For, in respect to the latter branch of the supposition, it should be considered that the most trifling variation in the facts of the two cases might give rise to the most important miscalculations, by diverting thoroughly the two courses of events; very much as, in arithmetic, an error which, in its own individuality, may be inappreciable, produces, at length, by dint of multiplication at all points of the process, a result enormously at variance with truth.  And, in regard to the former branch, we must not fail to hold in view that the very Calculus of Probabilities to which I have referred, forbids all idea of the extension of the parallel:  — forbids it with a positiveness strong and decided just in proportion as this parallel has already been long-drawn and exact.  This is one of those anomalous propositions which, seemingly appealing to thought altogether apart from the mathematical, is yet one which only the mathematician can fully entertain.  Nothing, for example, is more difficult than to convince the merely general reader that the fact of sixes having been thrown twice in succession by a player at dice, is sufficient cause for betting the largest odds that sixes will not be thrown in the third attempt.  A suggestion to this effect is usually rejected by the intellect at once.  It does not appear that the two throws which have been completed, and which lie now absolutely in the Past, can have influence upon the throw which exists only in the Future.  The chance for throwing sixes seems to be precisely as it was at any ordinary time — that is to say, subject only to the influence of the various other throws which may be made by the dice.  And this is a reflection which appears so exceedingly obvious that attempts to controvert it are received more frequently with a derisive smile than with anything like respectful attention.  The error here involved — a gross error redolent of mischief — I cannot pretend to expose within the limits assigned me at present; and with the philosophical it needs no exposure.  It may be sufficient here to say that it forms one of an infinite series of mistakes which arise in the path or Reason through her propensity for seeking truth in detail.

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FOOTNOTES—­Marie Rogêt

{*1} Upon the original publication of “Marie Roget,” the foot-notes now appended were considered unnecessary; but the lapse of several years since the tragedy upon which the tale is based, renders it expedient to give them, and also to say a few words in explanation of the general design.  A young girl, Mary Cecilia Rogers, was murdered in the vicinity of New York; and, although her death occasioned an intense and long-enduring excitement, the mystery attending it had remained unsolved at the period when the present paper was written and published (November, 1842).  Herein, under pretence of relating the fate of a Parisian grisette, the author has followed in minute detail,