537 
If the limits 2, and x, are known beforehand, it is easy to deter- 
mine 4 and w,, graphically. 
Indeed, putting 
Ld, 
u == log ———, 
Und 
s + Udy 
and operating with z and the numerus v= —— = 10 on loga- 
wb 
in 
rithmic paper, we obtain the graph of the equation: 
z= A(u—tn), 
which is a straight line with the (positive) slope 4; this line cuts 
the axis of w at the point «—=w, corresponding to the median #,. 
At the margin of the logarithmic paper we read at u, the nume- 
Uno , . 
rise 2 =v, = 10% = —, from which w„ can be calculated 
Un En 
Lo + Vm En ; : 
(==) when not yet determined by the figure on 
1 + vm 
ordinary squared paper. 
In practice we are obliged to estimate the values of 2, and a 
and to use, at least provisionally, erroneous values «,’ and z of 
the limits. So we operate with 
instead of w, and thus obtain a set of pairs (w', z) lying in a curve 
slightly deviating from the true straight line z= 4 (wu — Un). 
Let the errors in the presumed values zand «,' be o and r, so that 
@o — lo =O; 
Bi Dit. 
then, putting 
Ent En — 2 
and, accordingly 
Gea Jog. w = loge, 
we derive 
B,'v' +a 
Se ey 
U == 
and 
a (ap'v' Ho) (HI) _ (a,'— vo) + (wo — wo) be’ (e+ ro + 6 
‘ar (v'+1)an— wro -ra) — (en — nv + (vn — Beens tv! + (a—9) 
or, putting 
- , (10) 
5 —t 
=f ey, 
AEN a—6 
