783 
stration, that /’ PP" is a line, that is observed by the examined 
eye as horizontal, i.e. forms an image on the horizontal meridian 
of the retina. If now we represent to ourselves a plane through the 
horizontal meridian of the retina and P’ PP" and likewise a plane 
through OP and the meridian of the retina corresponding with it, 
then in normal cases, the angle between these 
two planes must be equal to / POR. We 
must however. take into consideration, that 
the angle between the mentioned planes is 
not expressed in the angle OPT, because the 
wall does uot stand perpendicularly to the 
secant line of the two planes, namely the 
line of vision (coinciding nearly with the line 
of regard). If we represent to ourselves however 
a plane in 7 perpendicular to tbe line of 
regard and further a globe constructed with P as central point and 
PO as radius (vide Fig. 4) then it is easy to see, that in the 
rectangular spherica: triangle ST" 7’ tg SPT’ = cos Stg SPT or 
cot O' PT'.= cos A cot OPT. 
If we call “~ OPT'= / B, then the difference between “ pand 
/ POR indicates the rotation we wanted to find. 
tg POR—tgp — PR- ROtgg 
EU Zet 
a { ln 1 + ty POR tg 2 ~~ RO+ PRtgB 
OPT oe es 
andes top == on the rotation (R) is expressed by the formula 
PR cos H—RO tg OPT 
RO cos H ze PRtg OPT’ 
Consequently we have to calculate ty OPT. If we no longer 
regard 7’ as the point of intersection of ?’ P?" with the spherical surface, 
but as the point of intersection of PP” with the. perpendicular 
ry) 
ty k= 
io PP" passing through O, then: tg OP?= are 
We must however carefully pay attention to the marks (+) 
in order to find the exact value for the rotation. In concurrence 
with the first part of the investigation we shall call PA positive, 
when P lies under the horizontal line and RO positive when /è 
lies temporalward from the vertical line. If now -we express 
/ POR in its tangent, tg POR is positive, when P lies under the 
horizontal line and temporalward from the vertical line or over 
the horizontal line and noseward from the vertical line. 
We shall likewise call O7' positive when © lies under the ee 
50 
Proceedings Royal Acad. Amsterdam. Vol. XIX. 
