(a) 
€ 
3 
It is easy to see that the areas 0 (2) ( x) =p and Orr furnish 
3 
a negative, 0 (0) (= =) ero and Ovp on the contrary furnish a 
positive value for /. For the octants 5 and 6 we find the same as 
for 3 and 4, only / takes here the opposite sign. 
In the figures 4 and 5 one finds the scheme of the /-diagram 
for « = 60° with the area-division discussed here; the secant planes 
the poles of which lie in the shadowed areas, form a positive angle /, 
the white areas form a negative angle. The squares into which the 
figures are divided, are 30° by 30°; the meridiancircles, on which 
5 is measured out, are drawn as parallel lines, so that a line equal 
in length to the equator takes the place of the pole Q. In fig. 4 
the octants 1—4, in fig. 5 the octants 5—8 are represented. 
In the first octant the curve AB indicates the locus of the 
poles of all the secant planes that produce A4==60°; the curve 
D) 
CD gives h=30°; symmetrically with regard to the line 
a 4 4 ; n ; 
o=5]|o= 5 | (e =,5]|¢= 9], to which corresponds h == 0 
lie in the 2ed octant the curves C’D’ with h=— 30° and A’B’ 
with #00 
= ' n . fo) T e 
If for o= a, 6 varies from 0° to >, then / takes successively 
all values from 60° to — 90°; here the curve Opv of fig. 3 
; Î 3 JE B 
begins going over the point Lg TOT E= 30) {0 
T (rn | ’ hj . 
(0 =e gO = a The curves LF and GH produce here again 
values 4 == 60° and A = 30°, the curves G’H’ and L’ B’ respectively 
SAP atid: = 60°. 
x é Res : 
The diagram for — = <6< 0° needs no further elucidation ; it 
plainly expresses the above-mentioned identity of the angle / for 
planes with poles + 9, + ¢ and — @, = 7. Consequently the octants 
1:2, 3:4, 5:6, 7:8 are but for the sign symmetrical with regard 
nr D MNN : Eet 
to the plane {> }:{> 7], ef. fig. 3, whilst the octantpairs (1,2) : (7,8) 
€ wes jj cS 
= Ge / 
and (5,6): (3,4) are symmetrical, but for the sign of 5 with regard 
to the plane (QO): (zr). 
As appears further from fig. 3 the diagram for « = 60° is the 
same as for @ = — 60°, if one substitutes for gy the value o + zr, 
