1366 
Some objections can however be raised against the results com- 
municated by VorkMANN and afterwards reproduced in the literature, 
namely : 
1. Too little attention is constantly paid to the fact that the 
figures supplied by VorkMANN are only averages, and that the 
extremes sometimes differ considerably. These extremes are not the 
consequence of errors made in the mensuration or calculation, but 
originate in anatomical individual oscillations. 
2. Voukmann’s calculation of z; from x; and y; is not exactly correct, 
as he has not sufficiently paid attention to the fact, that the center 
of rotation lies 1,29 mm. behind the central point. The formula used 
by him z= V tid ought to have been z;=| PS =o); 
in which 7 is the radius of the globe. 
3. The calculation of y, is very complicate and is found by the 
calculation of a great number of averages, so that it is very doubt- 
ful whether great signification may be attributed to a value obtained 
in this way, even if the mensurations are made in 30 cases. 
The first objection may be met by taking likewise account of the 
extremes in the succeeding calculations. The second objection requires 
only that the calculation is made a second time. The third objection 
can likewise be met in a degree by introducing a simpler calcula- 
tion from the data supplied by VoLkmann himself. VoLKMANN namely 
has measured with 33 different eyes the angle between the y-axis 
and the direction of the tendon projected upon the horizontal plane 
going through the center of rotation. For this he found: 
minimum: 40°10’, maximum: 61°3', average: 47°24’ 
VoLKMANN remarks here emphatically, that the probable error 
of his determinations amounts to only ‘/,,,, and that consequently 
the important difference between the two extremes proves, that 
the location of the m. obliquus superior and the mechanical opera- 
tions resulting from it, are subject to very great individual oscillations. 
If now we know z;, y; and «,, then it is very simple to calcu- 
late y, by means of the mentioned angle, which we shall call hence- 
forth “q, according to the formula y, = (7;—.,) cot. q + #- 
With the help of the minima, maxima and averages for #5, y; and q¢ 
we can now likewise calculate for y, a minimum, maximum and 
average. The results of the mensurations of VoLKMANN, somewhat 
modified on account of my considerations and calculations, are the 
following ones: 
v;: min. 0.5 mm., max. 5.5 mm., average 2.9 mm. 
i 
yi: min. —1.71 mm., max. — 6.71 mm., average — 4.41 mm. 
