( 473 ) 
where the elements of the last row are respectively in the four cases : 
6(b,b>'), 12b,b9, —(b,b,+2bym), Wb, bam, —2b,b,, be 
3 4) AS 0 
6(b,b9'), Sheba, —b,b,, Wibe bom, bom, —2b,7, b,d,, 0 
34? 
6(5,b,'), 0, —b,b,, 20,2, b,(m—6b,), bom —2),b,, b,b,, —3b3b, 
6(b,b,'), 0, —b,?, 2b,b,, b,(m—6b,), —2b,b,, b,b,-+2bjm, —12b,b, 
OE AS 
6. Following the same way in the general case, we obtain for 
Ht, the quotient of two determinants each of order 2n-+1. If we reduce 
these as before, the denominator will be seen to be independent of 
4 and u; and the numerator will only contain the quantities 
Unie Un—2-- By, Hy in two columns. Now pa, Un—2,-- U, may be 
expressed as linear functions of u,, and this proves at once that the 
numerator must be a polynomial of the second degree in u. If, 
therefore the necessary conditions are satisfied, the quantity u, is an 
integral of an equation of Rrccarr. The substitution which reduces 
the given differential equation to this equation of Rriccarr will then be 
found from 
gr Frit IH =9 
by determining wn—1,---U, in function of u, and expressing u, in 
function of y. 
Physics. — “The law of shift of the central component of a triplet 
in a magnetic field.” By Prof. P. Zeeman. 
In two communications to this Academy *) on “Change of wave- 
length of the middle line of triplets’ I gave conclusive evidence 
obtained by means of MrcnersoN's echelon-spectroscope that the 
central line of some triplets is shifted. The fact of this displacement 
was established simultaneously with my own observations by 
GMELIN?) and JAcK*). GMELIN first gave the law of shift in the case 
of the mercury line 5791. According to him the change of wavelength 
under consideration is proportional to the square of the magnetic force. 
In the second part of a former paper on “Magnetic resolution of 
spectral lines and magnetic force” measurements concerning the 
asymmetrical resolution of the mercury line 5791 are given“). 
1) P. Zeeman. These Procedings February 1908, April 1908. 
2) Guus. Physikalische Zeitschrift. 9. Jahrgang S. 212—214, 1908, 
8) Jack see Voter. Magneto-optik. S. 178. 
4) ZEEMAN. These Proceedings November 1907, 
