778 
right of À m2 or to the left of we are at once confronted with 
the fact that the observed values depart widely from the theoretical 
curve. The natural conclusion is that for wave-lengths less than A ml 
and greater than the rotation ip in the yellow band ceases to 
be exclusively controlled by the vibration 
(7) A 0 = 5,63.10" 5 cm 
to which that particular band is due; and the significant fact that 
another strong absorption band in the blue is shown by the solu¬ 
tion tends considerably to strengthen the presumption put forward. 
A definite step towards an explanation of the failure of the 
mono-electronic equation would be taken if we succeeded numeri¬ 
cally to trace the effect of adjoining absorption bands on the rota¬ 
tion within a given band. If we suppose, as I think we may. that 
the effects due to various vibrations can be simply superposed, we 
can write by equation (10) of Art. 4. — 
where A 0l refers to the vibration to which the band dealt with is 
due and i 02 , À 03 etc. are the corresponding characteristic wave¬ 
lengths of the adjoining bands. We have now to ascertain whether 
the differences between the observed values of ip and those calcul¬ 
ated on the mono-electronic hypothesis are amenable to the law 
embodied in formula (8). Suppose, as a legitimate approximation, 
that the series on the right-hand member of (8) can be restricted 
to one term only, on either side of the absorption band; the proce¬ 
dure is then much the same as before. We may conveniently have 
recourse to a graphical method. In Fig. 2. (p. 777) the ordinates 
of the curve bbb are equal respectively to the differences between 
the ordinates of the «observed» curve (obs.) and the former «mono- 
electronic» curve (aaa). The curve bbb having been drawn, it re¬ 
mains for us to examine whether its march can be correctly 
indicated by an expression of the form 
( 9 ) 
A (V - 4?) 
(*-4,*)» + A**' 
To take an example: in the case of M. Cotton’s solution with 
which we have dealt in the present Article, an inspection of the 
