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CONFIDENTIAL
Equation Al0 corresponds to the case in which the city and bomb patterns are completely
out of phase (w = 90 deg); Eq. All to the case in which they are completely in phase
(w = 0 deg). By letting \ and the different standard deviations assume various special
values, e.g., 0 and ©, it is easy to see that Result 3 and Eqs. Al0 and All withstandinspection.
When the center of the bomb pattern is not coincident with the center of the city
the effect is to degrade Result 3 by a certain negative exponential: the exponent is a homo-
geneous quadratic form in the coordinates of the aiming point with respect to the frame
of reference determined by the city. Consequently the locus of points such that a bomb
aimed at them underthese conditions gives rise to a fixed expected level of casualties — in
brief, the equicasualty contours — is an ellipse. This too is an observation that agrees
with experience, at any rate toward the center of a city. Away from the centerof the city
the bomb begins to pick out casualties in neighboring cities; hence the contours for the
lower casualty levels wander about, enclosing more than one center of population.
PROCEDURE FOR OBTAINING BINORMAL FIT TO CITY
A hypothetical population breakdown of a city into squares 2 by 2 miles each is shown
in Fig. A2 (0 to 9 columns and rows).
Any standard work on statistics may be consulted
on the question of computing the means, variances, and covariance. The interest in such
x —>
y
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102
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1309
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2303
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1240
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132
580
712
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7371
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me
Fig. A2 —- Hypothetical Distribution of Urban Population
SATA
;
!
Thousands of persons per 4 sq miles.
works, however, usually extends to further quantities that are of no concern here, and the
effect may be somewhat confusing. Consequently the method developed and employed
for this study is given here in full, and the results are shown in the A, B, C columns and
a, b, c rows of Fig. A2. One of the advantages of the method is that there is a check on
every computation immediately after it is made.
The following instructions were given
with no further comment to computers without previous experience in this work; the results were quite satisfactory.
1
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4
1
76
ORO—R—-17 (App B)