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THE Author of this Essay has been forewarned that the adoption of the subscript differential notation, which forty years ago was in some degree of favour but afterwards laid aside, will prove a serious hinderance to the acceptableness of the present Work, as it will be new to the generality of mathematical students, and therefore somewhat repellent. He regrets the circumstance, and feels that an explanation and apology are needed; and he finds both in the fact that the notation alluded to has been forced upon him by the necessities of the case ; and, moreover, he ventures to think that the reader after going through the Essay will agree with him in this, and be willing on this ground to excuse such an important deviation from established mathematical usage.
The Author denominates his Work an Essay, because as a TREATISE it would be very incomplete, there being many portions of the general subject not alluded to in these pages. For information on those portions he must refer the reader to Boole and Gregory and Carmichael, with whose admirable and valuable Works he has been careful to interfere as little