57 
In order to determine the otolith-plane, this line in itself does not 
suffice, other data must still be got from the otolith-membrane. For 
this purpose we choose a section lying halfway between the two extreme 
points of the long axis. In such a section the otolith-membrane 
shows itself as a line; (Pl. 7 representing part of the section in 
D. 
Pl. 7. Utricle and Saccule from Pl. 6, by greater enlargement, 
o. m. otolithmembrane. 
Pl. 6, by greater enlargement); a line however not cutting the long 
axis (middle-line). For the otolith-plane we take a plane brought 
through the long axis, running parallel to the line last mentioned. 
For the construction of an otolith-plane we thus must know the 
projections of four points, taken from the otolith-membrane: first 
the projections of the extremes of the long axis; secondly the projec- 
tions of two points of the middle-line. The execution of this con- 
struction thus depends on constructing a plane through a given line 
(the long axis) running parallel to another line (the middle-line) 
which two lines do not intersect. From the four planes (left and 
right utricle and saccule otolith-planes) thus obtained, the angles 
which they form between them, are similarly determined, as has 
been described for the planes of the semicircular canals; the same 
planes of projection serve here. 
§ 3. The information required in § 1 can be got not only by 
means of descriptive geometry, but also by anothér mathematical 
method. 
If of each of two given planes three points are known by their 
coordinates, with regard to three planes, running perpendicularly, 
we are able to determine the angle between the two given planes, 
with the aid of analytic geometry. 
