If we use for n and 5 the exact formulae (19) and (20) - again 
confining ourselves to the case n = n 0 - we still find an imaginary 
value for the ratio -. We can therefore define a real angle in the 
n 
first quadrant by the equation 
_ „IL.(46) 
cos V 
and it is for the direction of propagation determined by this angle, 
that we shall perform the following calculations. 
It follows from (33) that the angle which we introduce now 
becomes equal to the angle originally denoted by the same symbol 
when we take for n and 5 their former values. These are a little 
different from those which we must now ascribe to these quantities, 
and therefore the direction of propagation assumed in our present 
calculation does not exactly coincide with the direction which we 
considered in the preceding article as tbs boundary between t e 
regions of the longitudinal and the transverse effect. The deviation 
of one direction from the other is, however, insignificant; it wil 
even be found to be small in comparison with the new terms that 
will now become of importance. 
We shall again begin with the determination of f. For this purpose 
we have to use equation (12), for which, on account of (4b), we 
may write 
l* _ 1 _ 2t ££ cos — £ 2 cos 2 = ± rf ? *1^- 2 
Here, the terms on the left-hand side, the only ones with which 
we were concerned in our first approximation, form a complete 
square, and this is the reason why we found two principal beams 
identical with each other. . , 
In the approximation now required we must retain the erms on 
the right-hand side, but it will suffice to substitute in them the 
values of g, q, g obtained in our former calculation. Distinguishing 
these by the index 0, we get the following equation for g 
g + i; ms ± v'- h’n. ms ’ ~ S.S.’«»’ + 
As to the three quantities g„ n» £•> ,he last of ,hem 
(25), and we have, in virtue of (46), 
(47) 
; given by 
