If we could form a comparative estimate of the cost of organising in the first instance, and then provisioning and maintaining each of the three arms, and then again of the relative amount of service rendered by each in war, we should obtain a definite result which would give the best proportion in the abstract. But this is little more than a play of the imagination. The very first term in the comparison is difficult to determine, that is to say, one of the factors, the cost in money, is not difficult to find; but another, the value of men’s lives, is a computation which no one would readily try to solve by figures. Also the circumstance that each of the three arms chiefly depends on a different element of strength in the state—Infantry on the number of the male population, cavalry on the number of horses, artillery on available financial means—introduces into the calculation some heterogeneous conditions, the overruling influence of which may be plainly observed in the great outlines of the history of different people at various periods. As, however, for other reasons we cannot altogether dispense with some standard of comparison, therefore, in place of the whole of the first term of the comparison we must take only that one of its factors which can be ascertained, namely, the cost in money. Now on this point it is sufficient for our purpose to assume that, in general, a squadron of 150 horsemen, a battalion of infantry 800 strong, a battery of artillery consisting of 8 six-pounders, cost nearly the same, both as respects the expense of formation and of maintenance. With regard to the other member of the comparison, that is, how much service the one arm is capable of rendering as compared with the others, it is much less easy to find any distinct quantity. The thing might perhaps be possible if it depended merely on the destroying principle; but each arm is destined to its own particular use, therefore has its own particular sphere of action, which, again, is not so distinctly defined that it might not be greater or less through modifications only in the mode of conducting the war, without causing any decided disadvantage. We are often told of what experience teaches on this subject, and it is supposed that military history affords the information necessary for a settlement of the question, but every one must look upon all that as nothing more than a way of talking, which, as it is not derived from anything of a primary and necessary nature, does not deserve attention in an analytical examination. Now although a fixed ratio as representing the best proportion between the three arms is conceivable, but is an x which it is impossible to find, a mere imaginary quantity, still it is possible to appreciate the effects of having a great superiority or a great inferiority in one particular arm as compared with the same arm in the enemy’s army.