675 
The frequency in a certain segment pq between # = #, and « = ay 
consists of two equal parts: 
vy 
npe Pa [Aw Pd 
en v)e tut Ss de 
1 zal Jy (aye : 
vy 
Lp 
dk {0 i 
and A, vs el RAG efx)? de = 
Ly 
SMR 4 
= “| — f,'(a) eTA@? de=A, L. 
uy 
Fre.’ 
In order to construct the branch f(x) we join x, to <= 0, or 
/=4, and a point «=a; to the value z which satisfies 
<I. 
Wie 
1 
O(z,) = oq | cia =3+4+41 (a), 
— 00 
bP rl eg 
individuals between «x, and vz (thus smaller than «), divided by 
ihe: total number iV ==> Ii: 
In this way we obtain n—1 points (ej, er) (k=1,...n—1) of 
the positive branch of the curve. Evidently the negative branch 
will be the reflected image of the positive one. 
In reality neither of the limiting points 2, and w, is exactly 
determined by the rougb frequency-tigure. By tracing a continuous 
line through the »—1 points (xz, 2,) of the positive branch and 
another through their reflected images, and uniting these curves as 
smoothly as possible, we may fix pretty sharply the most probable 
situation of the point of intersection with the axis of « (w=r,, c—=0). 
In the same manner the asymptote «—w, must be determined 
by estimating. If it seems to lie very faraway, x, may often be put 
=o, as i.a. in the case of the above example z= + Vu. 
In general the form of the equation will be 
Ri ee Vage) : 
where g(#) is a one-valued function of «, which in the real domain 
only vanishes at «=z, and becomes infinite at #— a (C.q. &, == o). 
If we had applied the original method, founded on the two 
simplifications, « 
where / (xj) represents the quotient. - of the number of 
would have been joined to z= -- oo and a, to 
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