quaternions has attracted more notice. Yet how many of our teachers have in their own minds, much less can give to others, an answer to the question often asked, "What is a quaternion?" What is true of Geometry is equally true, though perhaps to a less extent, of the other branches of the Mathematics.

The want of our literature in this respect is very manifest by examining Davies & Peck's Mathematical Dictionary, recently published. This work is of great value, and we do not wish to be understood as depreciating it. For the older subjects, it is tolerably complete for a work of no greater size. It is, moreover, we believe, the only work of the kind that has been published in this country. But the word, "Quaternion," we were not able to find. Though the importance of this subject has, we believe, been overestimated, yet the term should be included in any Mathematical Dictionary. Neither could we find such words as "Determinant," "Anharmonic," &c.,-words that are central to wide domains of the science. Almost all the words that it has been necessary to invent during the present century are wanting. Still, with all its deficiencies, it is well worthy of a place in the library of a teacher.

Several articles have appeared in the Monthly that will do credit to American science. One or two deserve special mention. For various reasons the great comet of 1859 was more interesting in its physical changes than any comet that has appeared since the invention of the telescope. It is moreover upon just such objects that the largest telescopes can be most advantageously employed. It was with peculiar interest then that the reports from the great refractor at Cambridge were looked for. These were given in the first volume of the Monthly, together with two very valuable engravings. It is, we believe, the most valuable contribution of the kind ever made to our knowledge of comets.

Another memoir that has less popular interest, but, in our opinion, more merit, is by I'rof. W. Ferrel, "On the Motion of Fluids and Solids relative to the Earth's Surface." For fourteen years have the French Academy offered one of their prize medals for even a partial solution of problems here discussed. They have just withdrawn this subject and proposed another, because no essays were offered and the subject was regarded as too difficult. The problem is to determine the effect of the rotation of the earth upon the movements of the atmosphere. Prof. Ferrel has partially solved the problem, explaining much that has hitherto been inexplicable respecting the causes of the trade winds, the westerly winds of the Temperate Zone, the rotary ocean hurricanes,

and of the meteorological phenomena that are evidently connected with these great movements.

Though such memoirs as these are very desirable, yet we are glad that the educational character of the Monthly has been so well preserved. There is a strong temptation to make such a periodical too abstruse. We do not hesitate to commend it to the support of teachers and to all who are specially interested even in the simplest branches of Mathematics.

PROF. STRONG'S ALGEBRA.*-We call the attention of our scientific readers to this work of Prof Strong. They will find in it an actual advancement of the domain of the Algebraic Calculus. The author has completed the solution of Binomial Equations by pure Algebra, and discovered a method of extracting the highest roots of numbers, neither by a tentative process nor by the aid of logarithms. The famous case of cubic equations left irreducible by Cardan's method is no longer a pons asinorum, as it has been for more than three centuries for the ablest mathematicians of the world. We shall give a more full account of this work in the August number.

MISCELLANY.

SELF-HELP. This is a book which we should like to have circulated by tens of thousands in every State of the Union. Its object is to explain, illustrate, and enforce the maxim, "Heaven helps those who help themselves." There is no lesson more important for every young man and woman to learn than this. We would advise every parent, rich or poor, to purchase this book for his children. The rich man should buy it, for if he can teach his children this lesson, it will be worth more to them than the largest estate he can leave them. The poor man should buy it, for he cannot afford to let his children grow up ignorant of the fact that thousands with smaller means than they, and no better opportunities, have yet, by persevering application and energy, raised themselves to eminent positions of usefulness and influence in society.

The book is made up chiefly of sketches of the lives of those who have achieved success for themselves by industry, perseverance, and self

A Treatise on Elementary and Higher Algebra. By THEODORE STRONG, LL. D. New York: Pratt, Oakley & Co. 8vo. pp. 551.

Self-Help; with illustrations of character and conduct. By SAMUEL SMILES. Boston: Ticknor & Fields. 1860. pp. 308. 12mo. For sale by T. H. Pease.

culture. Being written for Englishmen, the characters selected for illustration are almost entirely from among their own countrymen, and an English author may well be proud that England can afford so many and such honorable examples, to inspire the rising generation. The book, however, is something more than a mere collection of sketches of individual success. The sketches, though some of them are drawn out at considerable length, are all introduced for a particular purpose, to show that opportunities always fall in the way of those who are ready to take advantage of them, or to illustrate some lesson of industry, application or self-reliance. The whole book, therefore, notwithstanding it is somewhat deficient in classification and arrangement, has a unity of plan, and cannot fail to inspire its readers with new hope and courage in their efforts to "help themselves" in the work of life. Clergymen will find here a perfect thesaurus of memorable facts and sayings which may serve as illustrations in their addresses and discourses.

NEW MISCELLANIES BY REV. CHARLES KINGSLEY.*-The many admirers of the Rev. Charles Kingsley will be glad to have placed within their reach a new volume of his miscellaneous essays. It contains several of the Articles that he has furnished to different English Reviews, together with three Lyceum Lectures. One or two of these essays are in his best vein, and all are pervaded by that same genial love of mankind, and desire for reform and the advancement of human happiness, that are so characteristic of his other published works. To these essays and lectures are added the Prefaces which he prepared for the Life of John Tauler, and the recent edition of Henry Brooke's "Fool of Quality." This last betrays views respecting some of the most important points of theology which some of his previous writings had prepared us to ascribe to him, but which we are none the less grieved to see so flippantly stated.

PRENTICEANA.-The lovers of a good laugh cannot do better than take an occasional dip into this book. It is made up of selections from the witty and humorous paragraphs which for nearly thirty years have made the names of G. D. Prentice and "The Louisville Journal" famous the country through. It is of course impossible to embalm wit

*New Miscellanies. By Rev. CHARLES KINGSLEY, Rector of Eversly. Boston: Ticknor & Fields. 1859. 12mo. pp. 375.

+ Prenticeana: or, Wit and Humor in paragraphs. By the Editor of the Louisville Journal. New York: Derby & Jackson. 12mo. 1860. pp. 306.

in a book; and now that the occasions which called it forth are forgotten, these paragraphs have lost much of that which gave them their original relish; yet the old jokes and repartees which once were copied into every newspaper from Maine to Missouri, and made the whole country ring, have still vitality enough in them to shake the sides of the reader right heartily.

THE ELEMENTS OF PERSPECTIVE.-The elements of perspective are here presented, by a distinguished master and teacher of art, in their simplest and most comprehensive form, yet with sufficient fullness for all the ordinary purposes of the draughtsman and artist, and with special reference to the wants of learners. The problems are interspersed with occasional remarks by way of familiar illustration, and with observations on many practical applications of the principles taught, particularly in architecture and painting. The name of Ruskin is sufficient, of itself, to render the work attractive; while the beauty of the letter-press will still further commend it to favor. It would be an excellent book in schools, for the use of which it was professedly prepared.

SPIRITUALISM TESTED.t-This is a new edition of a little work entitled "To Daimonion," published seven or eight years ago under the nom de plume of Traverse Oldfield, with a supplementary chapter on the later history of Spiritualism, and the speculations in regard to its origin. The book attracted some attention when first published, as a learned and concise resumé of the leading facts bearing upon the subject, both of ancient and modern times. Such facts are fully admitted, and a theory is propounded to account for them. That theory ascribes the facts, not to trickery, nor to the agency of spirits, good or bad, but to the "nervous principle." This is regarded as distinctively the "spiritual medium," that is, a force or agency intermediate between mind and matter, by which the mind, through the nerves, produces outward

* The Elements of Perspective, arranged for the use of schools, and intended to be read in connection with the first three books of Euclid. By JOHN RUSKIN, M. A. New York: John Wiley. 1860. pp. 144.

+ Spiritualism Tested; or, the Facts of its History Classified, and their cause in nature verified from ancient and modern testimonies. By GEORGE W. SAMPSON, D. D., President of Columbian College, Washington, D. C. Boston: Gould & Lincoln. 1860. pp. 186.

physical effects, and by which, under certain circumstances of diseased or abnormal action, it may, on this theory, become the source of the various phenomena of Spiritualism. As a candid and learned, though by no means complete examination of the subject, in a clear and attractive style, it is well worth the attention of those who are at all interested in the singular and abundant manifestations of the marvelous which have characterized the last few years and become the basis of what may be regarded as a new religious faith. Whether the author's explanation which is essentially that of Rogers, Mahan, Count de Gasparin, and others-does not itself need explanation as much as the difficult subject to which it is applied, we will not pretend to decide. To our mind, however, it leaves the solution of Spiritualism, in many respects, still an open question.

GOETHE'S CORRESPONDENCE WITH A CHILD.*-This beautiful volume, printed on the most delicately tinted paper, will open to many American readers a new page of German literature, and perhaps reveal to them a phase of German sentiment not easy to understand. The day of blind and passionate idolatry for Goethe is even in Germany slowly and surely waning; and with it, the value of such memorials as this correspondence contains, will, bye and bye, diminish, except as curiosities of Literary History.

We

BARTON'S HIGH SCHOOL GRAMMAR.t-This Grammar has been prepared with an especial aim at simplicity, without loss of fullness. had hoped to find some improvement in the Syntax, but we find all the complex relations that ought to be philosophically distinguished, disposed of as modifications of the subject predicate and copula. We should not call, as the author does, on page 177, brother the grammatical subject of the sentence, "Brother William wrote to me yesterday."

LIFE'S EVENING.-This is a sequel to the handsome volume published by Messrs. J. E. Tilton & Co., under the title of "Life's Morning

Goethe's Correspondence with a Child. Boston: Ticknor & Fields. 1859. 12mo. pp. 504.

High School Grammar; or, An Exposition of the Grammatical Structure of the English Language. By W. S. BARTON, A. M. Boston: Gould & Lincoln. 1860. 12mo. pp. 373.

Life's Evening; or, Thoughts for the Aged. 1860. Boston: J. E. Tilton & Co. 18mo. pp. 265.