it; and a remark to be added is that some minds appear incapable of distinguishing between intrinsic absurdity and extrinsic absurdity. The case before us illustrates this remark; and at the same time shows us how analytical faculties of one kind may be constantly exercised without strengthening analytical faculties of another kind—how mathematical analysis may be daily practiced without any skill in psychological analysis being acquired. For, if these gentlemen had analyzed their own thoughts to any purpose, they would have known that incongruous juxtapositions may, by association of ideas, suggest characters that do not at all belong to the things juxtaposed. Did Mr. Kirkman ever observe the result of putting a bonnet on a nude statue? If he ever did, and if he then reasoned after the manner exemplified above, he doubtless concluded that the obscene effect belonged intrinsically to the statue, and only required the addition of the bonnet to make it conspicuous. The alternative conclusion, however, which perhaps most will draw, is that not in the statue itself was there anything of an obscene suggestion, but that this effect was purely adventitious: the bonnet, connected in daily experience with living women, calling up the thought of a living woman with the head dressed but otherwise naked. Similarly though, by clothing an idea in words which excite a feeling of the ludicrous by their oddity, any one may associate this feeling of the ludicrous with the idea itself, yet he does not thereby make the idea ludicrous; and, if he thinks he does, he shows that he has not practiced introspection to much purpose.
By way of a lesson in mental discipline, it may be not uninstructive here to note a curious kinship of opinion between these two mathematicians and two littérateurs. At first sight it appears strange that men, whose lives are passed in studies so absolutely scientific as those which Professor Tait and Mr. Kirkman pursue, should, in their judgments on the formula of evolution, be at one with two men of exclusively literary culture—a North American Reviewer and Mr. Matthew Arnold. In the "North American Review," vol. cxx., page 202, a critic, after quoting the formula of evolution, says, "This may be all true, but it seems at best rather the blank form for a universe than anything corresponding to the actual world about us." On which the comment may be, that one, who had studied celestial mechanics as much as the critic has studied the general course of transformations, might similarly have remarked that the formula, "bodies attract one another directly as their masses and inversely as the squares of their distances," was at best but a blank form for solar systems and sidereal clusters. With this parenthetical comment, I pass to the fact above hinted, that Mr. Matthew Arnold obviously coincides with the critic's estimate of the formula. In Chapter V. of his work "God and the Bible," when preparing the way for a criticism on German theologians as losing themselves in words, he quotes a saying from Homer. This he introduces by remarking that "it is not at all a grand one. We are almost
