( 56 ) 
if Dor B lie in a plane through two principal directions, theri 
© or H lie in a plane through the two corresponding reciprocal 
principal directions. 
In order to facilitate somewhat what precedes a transformation 
of affinity may be applied, in which O remains fixed and the 
magnetic ellipsoid is transformed to a sphere with radius = 1, a 
transformation which we shall lateron apply frequently. If we take 
the magnetic principal axes as coordinate-axes, the transformation is 
represented by the formulae: 
a oy Hr y=yV Uy Jey. ../ ae 
if wrat + yy? + ze? =1 is the equation of the magnetic ellipsoid 
on its axes. By this transformation the electric ellipsoid becomes 
an ellipsoid with bj, bz and 6; as axes. Now we transform also the 
wave-front and the electric and magnetic induction (but not the 
electric and magnetic force). Now, in the transformation the relation 
of conjugate diameters is preserved, so that the magnetically conjugate 
diameters pass into mutually perpendicular lines. So the three prin- 
cipal directions pass into the axes of the transformed electric ellipsoid, 
and the section of similitude into a circular section of the transformed 
electric ellipsoid. 
7. The normal to the wave-front being perpendicular to the 
electric and the magnetic induction, we have: 
l m n 1 
————— —— 
ge—hb ha— fe iS ga A 
If this is substituted in equation (27), we find: 
v 9 Pp r 
A=—(ae+bfpticy)=—.8a Ue 
8 s 
We find the same, if we substitute in (28) and (29), but if we 
substitute in (50), (31) or (32), we find: 
As af PAGO Lee eae 
8 8 
If U is the total energy per unit volume, we find: 
aa-bPptey=fP+9gQ-sRainUS=82U,.=38 70, . (sn 
