Mr. Bragdon, after expatiating upon the vastness of the firmament, makes this extraordinary conclusion: “Viewed in relation to this universe of suns, our particular sun and its satellites shrink to a point. That is, the earth becomes no-dimensional.” The last word is in italics. Now this is manifestly a misconception, since the most minute atom, notwithstanding its insignificance in proportion to the universe, cannot be considered as an abstraction, which a point really is. Those who are not satisfied with the intuitive evidence of the limitation of space to three dimensions, solely because no logical proof can be adduced of this limitation, would do well to read the essay of Schopenhauer on _The Methods of Mathematics_, in which is cited as an instance of the undue importance of logical demonstration the controversy on the theory of parallels. The eleventh axiom of Euclid “asserts that two parallel lines inclining toward each other if produced far enough must meet,—a truth which is supposed to be too complicated to pass as self-evident and thus requires a demonstration…. _It is quite arbitrary where we draw the line between what is directly certain and what has first to be demonstrated._” (The italics are mine.) I believe with Schopenhauer, who quotes Descartes and Sir W. Hamilton in support of his contention, that the science of mathematics has no cultural value. Far from affording “a new way of looking at the world,” as Mr. Bragdon tries to convince us, “its only direct use is that it can accustom restless and unsteady minds to fix their attention.” That such mental concentration may be woefully misdirected is instanced in the cases of Swedenborg and Madame Blavatsky, reference to whom by Mr. Bragdon is alone sufficient to cause a sniff of suspicion. Indeed your author himself, while evidently well versed in bookish mathematics, has been unable to free his mind of its limitations. Upon a basis of phrases devoid of significance he builds his extravagantly mystical speculation, which dissolves in the light of reason, “into air, thin air.” PHILIP J. DORETY, M. D. TRENTON, N. J. EDITORIAL NOTES _Soldiers of All Nations_