LYMAN. — THE FALSE SPECTRA FROM DIFFRACTION GRATINGS. 47 



served " ^host." The former seem due to a so-called periodic error in 

 the grating ruling, an error which operates to displace every groove in 

 the grating surface by an amount depending on a sine function of the 

 position of the groove. It seems probable that the false spectra are due 

 to an error of another type. Here the error operates to displace one, 

 out of a given number of grooves, slightly, leaving the remainder in their 

 proper positions. In order to make theory and the observed facts agree, 

 this error must be considered somewhat irregular over the surface of the 

 grating. While the theories proposed by C. S. Pierce and Rowland ac- 

 count in every way for the phenomenon of ghosts, they do not either 

 qualitatively or quantitatively account for these false spectra, whereas 

 the theory proposed by Runge, and given above, explains the phenomena 

 qualitatively and very nearly quantitatively. That is to say, it explains 

 the production of lines far from the parent line, lying entirely on one side 

 of it; it explains their relative intensity, aud it explains very nearly 

 indeed their exact position. The maximum departure between the 

 positions of these false spectra demanded by the theory and observed 

 in the plates is not more than .4 Angstrom units. This is slightly 

 greater than the maximum difference found between sets of observa- 

 tions ; but it is to be remembered that the measurements depended upon 

 the wave-lengths of the parent group and upon the comparison iron 

 lines, both of which are borrowed data. 



Jefferson Laboratory, Harvard 

 University, 1903. 



