_Concentration and Isolation_.--The value of "concentration" is often insisted on, but the author desires to call attention to a misunderstanding on this point, to which he called attention in an essay in 1905. To the author, it seems that concentration is a means and not an end, and that the end is what he called "isolation" in the essay. If a man concentrates his mind on any subject, the advantage he gains is that he prevents other subjects from obstructing the application of his mental powers to that subject; he pushes to one side and isolates all other subjects. In this particular activity it does not matter whether we call his act "concentration" or "isolation" because the whole operation goes on inside of his own skull, and concentration on one subject automatically produces isolation or elimination of all others. But when concentration is attempted on external objects, the case is very different, for concentration may not produce isolation at all. For instance, if 4 ships in column _A_ concentrate their fire on the leading ship in column _B_, the other 3 ships in column _B_ are not isolated, and can fire on the ships of column _A_, even more effectively than if column _A_ was not concentrated on the leading ship of _B_, because they are undisturbed by being fired at. If, however, the 4 ships of _A_ "flank" or "T" the ships of column _B_, as shown in Fig. 2, and concentrate on the leader of B, they thereby isolate the other ships, and practically nullify their ability to fire at _A_. [Illustration: Fig. 2] This effect is approximated by an approximate "T-ing" or "flanking," such as is shown in Fig. 3; because the average distance from the ships of _A_ to the leading ship in _B_ is less than the average distance from the ships in _B_ to any ship in _A_; and because the direction of fire from each ship in _A_ is more nearly abeam than is the direction of fire from the ships of _B_. These positions are very difficult to gain, even if _A_'s speed is considerably greater than _B's_; since all _B_ has to do to prevent it is to head to the right, unless shoals or other dangers such as enemy battleships, _C_, are on that side, co-operating with _A_. [Illustration: Fig. 3] An interesting position is that shown in Fig. 4, which may be assumed by _A_, either for flight, or to get the advantage in torpedo fire. The advantage is that the _A_ ships are running away from torpedoes fired by _B_, while _B_ is running into torpedoes fired by _A_. This advantage is not great if the distance between _A_ and _B_ is so little that _B's_ torpedoes can reach _A_. But if _A_ is able to make this distance equal to the entire range over which _B's_ torpedoes can run, or near it, _B's_ torpedoes cannot reach _A_ at all. [Illustration: Fig. 4]