If we yield to this feeling, we are guilty of moral cowardice, and we vitiate all the results of all our labors. We must make a correct estimate of the situation—or rather we must estimate the situation to be as grave as it is—or our preparations will be of no avail. If we estimate the situation too gravely, we may spend more money and time on our preparations than is quite needed, and our preparations may be more than adequate. It may be that the preparations which Prussia made before 1870 for war with France were more than adequate. In fact, it looks as if they were, in view of the extreme quickness with which she conquered France. But does any military writer condemn Prussia for having made assurance too sure?

The Value of Superadequate Preparation.—No, on the contrary. The very reasons that make adequate preparation valuable make superadequate preparation even more valuable. The reason is very clear, as is shown by the table on page 284 illustrating the progressive wasting of fighting forces, which the writer published in the U. S. Naval Institute in an essay called "American Naval Policy," in April, 1905.[*]

[Footnote *: I have recently been informed that Lieutenant (now Commander) J. V. Chase, U. S. N., arrived at practically the same results in 1902 by an application of the calculus; and that he submitted them to the U. S. Naval War College in a paper headed, "Sea Fights: A Mathematical Investigation of the Effect of Superiority of Force in."—B. A. F.]

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

These tables grew out of an attempt to ascertain how the values of two contending forces change as the fight goes on. The offensive power of the stronger force is placed in the beginning at 1,000 in each case, and the offensive power of the weaker force at 900, 800, 700, 600, 500, 400, 300, 200, and 100. These values are, of course, wholly arbitrary, and some may say imaginary; but, as they are intended merely to show the comparative strength of the two forces, they are a logical measure, because numerical; there is always some numerical factor that expresses the comparative value of two contending forces, even though we never know what that numerical factor is. Two forces with offensive powers of 1,000 and 900 respectively may mean 1,000 men opposed to 900 men of equal average individual fighting value, commanded by officers of equal fighting ability; or it may mean 10 ships opposed to 9 like ships, manned by officers and men of equal numbers and ability; or it may mean two forces of equal strength, as regards number of men, ships, and guns, but commanded by officers whose relative ability is as 1,000 to 900. It may be objected here that it is ridiculous so to compare officers, because the ability of officers cannot be so mathematically tabulated. This, of course, is true; but the fact that we are unable so to compare officers is no reason for supposing that the abilities of officers, especially officers of high position, do not affect quantitatively the fighting value of the forces they command; and the intention in mentioning this factor is simply to show that the relative values of the forces, as indicated in these tables, are supposed to include all the factors that go to make them up.

Another convention, made in these tables, is that every fighting force is able to inflict a damage in a given time that is proportional to the force itself; that a force of 1,000, for instance, can do twice as much damage in a given time as a force of 500 can; also that a force can do an amount of damage under given conditions that is proportional to the time in which it is at work; that it can do twice as much damage in two hours, for instance, as in one hour, provided the conditions for doing damage remain the same. Another convention follows from these two conventions, and it is that there is a period of time in which a given force can destroy a force equal, say, to one-tenth of itself under certain conditions; that there is some period of time, for instance, in which, under given conditions, 1,000 men can disable 100 men, or 10 ships disable 1 ship, or 10 guns silence 1 gun. In the conflicts supposed to be indicated in these tables, this period is the one used. It will be plain that it is not necessary to know how long this period is, and also that it depends upon the conditions of the fight.

In Table I, it is supposed that the chance of hitting and the penetrability are the same to each contestant. In other words, it is assumed that the effective targets presented by the two forces are alike in the sense that, if the two targets are hit at the same instant by like projectiles, equal injuries will be done. In other words, if each contestant at a given instant fires, say a 12-inch shell, the injury done to one will be the same as that done to the other; not proportionately but quantitatively. For instance, if one force has 10 ships and the other has 9 like ships, all the ships being so far apart that a shot aimed at one ship will probably not hit another, the conditions supposed in Table I, column 2, are satisfied; the chances of hitting are identical for both contestants, and so is the damage done at every hit. Table I supposes that the chance of hitting and damaging does not change until the target is destroyed.

As the desire of the author is now to show the advantage of having a superadequate force, the following table has been calculated to show the effect of forces of different size in fighting an enemy of known and therefore constant size:

TABLE II
Col.
1		 Col.
2		 Col.
3
Value of offensive power at beginning A 1100 1500 2000
B 1000 1000 1000
Damage done in 1st period by A 110 150 200
B 100 100 100
Value of offensive power at end of 1st period A 1000 1400 1900
B 890 850 800
Damage done in 2nd period by A 100 140 190
B 89 85 80
Value of offensive power at end of 2nd period A 911 1315 1820
B 790 710 610
Damage done in 3rd period by A 91 131 182
B 79 71 61
Value of offensive power at end of 3rd period A 832 1244 1759
B 699 579 422
Damage done in 4th period by A 83 124 176
B 70 58 43
Value of offensive power at end of 4th period A 762 1186 1716
B 616 455 252
Damage done in 5th period by A 76 119 172
B 62 46 25
Value of offensive power at end of 5th period A 700 1140 1691
B 540 336 80
Damage done in 6th period by A 70 114 169
B 54 34 8
Value of offensive power at end of 6th period A 646 1106 1683
B 470 222 0
Damage done in 7th period by A 65 110
B 47 22
Value of offensive power at end of 7th period A 599 1084
B 405 112
Damage done in 8th period by A 60 108
B 41 11
Value of offensive power at end of 8th period A 558 1073
B 345 4
Damage done in 9th period by A 56 4
B 35 0
Value of offensive power at end of 9th period A 523 1073
B 289 0
Damage done in 10th period by A 53
B 29
Value of offensive power at end of 10th period A 494
B 236
Damage done in 11th period by A 49
B 24
Value of offensive power at end of 11th period A 470
B 187
Value of offensive power at end of 16th period A 422
B 0

It will be noted that if our force is superior to the enemy's in the ratio of 1,100 to 1,000, the fight will last longer than if it is superior in the ratio of 1,500 to 1,000, in the proportion of 16 to 9; and that if it is superior in the ratio of 1,100 to 1,000 the fight will last longer than if it is superior in the ratio of 2 to 1, in the proportion of 16 to 6. We also see that we should, after reducing the enemy to 0, have forces represented by 422, 1,073, and 1,683, respectively, and suffer losses represented by 678, 427, and 317, respectively.