Just Completed, and Patented in the United States, England and France. The Cut of this Furnace will enable every intelligent mind to comprehend at a glance a principle for constructing Furnaces, Steam Boilers, Stoves, and other heating apparatus, that must entirely supersede the common apparatus in use at the present day for the following reasons: 1st. It entirely changes the principle and character of Hot-Air Furnaces, developing another and a new principle, and thereby obviating all former objections to their use. 23. The smoke and gases are entirely controlled, in the cluster of cones which stand over the broad, shallow fire-pot, by holding them in the tapering cones or radiators, exposed to the direct action of the light and heat from the fire-pot, (which is brought to a focus at the top of each cone,) a powerful heat is created from the fuel consumed, by the action of the heat against the surface of these cones, similar to the action of the sun upon the Sun Glass, thus saving the heat from the fuel, that passes off in the common Furnaces and Stoves, in the shape of unconsumed smoke and gas. 3d. An immense radiating surface is formed by the arrangement of the cones, annular chamber and cross-pipe, compelling the heat to act upon the whole surface directly and equally at the same time. It also secures a free circulation of fresh air over all the heating surfaces, which has never before been done. 4th. There are no joints in this furnace, over the fire, so that any leakage of smoke or gas into the air chamber is prevented, which it is impossible to avoid in the common furnaces. 5th. The coal is burnt in a broad, shallow fire-pot, protected by Soapstone, Fire Brick or Iron Staves; thus preventing the pots from becoming over heated, and the Furnace from cracking, warping, or burning out; and securing thereby a perfectly healthy, fresh warmth throughout the building. We would respectfully invite the attention of all, and particularly the scientific portion of the community, to this most useful invention. We also manufacture the TRIO PORTABLE FURNACE, now known as the best Portable in use. Also, the TRIO COAL STOVE, upon the same principle. Also a WOOD VENTILATING STOVE, Designed particularly for School Houses, Academies, &c. VENTILATORS for Rooms, Chimneys, Roofs, &c. Special attention given to warming and ventilating buildings in any part of the country. CHILSON, GOULD & CO. 99 & 101 Blackstone St., Boston. Postage any distance in the United States, Twelve Cents per Year, payable in advance. DAMRELL & MOORE and GEORGE COOLIDGE, Printers, 16 Devonshire Street, Boston. ELISHA KENT KANE,. CONTENTS. AUGUST, 1857. HERMANN KRUSI-SPECIAL EDITOR. SOME THOUGHTS CONCERNING THE ORIGIN, RELA- 353, RESIDENT EDITOR'S DEPARTMENT: Our Educational Exchanges, 388; Oratory, 363 390; Free Schools, 391; Philosophy in Court, THE INFLUENCE OF TEACHING UPON THE HEALTH, 374 FELLENBERG, THE FOUNDER OF THE FIRST AGRI- 391. 379 MATHEMATICAL QUESTIONS AND SOLUTIONS,.......... 383 LITERARY RECORD,. 393 395 397 398 399 THE MASSACHUSETTS TEACHER is published on the first of every month in numbers of 48 octavo pages. It is the official organ of the State Teachers' Association, and is devoted exclusively to Home and School Education. Subscription price, $1 per annum in advance, or $1.50 at the close of the year. All communications should be addressed to the "Massachusetts Teacher," or to the Resident Editor. Advertisements should be forwarded by the 15th of each month, and, unless accompanied ba definite order, will be continued till forbidden. The ninth volume of the Teacher, neatly bound in cloth, can be obtained at our office for $1.50. Those who have the back numbers in good condition can exchange them for bound volumes by paying fifty cents. GREENLEAF'S HIGHER ARITHMETIC. THE NATIONAL ARITHMETIC, On the Inductive System, combining the Analytic and Synthetic Methods, forming a complete course of Higher Arithmetic. By BENJAMIN GREENLEAF, A. M., author of the "COMMON SCHOOL ARITHMETIC," " ALGEBRA," etc., and late Principal of Bradford, (Mass.,) Academy. New electrotype edition, with additions and improvements, 444 pages. Retail price 75 cents. The attention of teachers and others interested is respectfully invited to the great improvements in the revised edition of this work, which is just issued. In the present revision great labor and research have been expended, and the Publishers trust that it will be found, on examination, THE BEST TEXT-BOOK EXTANT, for ACADEMIES, NORMAL, and HIGH SCHOOLS. The author of this work wishing, if possible, to keep pace with the rapid march of improvement, has again thoroughly revised, rewritten, and considerably enlarged it. The results of a long experience as a mathematical instructor, and the suggestions of many distinguished teachers of the present day, are embodied in this volume. In preparing this as well as the former editions of his National Arithmetic, the author has regarded the end to be sought in the study of Arithmetic as twofold,-a practical knowledge of numbers and the discipline of the mind. With reference to the former, he has endeavored to present methods which are brief, accurate, and especially adapted to the wants of business life; with reference to the latter, he has aimed to give a clear and logical analysis of every operation, from the simplest to the most involved. The author flatters himself that the present edition of the National Arithmetic embraces many improvements on former editions. He has endeavored to present clearer definitions, more rigid analyses, and briefer and more accurate rules. While almost every topic included in earlier editions has been treated in a more elaborate and comprehensive manner, this volume comprises a large amount of new matter, which, it is believed, will be found useful in business. On comparing this with preceding editions, teachers will find extensive additions and improvements under the heads of Numeration, Addition, and the other fundamental rules, Properties of Numbers, Fractions, Ratio, Percentage, Notes and Banking, Roots, etc. Among the new material will be discovered methods of finding the greatest common divisor and the least common multiple of fractions, of reducing fractions to a common numerator, of contracting the operations in the multiplication and division of decimal fractions, of reducing continued fractions, of averaging accounts, of alligating, of extracting roots to any degree, and of reducing numbers from one system of notation to another. Especial attention is invited to the section on averaging accounts,—a subject rarely taught in schools, though of great importance in the counting-room,-to the manner of treating the roots, and to the many new problems which will be found in all parts of the book. Specimen copies will be furnished to teachers, by mail, (postage paid,) who will forward their address, and 60 cents in postage stamps to the publishers. We continue to publish GREENLEAF'S MATHEMATICAL SERIES, improved editions of each book, including three Arithmetics and the PRACTICAL TREATISE ON ALGEBRA, which are graded to the capacities of all classes of pupils, and the most popular series extant, being extensively used in the best institutions throughout the United States, and the British Provinces. GREENLEAF'S ELEMENTS OF GEOMETRY is in preparation, to form a volume about the size of the "National Arithmetic," and will be ready in a few months Descriptive Catalogues of all our VALUABLE SCHOOL BOOKS will be forwarded, on application, by mail. Constantly on hand a COMPLETE ASSORTMENT OF SCHOOL and CLAS SICAL BOOKS, whieh are offered to Teachers and others at the lowest market prices ROBERT S. DAVIS & CO., No. 118 Washington St., Boston, |