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: