Since maximum strength derives from a combination of all three arms, the question naturally arises what the optimum proportions would be. An answer is almost impossible.
If one could compare the cost of raising and maintaining the various arms with the service each performs in time of war, one would end up with a definite figure that would express the optimum equation in abstract terms. But this is hardly more than a guessing game. The first part of the equation alone is hard enough to estimate, except for the purely monetary factor; but the value of human life is another matter—one on which no one would be willing to set a price in cold figures.
There is also the fact that each arm really depends on a different sector of the national economy: infantry on the human population, cavalry on the equine, and artillery on finance. That fact introduces an outside determinant, which we clearly see to be dominant in the general historical phases of different peoples at different times.
But since for other reasons we cannot quite dispense with all standards of comparison, instead of taking the first part of the equation as a whole, we shall simply make use of the only ascertainable factor: the monetary cost. For our purposes it will suffice to state that, according to common experience, a squadron of 150 horses, a battalion of 800 men, and a battery of eight six-pounders cost approximately the same both for equipment and maintenance.
So far as the second part of the equation is concerned, it is even more difficult to work out definite figures. It might conceivably be possible if destructiveness were all that had to be measured; but each branch has its own particular use and thus a different sphere of effective action. But the spheres are by no means fixed; they could be expanded or contracted, and the consequence would merely be to modify the conduct of the war without incurring any special disadvantage.