781 
three the point P, must coincide. Consequently ? must lie on the 
line @ QQ". 
Thereupon we turn the rods of Mappox in the trial-frame about 
90° and now move the flame along the line Q QQ" or its prolon- 
gation. At a given moment the red line will again apparently be seen 
in Q. This point is marked and will, as can easily be understood, 
be the point P we were in search of. 
How are we now to describe more accurately the position of the 
point P, which we have found, or the direction of the line of regard > 
For this purpose we can follow two ways. In the first place we can 
express the direction of the line of regard in its abduction or adduction 
and in its deorsumduction or sursumduction. 
By abduction and adduction we understand the smallest angle that 
the line of regard makes with the sagittal plane. If now we seek a 
formula for the abduction (A), then we shall eall OF positive, when 2 
OR 
Va? + PR 
If OR is negative, then fg A is negative and there exists adduction. 
by deorsumduction or sursumduction we shall understand the smallest 
angle that the line of regard makes with the horizontal plane. If 
now we seek a formula for the deorsumduetion (D) we shall call 
PR positive, when / lies under the horizontal line, so that the 
PR 
formula is: ig D= 
: Va? a ON 
If PR is negative (as in the Fig. 1 and 2) then fy D is negative, 
and there is sursumduction. We have not to take account here of 
angles larger than 90°. If we wish to indicate the position of the 
line of regard in the manner as Hermnorrz has taught us (inclination 
of the plane of regard) then the deorsumduction is expressed by the 
PR 
formula: ig D’ = —. 
a 
lies temporally from Q, so that the formula is: fg A = 
A second method of describing the direction of the line of regard 
is the following one. In the first place we can calculate the angle, 
that the line of regard in the position we have found, makes with 
the line of regard in the primary position, and afterwards the angle 
that OP makes with OR. We shall call these angles respectively 
OP V PR?+-OR? 
ZH and / a: For / H the formula is :ig = — = —— Ly, 
a a 
. N EN 3 PR PR 
For / « the formula is sin a = ————— and ig a.= —.. 
V PR?+ OR? OR 
As « can have all values from 0° to 360° we shall agree, that 
