But it is precisely mathematics, and the pure science generally, from which the general educated public and independent students have been debarred, and into which they have only rarely attained more than a very meagre insight. The reason of this is twofold. In the first place, the ascendant and consecutive character of mathematical knowledge renders its results absolutely insusceptible of presentation to persons who are unacquainted with what has gone before, and so necessitates on the part of its devotees a thorough and patient exploration of the field from the very beginning, as distinguished from those sciences which may, so to speak, be begun at the end, and which are consequently cultivated with the greatest zeal. The second reason is that, partly through the exigencies of academic instruction, but mainly through the martinet traditions of antiquity and the influence of mediaeval logic-mongers, the great bulk of the elementary text-books of mathematics have unconsciously assumed a very repellant form,—something similar to what is termed in the theory of protective mimicry in biology “the terrifying form.” And it is mainly to this formidableness and touch-me-not character of exterior, concealing withal a harmless body, that the undue neglect of typical mathematical studies is to be attributed.

These turdy-facy-nasty-paty-lousy-fartical rogues, with one poor groat's worth of unprepared antimony, finely wrapt up in several scartoccios, are able, very well, to kill their twenty a week, and play; yet, these meagre, started spirits, who have half stopt the organs of their minds with earthy oppilations, want not their favorers among your shrivell’d sallad-eating artizans, who are overjoyed that they may have their half-pe’rth of physic; though it purge them into another world, it makes no matter.