( 337 ) 
the rule that the vector 21 describes equal areas in equal times; 
consequently, the velocity of rotation is greatest when the vibration 
has the direction of the minor axis of the ellipse. 
Let x be the angle between the vector ’21 and the axis of x'. Then 
the above formulae give the following value for the rotation of the 
plane of polarization per unit of length 
jg._ V sinoy _ , . . . : . (45) 
dz' 1-b coso) cos (2</>*' + co) 
an expression that is constant only for # = .0 (o> = 4 n). For any 
other value of the angle & we may also consider the mean value 
of the rotation. As the vector '21 makes a complete revolution while 
z' increases by 2 ~, we find for this mean rotation 
* 
n n 0 fi 0 2pv cos & sinv > 
V+? * 
It takes the value (27) for & = 0 (to = 4*r) and vanishes for (*>=0). 
It must be noticed that, even in the neighbourhood of this latter 
direction of propagation, whereas the mean rotation per unit of length 
becomes very small, the rotation — may very well have an appre¬ 
ciable magnitude, if the direction of vibration be properly chosen. 
In fact, the maximum value of (45) is 
i!> sin to n 0 p 0 608 & cos * ^ 
rzr c ^1 ,r 
and this can be of the same order of magnitude as (27), even for 
a value of & very near ^({0 = 0). 
The ellipse described by the extremity of the vector 21 is similar 
in form and position to the characteristic ellipse ot which we have 
spoken in $.8. 
$ 10. Summing up the above results (and always confining our¬ 
selves to the particular frequency n 0 ) we may say that in the interval 
between &z=& l and # = £ n the phenomena are in the main of 
the same kind as the true transverse ZEKMAN-effect that is observed 
at right angles to the lines of force; the principal beams present a 
rectilinear polarization and differ from each other by their indices 
of absorption, whereas the velocity of propagation is the same for 
both of them. For values of & smaller than ^, on the contrary, 
the effect is similar to the true longitudinal one. In this interval it 
