Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

where moL.t cf the symbols have the same meaning as before and,
a t = .7983, the coefficient of regression (11)
3 w = 1
a r = 6,842 C r •
0
E 21 = X 21 the money estimate of the quality difference between
rail and barge transportation.
This new equation form is identical to the form of equation (8), so
that the boundary is made up of segments of hyperbolas. The other
boundary equations of Section 2 can be easily modified in the same way.
Again, the water-truck boundary is made up of segments of parabolas, and
the, rail-truck boundary is a circle.
The results of the linear regressions of the rates on distance
. were very good ih the'case of river and road transports. As to rail
transport results, they were good enough for our purpose, most of the R 2
being above .60, and the coefficients significant. However, railway A's
'regression was very bad, for the reason that its rates hardly vary with
distance, and a few of them are completely out of line (1) . A graphic
inspection of the rate structures of the railways revealed that they were
best summarized by a linear relationship between rate and distance, despite
some tariff peculiarities. In these conditions, the linearity assumptions
of the model could be used without reservations.
The actual boundary equatibns can then be computed on the basis of
this information plus what has been gathered in Chapter III. These equations
are given in Table XIII (2) . Note that the time cost was not included in
their computation. The little role that time plays in this particular
problem did not warrant the additional complication. The next task is to
draw all the curves corresponding to these equations on the Illinois map,
using the Chicago-Lacon axis as an abscissa. Note that there are one
OSCIONIIM
• (1) These rates relate to points of origin which are not located on railway
A network but on another railway feeder line.
(2) In the case of the rail-truck boundaries, only the radius of the circles
have been given.
05