682 
Now the frequency in the interval p...q, belonging to the three- 
valued zone, consists of three parts, viz. : 
vq U) 
1 1 r bare l k ie r 7s) 
VAV | a = ff (je ON da Ar =| J. (2) e—Lh!a)? dx. ,. 
Xp vg 
Ly 
eee fi (0) eLAOFd 
= -— BE) Cra LIS INS EF 
3 Va, ig 
Ly 
which are all positive, because we travel along the axis of w in a 
D negative sense in the part (4,/), where f '(w) < 0. 
Now for «5 < #«< «, the integral 
! | | 
abt | P (a), = F(a) e LA! da 
af 
ob Ep Xe xn 
Fis. 16. may be broken up into three parts: 
& Ul 
i! er. \19 1 : an] Tr flax) 12 
BD, (z) = desk fii (a)etA@Pdz , PD, (©) = ge Fy (2) eH) F da, 
v 
wv 
» 
1 pron 
Db, (z) = Vx AG eLf) de 
Lh 
The function (x) is represented by the part Ab,C,,, the 
1 ees 
function — ®, OE f me verde by “the part C,, B. the 
re 
Lp 
function ®, («) by the part B,,C,D. 
The total frequency [== D(o,) in the point a w, is therefore 
represented by 
[=pP,—pP,+pP,;=pP, + P,P,=pP,;,—P,P.=pF (see fig. 15 and 16). 
So we may put the following problem : 
To transform the discontinuous integral-curve (fig. 15) furnished 
directly by observation into a continuous curve (fig. 16), which in 
the range «,..,. has three branches, such that 
PP, + P,P, = pP, 
or what comes to the same, 
pi ig 
where pP is the ordinate in the given discontinuous curve. 
