In recent years there has been much discussion on the subject of the accuracy of our naval guns at long ranges, brought about not only by the natural increase in practicable ranges, due to the development of guns of larger caliber and greater velocity, but also to the laudable desire to push the effective battle range to the extreme limit possible.
Undoubtedly greater accuracy of weapons and superior skill of personnel have their most telling effects at long ranges, for at these ranges superior accuracy and skill affect most decidedly the relative number of hits obtained.
Some 17 years ago, I undertook a mathematical investigation to ascertain the value of the advantage accruing to a naval force engaging an adversary numerically equal but so placed that a portion of his force was masked or beyond effective range. The result of this investigation showed that the advantage was measured, not by the ratio of the number of the opposing ships actually engaged, but by the square of this ratio. Here was the first statement of the so-called “n square law,” a law discovered independently some years later by an English writer.