51 
§ 2. We now come to the question, how to obtain the knowledge 
of the desired data. Various attempts have been made to define the 
angles between the macula-planes and the planes of the semicircular 
‘canals, by direct measuring either on casts from the labyrinth, or 
on enlarged models of it. We shall more fully refer to this elsewhere. 
Suffice it to say, that according to our opinion, the question put 
here, first of all lends itself to a mathematical treatment, as it 
guarantees a great deal of accuracy. Let us first discuss that which 
refers to the position of the planes of the semicircular canals, later 
on that which refers to the position of the Macula-planes. 
A. The planes of the semicircular canals. 
The first difficulty which offers is that a plane of a semi- 
circular canal in general does not exactly lie in one level. Apart 
from the thickness of the tube, the semicircular canals show a diverg- 
ence from the level plane, which may perhaps best be indicated 
by the term “swaying”. In our determination no account has been 
taken of this factor however; we have been contented with charac- 
terizing a plane of a semicircular canal by taking three fixed points. *) 
Two of these points coming into consideration for the determi- 
nation of the plane of the semicircular canal are obvious, they are: 
point a, the place where the semicircular canal runs into the 
utricle, 
point 6, the place where the ampulla narrows into the actual 
semicircular canal. 
The third point (c) must be determined on the circumference of 
the semicircular canal. In order to get to work systematically, this 
point was taken at an equal distance from a and 5, with all semi- 
circular canals, measured on the circumference. 
In Pl. 2 a semicircular canal is shown; the plane through the 
points a, 4, and c of this semicircular canal is plane S. Plane S 
-euts the interperpendicular planes of projection of P,, P, and P, 
along the lines S,, S,, and $,. 
The distances between the points a, 6, and c to the three planes 
of projection (being the projections from a, 6 and c) are known, as 
will be expounded later on. This enables us to determine the pas- 
sages of plane S, by means of the method usual in descriptive geo- 
1) Greater accuracy may be obtained in this respect. With the aid of analytic 
geometry one can attain the determination of a plane, which takes into account 
the swaying of the semicircular canal and consequently gives us the position of 
it more accurately. 
