( ?34 ) 
• fcirt "° P ° in,S 0f " ,e preceding > ,he othCT "> points of the 
tbl outf ,rVeS ’ f COnVergeS either t0 a si "g |e Angular point, or to 
of of simpIe closed tangent curve8 ’ 
^s^Trrrjrr^*rr 
asXVZL^r 10 a “ redUCed distributio "”< possessing 
ZeZl,7rT ! radiat,ng p0in(S and reflexi 0“ points, and wf 
f geDt CUrVeS 0f that reduced distribution. 
■ , . angent curve can possess no radiating points but reflexion 
Cd). “ “ P "~ (itS tange "‘ direction shows 8 Lre ’a ^Z 
We toV'lr " ta T en ' CUrl ' e Ca " on, y st0 P ^ a radiating point. 
7 it is either^an 6 arc” ^! tPa ’^ tangent curve: according to theorem 
or it gives rise t oTs Tl* T" joinin e ,wo Minting points, 
the sphere into two domains 6 ©S *""* J ” divW “ 
« - -A i Z b “ f ^ 8ha " ^ thati ” 
within G a new Tangent 0 radwtm S P 01nt in G < we could consider 
stop in G it would \ 6 ’ Md 88 ,h ‘ S would not be able to 
simple died JgS ZXTt ? 2 g “' e *> a new 
of G. Within G t we could ““f a d ° [nain °' bein g a part 
and in this way we should a m W ' aS ' 61 an arbitrary tangent curve, 
j, enclosing a domain G, beineT plr^of ^ ^ 
— we . ;:6 “ “ P “" d — 
reflexion° p^inT^^^^ “ n ^ r a rad^g-“nor a 
vicinity. On account of thellTf', I" an indefinitely small 
there must thus be at least one d, ^ n th ® be % mnm g of this § 
closed tangent curve ,* anH d T" G *> funded by a simple 
G»G 9 ,gJ... *" COntained in ea °h Of the domains 
bounding a domain * ^ osed Angent curve ; w+1 
this process to any index A f n, P of and we could continue 
on the other hand is imnnoshi & Second class of numbers, which 
G,—G,,... G^G “ G ? 38 ,he 861 0f domains G ~ G >’ 
So we finally formulate- * * +1 * *' must remai n denumerable. 
iwo radiating points. distribution on a sphere possesses at least 
