458 MR. A. FOWLER ON THE SPECTRUM OF MAGNESIUM HYDRIDE. 



It will be seen that, apart from the influence of a probably compound line, the 

 second differences are sensibly constant throughout the range of visibility of this 

 short series. In the case of the longer series the second differences diminish in 

 passing from the heads, and they are apt to be less regular in the more refrangible 

 parts of the nutings because of the greater overlapping of different systems and the 

 conseqiient uncertainty as to the wave-lengths of the components of the unresolved 

 lines. 



Some of the formulae which have been suggested for the mathematical represen- 

 tation of series have been tested on series identified in the green fluting. In place of 

 the oscillation frequencies which should strictly have been employed, all the calcu- 

 lations have been made in terms of wave-lengths. In short series the possible error 

 introduced in this way is inappreciable, and some of the equations used are of the 

 same form whether frequencies or wave-lengths are used. 



DESLANDRES' simple formula 



\ m = abm 2 , 



where A. is the wave-length, a and b are constants, and m has integer values, is quite 

 inadequate for the magnesium hydride series. 



