puff) " employ counsel in the matter, eh?" (puff, puff, puff). "Do you remember the story they tell of Abernethy?" "No; hang Abernethy!" "To be sure! hang him and welcome. But once upon a time a certain rich miser. conceived the design of sponging upon this Abernethy for a medical opinion. Getting up, for this purpose, an ordinary conversation in a private company, he insinuated his case to the physician as that of an imaginary individual. How much was the reward offered, did vice, and to pay for it. I would really give you say?" asked Dupin. "Why, a very great deal-a very liberal reward: I don't like to say how much precisely. But one thing I will say that I wouldn't mind giving my individual cheque for fifty thousand francs to any one who could obtain me that letter. The fact is it is becoming of more and more importance every day, and the reward has been lately doubled. If it were trebled, however, I could do no more than I have done." fifty thousand franes to any one who would "In that case," replied Dupin, opening a drawer and producing a cheque-book, “you might as well fill me up a cheque for the amount mentioned. When you have signed it, I will hand you the letter." I was astounded. The prefect appeared absolutely thunder-stricken. absolutely thunder-stricken. For some minutes he remained speechless and motionless, looking incredulously at my friend with open mouth and eyes that seemed starting from their sockets; then, apparently recovering himself in some measure, he seized a pen, and after several pauses and vacant stares finally filled up and signed a cheque for fifty thousand franes and handed it across the table to Dupin. The latter examined it care"Why" (puff, puff), "you might" (puff, fully and deposited it in his pocketbook; "Why, yes," said Dupin, drawlingly, between the whiffs of his meerschaum; "I really-think, G— you have not exerted yourself—to the utmost in this matter. You might do a little more, I think, eh ?" "How? In what way?" then, unlocking an escritoire, took thence a letter and gave it to the prefect. This functionary grasped it in a perfect agony of joy, opened it with a trembling hand, cast a rapid glance at its contents, and then, scrambling and struggling to the door, rushed at length unceremoniously from the room and from the house without having uttered a syllable since Dupin had requested him to fill up the cheque. When he had gone, my friend entered into some explanations. "The Parisian police," he said, "are exceedingly able in their way. They are persevering, ingenious, cunning and thoroughly versed in the knowledge which their duties seem chiefly to demand. Thus, when G detailed to us his mode of searching the premises at the Hôtel D, I felt entire confidence in his having made a satisfactory investigation so far as his labors extended." "So far as his labors extended?" said I. "Yes," said Dupin. "The measures adopted were not only the best of their kind, but carried out to absolute perfection. Had the letter been deposited within the range of their search, these fellows would, beyond a question, have found it." I merely laughed, but he seemed quite serious in all that he said. "The measures, then," he continued, "were good in their kind, and well executed; their defect lay in their being inapplicable to the case and to the man. A certain set of highly-ingenious resources are with the prefect a sort of Procrustean bed to which he forcibly adapts his designs. But he perpetually errs by being too deep or too shallow for the matter in hand, and many a schoolboy is a better reasoner than he. I knew one about eight years of age whose success at guessing in the game of even and odd' attracted universal admiration. This game is simple, and is played with marbles. One player holds in his hand a number of these toys and demands of another whether . that number is even or odd. If the guess is right, the guesser wins one; if wrong, he loses one. The boy to whom I allude won all the marbles of the school. Of course he had some principle of guessing, and this lay in mere observation and admeasurement of the astuteness of his opponents. For example, an arrant simpleton is his opponent, and, holding up his closed hand, asks, ‘Are they even or odd?' Our schoolboy replies, 'Odd,' and loses; but upon the second trial he wins, for he then says to himself, 'The simpleton had them even upon the first trial, and his amount of cunning is just sufficient to make him have them odd upon the second; I will therefore guess odd;' he guesses odd, and wins. Now, with a simpleton a degree above the first, he would have reasoned thus: This fellow finds that in the first instance I guessed odd, and in the second he would propose to himself, upon the first impulse, a simple variation from even to odd, as did the first simpleton; but then a second thought will suggest that this is too simple a variation, and finally he will decide upon putting it even, as before. I will therefore guess even;' he guesses even, and wins. Now, this mode of reasoning in the schoolboy, whom his fellows termed 'lucky'what, in its last analysis, is it?" "It is merely," I said, "an identification of the reasoner's intellect with that of his opponent." "It is," said Dupin; "and upon inquir-tigations; at best, when urged by some uning of the boy by what means he effected usual emergency-by some extraordinary rethe thorough identification in which his suc- ward-they extend or exaggerate their old cess consisted, I received answer as follows: modes of practice, without touching their 'When I wish to find out how wise or how principles. What, for example, in this case stupid or how good or how wicked is any of D— has been done to vary the prinone, or what are his thoughts at the moment, ciple of action? What is all this boring, I fashion the expression of my face, as accu- and probing, and sounding, and scrutinizing rately as possible, in accordance with the ex- with the microscope, and dividing the surpression of his, and then wait to see what face of the building into registered square thoughts or sentiments arise in my mind or inches-what is it all but an exaggeration heart, as if to match or correspond with the of the application of the one principle or set expression.' This response of the schoolboy of principles of search, which are based upon lies at the bottom of all the spurious pro- the one set of notions regarding human infundity which has been attributed to Roche-genuity to which the prefect in the long roufoucault, to La Bougive, to Macchiavelli and tine of his duty has been accustomed? Do to Campanella." "And the identification," I said, "of the reasoner's intellect with that of his opponent depends, if I understand you aright, upon the accuracy with which the opponent's in tellect is admeasured." "For its practical value it depends upon this," replied Dupin; "and the prefect and his cohort fail so frequently, first, by default of his identification, and secondly by ill-admeasurement—or, rather, through non-admeasurement of the intellect with which they are engaged. They consider only their own ideas of ingenuity, and in searching for anything hidden advert only to the modes in which they would have hidden it. They are right in this much-that their own ingenuity is a faithful representative of that of the but when the cunning of the individual felon is diverse in character from their own, the felon foils them, of course. This always happens when it is above their own, and very usually when it is below. They have no variation of principle in their inves you not see he has taken it for granted that all men proceed to conceal a letter, not exactly in a gimlet-hole bored in a chair-leg, but, at least, in some out-of-the-way hole or corner suggested by the same tenor of thought which would urge a man to secrete a letter in a gimlet-hole bored in a chairleg? And do you not see, also, that such recherchés nooks for concealment are adapted only for ordinary occasions, and would be adopted only by ordinary intellects? for in all cases of concealment a disposal of the article concealed a disposal of it in this recherché manner-is, in the very first instance, presumable and presumed, and thus its discovery depends, not at all upon the acumen, but altogether upon the mere care, patience and determination, of the seekers; and where the case is of importance-or, what amounts to the same thing in the political eyes, when the reward is of magnitude-the qualities in question have never been known to fail. You will now understand what I meant in suggesting that had they have insinuated the term analysis' into application to algebra. The French are the originators of this particular deception; but if a term is of any importance-if words derive any value from applicability-then analysis' conveys 'algebra' about as much as, in Latin, ambitus' implies ambition,' 'religio' 'religion,' or homines honesti' a set of honorable men.' the purloined letter been hidden anywhere | an error for its promulgation as truth. With within the limits of the prefect's examina- an art worthy a better cause, for example, tion-in other words, had the principle of its concealment been comprehended within the principles of the prefect-its discovery would have been a matter altogether beyond question. This functionary, however, has been thoroughly mystified, and the remote source of his defeat lies in the supposition that the minister is a fool because he has acquired renown as a poet. All fools are poets; this the prefect feels, and he is merely guilty of a non distributio medii in thence inferring that all poets are fools." "But is this really the poet?" I asked. "There are two brothers, I know, and both have attained reputation in letters. The minister, I believe, has written learnedly on the differential calculus. He is a mathematician, and no poet." "You are mistaken; I know him well: he is both. As poet and mathematician he would reason well; as mere mathematician he could not have reasoned at all, and thus would have been at the mercy of the prefect." 6 "You have a quarrel on hand, I see,' said I, "with some of the algebraists of Paris; but proceed." "I dispute the availability, and thus the value, of that reason which is cultivated in any especial form other than the abstractly logical. I dispute, in particular, the reason educed by mathematical study. The mathematics are the science of form and quantity; mathematical reasoning is merely logic applied to observation upon form and quantity. The great error lies in supposing that even the truths of what is called pure algebra are abstract or general truths. And this error is so egregious that I am confounded at the universality with which it has been received. Mathematical axioms are not axioms of general truth. What is true of relation-of form and quantity-is often grossly false in regard to morals, for ex "You surprise me," I said, "by these opinions, which have been contradicted by the voice of the world. You do not mean to set at naught the well-digested idea of centuries? The mathematical reason has long been regarded as the reason par example. In this latter science it is very cellence." 666 666 “Il y a à parièr,'” replied Dupin, quoting from Chamfort, que toute idee publique, toute convention reçue, est une sottise, car elle a convenue au plus grand nombre.' The mathematicians, I grant you, have done their best to promulgate the popular error to which you allude, and which is none the less usually untrue that the aggregated parts are equal to the whole. In chemistry also the axiom fails. In the consideration of motive it fails, for two motives, each of a given value, have not necessarily a value when united equal to the sum of their values apart. There are numerous other mathematical truths which are only truths with in the limits of relation. But the mathema- | ordinary political modes of action. He could tician argues from his finite truths, through not have failed to anticipate—and events have habit, as if they were of an absolutely gen- proved that he did not fail to anticipate-the eral applicability—as the world, indeed, im- waylayings to which he was subjected. He agines them to be. Bryant in his very must have foreseen, I reflected, the secret inlearned Mythology mentions an analogous vestigations of his premises. His frequent source of error when he says that al- absences from home at night, which were though the pagan fables are not believed, hailed by the prefect as certain aids to his yet we forget ourselves continually, and success, I regarded only as ruses to afford make inferences from them as existing re- opportunity for thorough search to the police, alities.' With the algebraists, however, who and thus the sooner to impress them with are pagans themselves, the 'pagan fables' the conviction to which G, in fact, did are believed, and the inferences are made, finally arrive-the conviction that the letter not so much through lapse of memory as was not upon the premises. I felt, also, that through an unaccountable addling of the the whole train of thought which I was at brains. In short, I never yet encountered some pains in detailing to you just now conthe mere mathematician who could be cerning the invariable principle of political trusted out of equal roots, or one who action in searches for articles concealed-I did not clandestinely hold it as a point felt that this whole train of thought would of his faith that x2+ px was absolutely and necessarily pass through the mind of the unconditionally equal to q. Say to one of minister. It would imperatively lead him these gentlemen, by way of experiment, if to despise all the ordinary nooks of concealyou please, that you believe occasions may ment. He could not, I reflected, be so weak occur where + px is not altogether equal as not to see that the most intricate and reto I and, having made him understand what mote recess of his hotel would be as open as you mean, get out of his reach as speedily his commonest closets to the eyes, to the as convenient, for beyond doubt he will en- probes, to the gimlets and to the microscopes deavor to knock you down. of the prefect. I saw, in fine, that he would be driven, as a matter of course, to simplicity, if not deliberately induced to it as a matter of choice. You will remember, perhaps, how desperately the prefect laughed when I suggested, upon our first interview, that it was just possible this mystery troubled him so much on account of its being so very self-evident." I mean to say," continued Dupin, while I merely laughed at his last observations, "that if the minister had been no more than a mathematician, the prefect would have been under no necessity of giving me this cheque. I knew him, however, as both mathematician and poet, and my measures were adapted to his capacity with reference to the circumstances by which he was surrounded. I knew him as a courtier, too, and as a bold intriguant. Such a man, I considered, could not fail to be aware of the |