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a loss of only about 134 men of the "Blue" force, leaving 866 to meet the remaining 500 of the "Red" force with an easy and decisive victory; this is shown in Fig. 2 (b), the victorious "Blues" having annihilated the whole "Red" force of equal total strength with a loss of only 293 men.

Fig. 3a.

Fig. 3b.

In Fig. 3a a case is given in which the "Red" force is inferior to the "Blue" in the relation 1 : √2 say, a "Red" force 1,000 strong meeting a "Blue" force 1,400 strong. Assuming they meet in a single pitched battle fought to a conclusion, the upper line will repre-

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