572 DR J. HALM ON 
It may be shown that an interesting geometrical relation exists between the 
line-series belonging to the same m-group. Jf, in fig. 1, the points a,, a. :. am, 
are fixed upon the straight line AB so that the distance Aa, =(m+ )?, and if from 
any point O outside this line we draw the straight paths Ov, Ov, , Ory... Orn . q 
Ov. , through A, a, a... dm... ao, any line-sertes belonging to this particular 
group, which has been arranged oe a transversal line CD so that the distane € 
Fic, 1. 
the spectral lines fall exactly upon the rays Ov, Ov,, Ove... . The proof of this 
theorem is very simple. If the dotted line, CH, be drawn parallel to AB, we have: 
and generally 
CO 
Sea en, S 
04% =z (17 + ) 
