



We may now examine more closely the spectrum that 

 is nearest to A' the spectrum of the first order. Be- 

 ing completely separated from the others, it presents the 

 special facts most distinctly. At the point where the 

 light first becomes visible, the violet or inner end of this 

 spectrum, the wave-length of the incident radiation is, as 

 Angstrom has proved, 3933, and the wave-length of the 

 last visible radiation at the outer or red end is 7604, 

 ten millionths of a millimeter. If we accept the velocity 



