( 734 ) 
see where the curves /,(@,) and 4, («,) meet. The meeting point 
indicates the pole (9,4) of the required secant plane. 
In fig. 6 the graphical solution of two of the above discussed 
problems is represented. If one takes (cf. fig. 2) the rhombododeca- 
hedronplane (110) as equatorplane, then the planes (LOL) and (O11) form 
angles with it equal to «, = — 60° and «@, = 60 . The secant plane S 
gives h, — 60°, h, = — 60°; y = — 109°28'17". If the diagram for 
“, is removed 109°/, with regard to the diagram for «¢,, and both 
are placed on each other, then it appears, that the curves A, (60°) 
and /, (-- 60°) meet only in the 5'* octant. In the figure the curves 
for ¢ >0 and «<0 are drawn side by side. If the azimuth of 
A is = 0, the curve AB (a, = 60°) indicates the poles for h, = 60° 
with « >0; BC the poles for h, = —- 60° with 5 <0, AC those 
for h,=60° with o<0. The azimuth of D=109%/,; FD gives 
the poles for 4, =— 60° with o >0; FE and DE give those for 
h, = 60° resp. h, =-—-60° with « <0. The meeting point of the 
curves BC and FH gives the pole of the required secant plane with 
o=—54°/, with regard to A, or 9=—54™%/, with regard to D, 
and o = —. 54°*/,. 
The second problem refers to the amphibole-crystal spoken of on 
page 732, which is cut by the section plane in such a way that the 
apparent angles between the planes (110): (110) and (O10) : (110) 
amount respectively to 4, = 438° and 4, = — 79° 
In fig. 6 the zone-axis (oe —0) is indicated by AK; the curves 
LOM and HNA indicate the locus of the poles for , = 48° 
with o >0O (1% oetant) and 5 < 0 (8 octant); the curves /O and 
IN indicate the locus of the poles for 4, = — 79° with a >0 
(dst octant) and + <0 (8" octant). The meeting point of the curves 
LM:10 and HA:IN gives the points O(e = 35°, a = 31°) and 
N (e=— 35°, 6 =— 31°) which values likewise correspond entirely 
to those found above in the analytical way. 
Mathematics. — “On the Integral equation of Frupuorm.” By 
Prof. W. KAPTEYN. 
1. Let 
b 
g(x) =f(e) + i FO GEG AEN eN a Po ee 
be the integral equation of Frrpuoim, in which the constants a, 6, 4, 
and the functions f(7) and A (ry) are known, and g(r) is the funetion 
to be determined. 
