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Rh operation of the n-square law can be presented is given in Fig. 7; here the strengths of a number of separate armies or forces successively mobilised and brought into action are represented numerically by the lines a, b, c, d, e, and the aggregate fighting strengths of these armies are given by the lengths of the lines A, B. C, D, E, each being the hypotenuse of a right-angle triangle, as indicated. Thus two forces or armies a and b, if acting separately (in point of time), have only the fighting



strength of a single force or army represented numerically by the line B. Again, the three separate forces, a, b, and c, could be met on equal terms in three successive battles by a single army of the numerical strength C, and so on.

§ 35. Special or Extreme Case. From the diagram given in Fig. 7 arises a special case that at first sight may look like a reductio ad absurdum, but which, correctly interpreted, is actually a confirmation of the n-square law. Referring to Fig. 7, let us take it that the initial force (army or fleet), is of some definite finite magnitude, but that the later arrivals b, c, d, etc., be very small and numerous detachments—so small, in fact, as to