Every operation in war entails a risk more or less great; and if no risks were to be taken, it would be better not to go to war. It is true that some wars have been undertaken in which the preponderance of force was so great that there was very little doubt of the actual outcome, and very little risk taken by one of the two parties. Such wars, however, have been very few; and they were hardly wars in the usual sense, any more than the beating of a little boy by a big boy could properly be called a "fight."

Reference may again be made here to Table I on next page, which shows the way in which fights between unequal forces proceed, and the advantage of fighting the separated parts of an enemy rather than the united force. We can see this clearly if we note that, if two forces each aggregating 1,000 were in each other's vicinity, and if the entire force A was able to engage half of B, or 500, it would whip half of B, and have 841 remaining, with which to engage the other half (500) of B. Reference to the end of the third period in this table shows also that if a force of 789 engages a force of 523, it will have 569 left, after the other has been reduced to zero. So, a force of 1,000 that engages two forces of 500 separately, will have more than 500 left, after the others have both been reduced to zero: whereas, if it engages both, when they are united, both sides will be gradually reduced to zero, remaining equal all the time.

TABLE I
Col.
1		 Col.
2		 Col.
3		 Col.
4		 Col.
5		 Col.
6		 Col.
7		 Col.
8		 Col.
9		 Col.
10
Value of offensive power at beginning A 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
B 1000 900 800 700 600 500 400 300 200 100
Damage done in 1st period A 100 100 100 100 100 100 100 100 100 100
B 100 90 80 70 60 50 40 30 20 10
Value of offensive power at end of 1st period A 900 910 920 930 940 950 960 970 980 990
B 900 800 700 600 500 400 300 200 100 0
Damage done in 2nd period A 90 91 92 93 94 95 96 97 98
B 90 80 70 60 50 40 30 20 10
Value of offensive power at end of 2nd period A 810 830 850 870 890 910 930 950 970
B 810 709 608 507 406 305 204 103 2
Damage done in 3rd period A 81 83 85 87 89 91 93 95
B 81 71 61 51 41 31 20 10
Value of offensive power at end of 3rd period A 729 759 789 819 849 879 910 940
B 729 626 523 420 317 214 111 8
Damage done in 4th period A 73 76 79 82 85 88 91
B 73 63 52 42 32 21 11
Value of offensive power at end of 4th period A 656 696 737 777 817 858 899
B 656 550 444 338 232 126 20
Damage done in 5th period A 65 70 74 78 82 86
B 65 55 44 34 23 13
Value of offensive power at end of 5th period A 591 641 693 743 794 845
B 591 480 370 260 150 40
Damage done in 6th period A 59 64 69 74 79 85
B 59 48 37 26 15 4
Value of offensive power at end of 6th period A 532 593 656 717 779
B 532 416 301 186 71
Damage done in 7th period A 53 59 66 72 78
B 53 42 30 19 7
Value of offensive power at end of 7th period A 479 551 626 698 772
B 479 357 235 114 0
Damage done in 8th period A 48 55 63 70
B 48 36 24 11
Value of offensive power at end of 8th period A 431 515 602 687
B 431 302 172 44
Damage done in 9th period A 43 52 60 69
B 43 30 17 4
Value of offensive power at end of 9th period A 388 485 585 683
B 388 250 112 0
Damage done in 10th period A 39 49 59
B 39 25 11
Value of offensive power at end of 10th period A 349 460 574
B 349 201 53
Damage done in 11th period A 35 46 57
B 35 20 5
Value of offensive power at end of 11th period A 314 440 569
B 314 155 0
Damage done in 12th period A 31 44
B 31 16
Value of offensive power at end of 12th period A 283 426
B 283 111
etc.
Total damage done by A 717 789 800 700 600 500 400 300 200 100
B 717 574 431 317 228 159 101 60 30 10

It is interesting to note how this simple fact is the key to most of the operations of strategy and tactics; how—the mechanical tools in the way of ships and guns and torpedoes having been supplied—the key to their successful use is simply to take advantage of all opportunities of isolating one part of the enemy's force from the rest, and then attacking one of the parts with a force superior to it. Opportunities lacking, one must, of course, try to create opportunities by inducing the enemy to detach some part of his force, under circumstances such that you can attack it, or the weakened main body, with a superior force. Naturally, one must try to prevent a similar procedure by the enemy.

This does not mean that the sole effort of naval operations is finesse in either strategy or tactics; sometimes the sole effort is to force a pitched battle by the side that feels superior, and to avoid a pitched battle by the side that feels inferior. Before the actual inferiority or superiority has been ascertained, however, the strategy of each commander is to bring about a situation in which his force shall have the advantage. The advantage having been gained and recognized (or an advantage existing and being recognized), strategy insists on forcing a battle, for the reason that every contest weakens the loser more than it does the winner.

This does not mean that it is always wise to engage a weaker force that is temporarily separated from its main body. It is readily understandable, for instance, that it would be unwise in two cases:

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."