In contrast to targeted fire, area fire requires that fire effect be calculated as the product of (1) the volume of fire rained upon the enemy-held area, and (2) the density of enemy numbers therein, such that in a firefight between numerically unequal forces occupying equal areas, the advantage of the stronger force in volume of fire is exactly offset by the lower density of the weaker, whose own advantage in having a more densely-packed enemy at which to shoot is exactly offset by a lower volume of fire with which to hit it. The loss exchange ratio, both instantaneous and cumulative, begins and remains throughout the battle at 1 to 1, notwithstanding the growing disparity between the opposing forces in gross firepower ratio. As long as the spaces occupied by the two forces remain equal, the loss exchange ratio can be budged from unity only through the introduction of inequality in firepower-per-man, by which one side's volume of fire may be increased without itself presenting any denser a target to its enemy. As Lanchester puts it:

"The rate of loss is independent of the [ratio of] the numbers engaged, and is directly as the efficiency of the weapons . . . There is no direct value in concentration, qua concentration, and the advantage of rapid fire is relatively great."

To recur to the same set of examples used previously:

A firefight between two forces in the initial ratio of 5 to 4, of equal firepower-per-man, continued unto the reduction of the weaker to 2/4 its original number, would see only 3/5 of the stronger yet standing - the same number as would survive the total annihilation of the weaker force under the targeted fire theory.

A firefight between two forces of equal number, but with one side enjoying 3/2 the firepower-per-man of the other, continued unto the reduction of the slower-firing force to 1/2 its original number, would see 2/3 of the faster-firing force yet standing.

A firelight between two forces, one 3/2 as numerous as the other, but the numerically-weaker having 3/2 the firepower-per-man of the stronger, continued unto the reduction of the weaker to 1/2 its original strength, sees the stronger reduced to its original number likewise.

To improve the 1 to 1 loss-exchange ratio without introducing an inequality in firepower-per-man requires introducing an inequality between the two forces in spaces occupied, such as might be achieved either (1) by spreading the existing number of one's own force over a wider space, thereby reducing its density relative to the enemy's volume of fire without changing one's own volume of fire relative to the enemy's density; or (2) by directing upon the same enemy the fire of an additional space-full-of-soldiers not otherwise engaged, thereby increasing the volume of friendly fire relative to the enemy's density without changing one's own density relative to the enemy's volume of fire. A like increase in space occupied using either tactic will produce an equal improvement in the loss-exchange ratio; however, the second tactic will compress the time required to arrive at any particular level of cumulative losses.

Against an interval-less or "en muraille" battle line, the additional space required to implement either tactic must be sought on the flanks.

To lower the density of one's own force, as under the first tactic, is to increase its vulnerability to enemy cavalry.

An inequality in spaces-occupied may be used to magnify or to offset an inequality in firepower-per-man. For example, a force equal in numbers but with only 2/3 the firepower-per-man of its enemy might re-establish a loss-exchange ratio of 1:1 [up from 2:3] by spreading itself over a space 3/2 as extensive - provided, again, that the additional space could be found within like range, and that the enemy not be possessed of a force of cavalry able to exact a severe penalty for such dispersion.

Although of no direct relevance to the loss-exchange ratio of the instant firefight, the productivity of one's musketry may also be improved through the generosity of the enemy in deploying his battalions with a non-firing fourth rank, or in stationing his second line-of-battle too close behind his first, or by any other act which puts more of his flesh in the way of your blind bullets without increasing the volume of bullets sent back at you.

Infantry Fire and Wargame Design

Introduction
Targeted or "Concentrated" Fire
Area Fire
Ineffective Fire
Conclusion

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