676 
g=-+to. The first frequency-number Y, being large, the value of 
z now rises in a very short interval «,..., from —o to a value 
slightly below zero, or perhaps above zero. 
Although /'(«,) becomes infinite, yet in the ideal frequeney-curve 
aye ae se 
Lim y = Lim —— f(a) e-|\f@P = 0 
U, at VT 
unless an improbable form is assumed for f(«). But also, very 
peculiar forms of f{#) being excluded, 
dy 1 . 
Ef" (a) — 2 f (a). Lf Ne VOF 
de Ya" FC 
will approach to zero, that is: the ideal frequency-curve will touch 
: n , at ‘ dy 
the axis of « in «=~a,. Then neither y nor 5 shows a disconti- 
ar 
nuity in a. 
Since however the area must already assume a considerable value 
in the first interval, not only the slope but 
also the ordinate must increase rapidly (fig. 4). 
This case is realised for instance with 
ZE: 
So the discontinuity of the rough frequency- 
curve appears as an accumulation of elemen- 
tary frequencies which are finite, continuous 
and descending to zero. 
PG. 4. Whether the original simplified or the 
extended method is preferable, is difficult to decide a priori. Perhaps 
it is possible to refine the data in the first interval and to obtain 
frequency-numbers for portions of the first class-interval. If these 
numbers, after continued subdivision, at last begin to decrease as 
we approach «,, then the original method (of the continuous frequency- 
figure) is to be preferred. If on the other hand even by the finest 
subdivision an increase of the frequencies towards «, is found, then 
it is necessary to admit discontinuity, and the extended method 
must be applied. 
Of the integral-curve 
ke 
T= yee 
ry 
observation furnishes the ordinates 
vi Y eae Y + Yo a ee 
