time the "Blue" are found to have lost 100 against 200 loss by the "Red," the proportions of the forces will have suffered no change, and they may be regarded (due to the superiority of the "Blue" arms) as being of equal strength.
If the condition of equality is given by writing M as representing the efficiency or value of an individual unit of the "Blue" force, and N the same for the "Red," we have:—
Rate of reduction of "Blue" force:—
- db⁄dt = - N r × constant (3)
and "Red,"
- dr⁄dt = - N b × constant (4)
And for the condition of equality,
- db⁄b dt = dr⁄r dt,
or
- -N r⁄b = -M b⁄r,
or
- N r2 = M b2 (5)
In other words, the fighting strengths of the two forces are equal when the square of the numerical strength multiplied by the fighting value of the individual units are equal.
§ 27. The Outcome of the Investigation. The n-square Law. It is easy to show that this expression (5) may be interpreted more generally; the fighting strength of a force may be broadly defined as proportional to the square of its numerical strength multiplied by the fighting value of its individual units.
Thus, referring to Fig. 5b, the sum of the squares of the two portions of the "Red" force are for all values equal to the square of the " Blue " force (the latter
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