THE task of an author;" says Dr. Johnson, is to teach what is not known, or to recommend known truths by his manner of adorning them." To attempt the former is sufficiently irksome to enervate endeavour, and to succeed in the latter, he must surmount obstcles that no sagacity can avoid, and encounter diffi culties which prevision cannot alleviate. He must appeal to judges prepossessed by passions or biased by prejudices to some who are more willing to go wrong by their own judgment, than to be indebted for a better or a safer way to the wisdom of another; and to others, whose good taste and perspicacity will not allow them to read any thing until its reputation is eetablish~ ed by the Ministers of Criticism." But, of those who are more inclined to be pleased, who may be persuaded to remit their censure at those errours into which the author has inadvertently or unavoidably fallen, and who will pass with a friendly eye over those imperfections that are inseperably connected with all human productions; it is hoped, though the reader should not find his feelings imperceptably stolen from him by the enchantment of novelty, or his understanding captivated by the profundity of invention, that if his patience can endure a careful perusal of the following work, he will dismiss it with, at least this negative encomium," that it is a laudable attempt to improve the instruction of the unlearned, and furnish schools in general with a useful and comprehensive system of Practical Arithmetick. He who is resolved to attain any degree of eminence in the science of Mathematicks, dooms himself to wade through a toilsome course of severe, uninteresting labour, unaccompanied with any of those charms that can engage the feelings by their novelty, or delight the imagination by their lusture; without any hope of honorable reward to stimulate to exertion, or soften the asperities of study. But the writer of Common Arithmetick has a much easier task The labours of many that have gone before him as "pioneers," who were distinguised by profound investigation and mathematical researches, have rendered his path comparatively easy, even where their feet have never trodden; "" as the sun dissipates the shades of darkness, and spreads a twilight beyond the immediate influence of his direct beams." Indeed, it may be said that the only necessary resourse of the writers of the present age, is to copy the best examples of their predecessors with such modifications and amendments. as the differnnt modes of reckoning in business, the fluctuation of coins, weights, and measures, and as the invention of means to facilitate the same solutions require. The practical systems of Vulgar Arithmetick already extant are very numerous; and the authors of some of them have exhibited great knowledge and ability. it may therefore be expected, that he who ventures to add to their number should produce a substantial plea for such an obtrusion on the publick notice. It may justly be expected that he should be either an accurate schollar or a profound mathematician. The writer has no claim either to the one or the other of these distinctions; and must therefore picad another apology. Having been repeatedly solicited by a number of gentlemen respectable for their understanding and skill in Mathematical Science, to publish his TABLE of LOGARITHMS constructed only for private use, together with their numereus and important uses in the more difficult parts of Arithmetick Trigonometry &c. and believing, notwithstanding the endless variety of books now extant on Vulgar Arithmetick, there is yet room to introduce usefulness with novelty, the author of the following work humbly ventures to assume the responsibility of endeavouring to avoid the redundencies of some, and to supply the deficiencies of others. It is believed that a more accurate and extensive SYSTEM LOGARITHMS for natural numbers was never before published in this country. The best American Tables are carried only to six places besides the index, which, though capable of giving answers sufficiently exact in most solutions, are, notwithstanding, deficient where great accuracy is required. In constructing the following table the author has pursued the " Differential Method" hinted at by Mr. Henry Briggs, Professor of Geometry in Gresham College London, and Dr. Hutton's " Practical Rule for the Construction of Logarithms." He was also solicited to publich with this, a Table of Logarithmick Signs, Tangents, &c. carried to seven places decimal, which should correspond with those for natural numbers; but as this would render the work too voluminous for a common school-book, it was thought unadvisable to augment the expense without proportionably increaseing the advantage. Should their occur sufficient reason for publishing such a system of Logarithms and Logarithmick Sines and Tangents, together with oth-. er Logarithmick and Mathematical Tables, they may be given to the publick at some future period. THE METHOD OF COMPUTING BY LOGARITHMS, where it can be adopted, aa in the evolving of roots, is manifestly the most expiditious of any that human powers have hitherto invented. The learner, who before was unacquainted with their proper ties, o has had the patience and assiduity to toil through the tedious course of evolution by the usual process, wili admire to find that so much labour should ever be reduced to so much ease! The author has endeavoured, though in some instances at the expense of deviating from ancient usage, to arrange the several parts of Vulgar Arithmetick according to their relative importance, and their mutual dependence upon each other; and to render the whole as easy and familiar as the nature of the subjects would admit. From what experience the author has had in the instruction of youth, aud the general complaint of the want of some work adapted to accompany those elementary treatises on Astronomy which are used in our Schools and Academies, the writer was induced to subjoin a short, though imperfect sketch of Practical Astronomy. And in this, he has been more desirous to be useful than to appear original. All the Tables except the II, XVIII and XIX, together with the method of calculating the time of New and Full Moons and Eclipses, were taken from Dr. Brew. ster's edition of Fugeson's Astronomy lately published. The method ef Projecting Eclipses is purely mathematica, and is not subject to those inacuracies which the use of the sector is liable to produce. Whatever merit justice may award to the following primetial pages, the author cannot forbear repeating, that it was the hope only of being useful, that induced their submission to publick scrutiny. If he has failed in the attempt, the disquietude of disappointment will be allayed by the reflection, that he is not the first" qui magnis excidet ausis" who have misjudged in their abilities. To suppoae the work wholly exempt from errours, whether of the press or of the pen, would be to suppose what the most vigilant care has seldom performed. And whether these will be found to have a counterbalance of good, is refered to the candour of those who may read to decide ;-they are the constituted judges, and to them he submits with defference and respect. Williams College, October, 1818. E. H. B Practical Questions in Multiplication and division Simple Proportion or Rule of Three Another Method of Computing Logarithms Directions for taking Logarithms and their |