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 example. In this latter science it is very usually untrue that the aggregated parts are[23] 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 within the limits of relation. But the mathematician argues from his finite truths, through habit, as if they were of an absolutely general applicability, as the world indeed imagines them to be. Bryant, in his very learned Mythology, mentions an analogous source of error when he says that 'although the pagan fables are not believed, yet we forget ourselves continually and make inferences from them as existing realities.' With the algebraists, however, who are pagans themselves, the 'pagan fables' are believed, and the inferences are made, not so much through lapse of memory as through an unaccountable addling of the brains. In short, I never yet encountered the mere mathematician who could be trusted out of equal roots, or one who did not clandestinely hold it as a point of his faith that x²+px was absolutely and unconditionally equal to q. Say to one of these gentlemen, by way of experiment, if you please, that you believe occasions may occur where x²+px is not altogether equal to q, and, having made him understand what you mean, get out of his reach as speedily as convenient, for, beyond doubt, he will endeavour to knock you down.

[23]

"I mean to say," continued Dupin, while I merely[24] 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 check. 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 ordinary policial modes of action. He could not have failed to anticipate—and events have proved that he did not fail to anticipate—the waylayings to which he was subjected. He must have foreseen, I reflected, the secret investigations of his premises. His frequent absences from home at night, which were hailed by the Prefect as certain aids to his success, I regarded only as ruses to afford opportunity for thorough search to the police, and thus the sooner to impress them with the conviction, to 

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