the Eclectic School Reading Series, New York, The American Book Company, 60 cents; PRACTICAL PUBLIC SPEAKING, a text-book for colleges and secondary schools, by S. H. Clark and F. M. Blanchard, containing excellent classified selections for public speaking, published at $1.00, by Charles Scribner's Sons, New York; PITMAN'S PRACTICAL SPANISH GRAMMAR, with conversation, vocabulary and imitated pronunciation, by Don Baltasar Vitoria and W. G. Isbister; published by Sir Isaac Pitman & Sons, London and New York, boards 40 cents, cloth, 50 cents; L'ARRABBIATA, von Paul Heyse, edited for school use by Max Lentz, New York, American Book Company; SPEECH OF EDMUND BURKE on moving his resolutions for conciliation with the colonies, edited with Introduction and Notes by Anna A. Fisher, being No. 2 of the Cambridge Literature Series, Boston, Benjamin H. Sanborn and Co., 25 cents; PRACTICAL PHYSICAL EXERCISES, for public and private schools, arranged by Louis Lepper and Wm. H. Wiley, fully illustrated,-a choice little volume showing how to introduce physical training in an effective and practical way, to the certain and lasting benefit of the children, The Inland Publishing Company, Terre Haute, Ind., 80 cents; George Eliot's SILAS MARNER, with an Introduction by George Armstrong Wauchope, the latest addition to Heath's English Classics Series, Boston, D. C. Heath & Co., 40 cents; THE CONSTITUTIONS of the United States, France, Switzerland, Articles of Confederation, rearranged for class study; Boston, Benjamin H. Sanborn & Co., 15 cents each; A PLAIN TALK ABOUT THE KINDERGARTEN, sent for 2 cents by the Milton Bradley Co., Springfield, Mass. PERIODICALS. Appleton's Popular Science Monthly for November contains an interesting illustrated article on the "Kissing Bug" delusion; also valuable papers on Food Poisoning and the Mosquito Theory of Malaria, with other articles, making this an exceptionally valuable and readable number.—Dr. Weir Mitchell contributes to the November Century the first chapters of a new novel or story called "The Autobiography of a Quack." In the same number will appear a chapter of autobiography by Mark Twain, entitled “My Debut as a Literary Person.-Pearson's Magazine is rapidly coming to the front. It is equal to the best of the popular ten-cent magazines. The opening article of the November number, by E. H. Rydall, on Big Fruit Farming Operations, is beautifully illustrated, and gives in a concise form many interesting facts about one of the great industries of California.- The Medical Record, New York, has for years been the leading organ of the medical profession in America, and has gained a world-wide reputation as the recognized medium of intercommunication between the profession throughout the world. It is intended to be in every respect a medical newspaper, and contains among its Original Articles many of the most important contributions to medical literature. The busy practitioner will find among the Therapeutic Hints and in the Clinical Department a large fund of practical matter, carefully condensed, and exceedingly interesting. Medical news from all parts of the world is supplied through special correspondents, by mail and telegraph; New publications and inventions are reviewed and described; in the Editorial Department matters of current interest are discussed in a manner which has established The Medical Record in the estimation of the whole profession as a thoroughly independent journal and the most influential publication of its class. It is announced that The Cosmopolitan will be sold, and that Mr. J. B. Walker, its editor, will devote his time to the manufacture of automobiles.-—Everybody's Magazine is the title of a new publication issued by John Wanamaker. The American Review of Reviews continues to furnish the busy man with the best summaries and ablest articles on the various departments of life of any of the publications coming to our table. It is always packed full of important matter that no intelligent American can afford to pass over. The Youth's Companion is still at the front as a juvenile publication, and has many adult readers. Its menu for the coming year is appetizing. EDUCATION DEVOTED TO THE SCIENCE, ART, PHILOSOPHY AND LITERATURE OF EDUCATION. VOL. XX. DECEMBER, 1899. No. 4. THE EVOLUTION OF THE ARITHMETIC IN THE UNITED STATES. J. M. GREENWOOD, SUPERINTENDENT OF SCHOOLS, KANSAS CITY, MO. HE subject I have chosen to sketch briefly is not preten THE tious, a simple, everyday matter-of-fact description of the rise and progress of arithmetical bookmaking in the United States for a century. From the very nature of the subject-matter it does not admit of much adornment. I address myself, therefore, to one phase of the subject; namely, the difference between the arithmetics of a hundred years ago and those of to-day. In 1788 Nicolas Pike, A.M., printed by subscription his New and Complete System of Arithmetic, and nine years later a second edition was revised, enlarged and corrected by Ebenezer Adams, A.M., preceptor of Leicester Academy. This book was printed at Worcester, Mass. The author, Nicolas Pike, secured in 1785 and 1786 letters of commendation from J. Wheelock, president of Dartmouth University, B. Woodward, professor of Mathematics and Philosophy, and from John Smith, professor of the Learned Languages. It appears also that in 1785 Benjamin West had read the manuscript before it was printed, and his testimonial is unique. I transcribe an extract: The arrangement of the work, and the method by which it leads the tyro into the first principles of numbers, are novelties I have not met with in any book I have seen. Wingate, Hatton, Ward, Hill, and many other authors whose names might be adduced if necessary, have claimed a considerable share of merit; but when brought into a comparative point of view with this, treatise they are inadequate and defective. This volume contains, besides what is useful and necessary in the common affairs of life, a great fund for amusement and entertainment. The mechanic will find in it much more than he may have occasion for; the lawyer, merchant and mathematician will find an ample field for the exercise of their genius; and I am well assured it may be read to great advantage by students of every class, from the lowest school to the university. More than this need not be said by me, and to have said less would be keeping back a tribute justly due to the merit of this work. (Signed) BENJAMIN WEST. There are also strong testimonials from the presidents of Harvard and Yale, dated in 1786; and when the book came from the press the author forwarded an elegantly bound copy to General Washington, who complimented the author very highly for his performance in the direction of sound learning in America. The book is a heavy 12mo of 516 pages, bound in leather. The author devotes 472 pages to arithmetic, including about everything that was then known upon the subject, and to all subjects to which it could be applied. The remaining pages contain a brief treatise on algebra and the conic sections. All the exercises touching business affairs, instead of having the decimal system of money as now used in American treatises, are in English money, and the space given to converting the money of one colony into that of another colony occupies no inconsiderable part of the book. In one place Federal money is introduced sparingly. It was just coming into use. An examination of the work shows what Benjamin West meant when he spoke of the "exercise of their genius." Here are a few specimens : 66 "1. Having the sum of two numbers, and the sum of their square given, to find the numbers." 2. To find the true depth of a well, by dropping a stone into it, also the time of the stone's descent, and of the sound's ascent." "3. How to discover the quantity of adulteration in metals." "4. How to test spirituous liquors." Many years ago, around the fireside on a winter's evening, it was no uncommon thing for the boys to spend their time in try ing to work out difficult arithmetical problems and other puzzles, and these conundrums passed currently from one group or neighborhood to another. It was a narrow way of developing thought, yet it was very much better than doing nothing. Nicolas Pike's arithmetic had more to do in shaping the size and determining the amount of matter that arithmetics ought to contain than any other one book published in the United States on this subject. It was a change from the English books to a native one soon to be followed by a numerous host. Little space is given by Pike to illustrations, but much to examples and rules; and with the exception of two or three large books still in common use it is the most formidable treatise ever issued in this country. Brooks' Higher Arithmetic contains more matter, but it does not extend into algebra or geometry. Dropping down forty years brings the reader to an arithmetic by T. H. Babcock, who wrote a compact little volume of 180 pages, one of the best works of that period. He doubtless was acquainted with Leybourn's Diary Questions, published in England from 1704 to 1816, judging from the poetical effusions interspersed throughout the miscellaneous collection in this volume. At the end of each subject the author printed questions, which he regarded as a very decided improvement over previous works. Forty years had completely changed the currency system of the country. Nearly all the problems involving money are in United States money. Instead of 472 pages devoted to the arithmetic proper, as Pike had done, he compressed what he had to say on arithmetic into 138 pages of closely printed matter. The remaining forty pages is placed under the head "Miscellaneous," beginning with Chronological Problems, followed by Gravities of Bodies, Falling Bodies, Mechanical Powers, Mensuration of Surfaces and Solids, an introduction to Algebra, Geometry and Trigonometry, and seven pages of miscellaneous questions. I insert a few for the benefit of the boys and girls who may be interested in knowing what their great-grandfathers did. "1. If a large vessel be kept full, it is required to find how far water will spurt from it through a hole D, on the plane BC?" 2. A country clown addressed a charming belle, 4. A wretch, who spurned the virtuous path below, He by mechanic art a ladder raised, Its height the vulgar and the learn'd amazed. Scale heaven as well as he? At least I'll try.' Now wrapped in clouds unpierced by human eyes, Which fires a cannon at the base, whose sound Or how far soaring from this earthly spot." There are sixteen of these poetical problems, of which the four quoted are good specimens. I insert the 77th problem, next to the last in the miscellaneous collection, as a curious illustration the mathematical mind took in those days to express itself on religious subjects. Here it is : "Suppose the natural increase of mankind to be such that they double once in fifty years; and suppose a general resurrection had taken place Anno Mundi 5800: what would have been the number of souls? And suppose the whole globe of the world, sea and land, rocks and mountains, to be equally divided among them, how large a part would each have drawn?" |