A few illustrations, drawn from daily experience, will, perhaps, serve to explain my meaning. Generally speaking, the most important arts and pursuits of life are ultimately based on mathematics. This science furnishes them, as it were, with the method they observe; but it is not practicable, nor, indeed, has man the leisure, to revert on every occasion, with methodical exactness, to these elements, but, assuming the principles to be well known and admitted, he attends rather to the results essential to the end he has in view. The economical management of the smallest as well as of the largest household, rests, in the end, on the elementary principles of arithmetic; but what would come of it if, on every occasion, we were to go back to the simple "one-times-one" of the multiplication table, and reflected upon and sought for the proofs that the principle is really valid and can confidently be relied on in practice? In the same way the art of war is founded on geometry; but when the general arranges his troops for battle, does he consult his Euclid to satisfy himself of the correctness and advantages of his position? Lastly, when the astronomer, whose vocation is pre-eminently dependent on accurate calculation, when he would make us acquainted with the phenomena of the sidereal heavens, confines himself almost entirely to them, without wearying those whom he wishes to interest, with the complicated reckonings which, however, in all probability, he was obliged himself to go through. With all these arts and pursuits of practical life, the intellectual business of thinking--of such thinking at least as is common to most men--and of communicating thought, has a sort of affinity and resemblance. For, unquestionably, it is one among the many problems of philosophy to establish a wise economy and prudent stewardship of that ever-shifting mass of incoming and outgoing thoughts which make up our intellectual estate and property. And this is the more necessary the greater are the treasures of thought possessed by our age. For, in the highly rapid interchange of and traffic in ideas, which is carrying on, the receipts and disbursements are not always duly balanced. There is much cause, therefore, to fear lest a thoughtless and lavish dissipation of the noblest mental endowments should become prevalent, or a false and baseless credit-system in thought spring up amid an absolute deficiency of a solid and permanent capital safely invested in fundamental ideas and lasting truths. As for the second simile: I should, by all means, wish to gain a victory, not indeed for you, but with you, over some of the many errors and many semblances of thought, which are, however, but cheats and counterfeits which distract the minds of the present generation, disturb the harmony of life, and banish peace even from the intellectual world. And as respects the third illustration: I should indeed rejoice as having, in a great measure, attained my object, if only I shall succeed in directing your attention to some star in the higher region of intellect, which hitherto was either totally unknown, or, at least, never before fully observed.