1.  A case in which the weaker force were so little weaker, and were part of a force so much larger than the total of the smaller force, that the gain as between the two forces actually engaged would not be great enough to compensate for the loss entailed.  For instance, a reference to Table I shows that an A force of 1,000 engaging a B force of 800 would have 569 left when B was reduced to zero.  This is impressive:  but if the B force of 800 were part of a total B force of 2,000, in other words if there were an A force of 1,200 near at hand, B would have 569 left with which to oppose 1,200, a proportion a little less advantageous than the proportion he started with—­1,000 to 2,000.

2.  A case by which the B force may have divided with the express purpose of luring A to attack; arrangements having been made whereby the inferior B force would simply hold the A force until the whole B force could come to its assistance; arrangements having been also made that this would be accomplished before the detached part of B should get very badly damaged.

Attention is invited to Table III, which is a continuation of Table I. It represents what would happen if a force of 1,000 should fight separately two forces, one of 800 and the other of 200.  In column 1, A is supposed to have engaged the 200 first, and so to have become reduced to 970, and to engage 800 afterward.  In column 2, A is supposed to have engaged 800 first, thereby becoming reduced to 569, and then to engage the 200 force.  The table indicates that it makes no difference whether A engages the stronger or the weaker force first.

Column 3 shows that a force of 841, the part remaining after a force of 1,000 had annihilated a force of 500, would have 653 left after annihilating a second force of 500.  Taken in connection with columns 1 and 2, this indicates that it is easier to defeat two separated equal forces than two separated unequal forces of the same aggregate value; that the weakest way in which to divide a force is into equal parts.  This fact is mathematically demonstrated by Mr. F. W. Lanchester in a recent book called “Air Craft in Warfare.”

TABLE III
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|                                             |Col. 1|Col. 2|Col. 3|
|---------------------------------------------|------|------

|------|
|Value of offensive at beginning             A|  970 |  569 |  841 |
|                                            B|  800 |  200 |  500 |
|Damage done in 1st period by                A|   97 |   57 |   84 |
|                                            B|   80 |   20 |   50 |
|Value of offensive power at end 1st period  A|  890 |  549 |  791 |
|                                            B|  703 |  143 |  416 |
|Damage done in 2d period by                 A|   89 |   55 |   79 |