below the letter, the usual number value of the letter was multiplied by one thousand. Leslie is authority for the statement that the Romans at a late period of their history adopted an alphabet notation similar to that of the Greeks. "The letters a, b, c, d, e, f, g, h, i represented the nine digits, 1, 2, 3, 4, 5, 6, 7, 8, 9; the next series, k, l, m, n, o, p, q, r, s expressed 10, 20, 30, 40, 50, 60, 70, 80, 90; and the remaining letters t, u, x, y, z, denoted 100, 200, 300, 400, 500." I, V, hi, hu, represented 600, 700, 800, 900. This system was never very generally used. The use of alphabet notations has been very general among civilized nations. The Hebrews are a notable example. Among many oriental nations the alphabet was used for the smaller numbers and either abbreviations or arbitrary characters for the larger ones. [To be continued.] PERCENTAGE. The questions proposed in the outline can be best answered by a life insurance agent, a member of a tax-board, a merchant, and a banker. These men should be interviewed by every teacher who can possibly get the opportunity of doing so. Knowledge fresh from the men engaged in these lines of work is worth more than book statements upon the subject. An agent was paid $99 for selling at 2 per cent. commission. How much did he remit to his principal? If the pupil already understands the nature of commission he will see in the $99 the product of 2% and the amount of sales. Seeing this, he knows that the amount of sales must be the quotient of $99 by 2%. Hence his solution would be $99÷.023=$99 ÷ 1=$99 × 4oo=$3600. $3600— $99= $3501. The question is asked, "How would a business man's solution differ?" A business man would in all probability never have such a problem to solve. The agent would know the amount of sales, and would therefore compute his commission, take it out and remit the balance. In his letter remitting the balance, the principal would be informed of the amount of sales and the commission deducted. If, however, a business man should have such a problem, I presume he would solve it in a direct, straight-forward way, just as the schoolboy ought to solve it. If the business man has a better way than the school-boy, then the schoolboy deserves pity. The school-boy should have the business man's short methods, plus a conscious understanding of the underlying principles. A NEW ALGEBRA. Text-Book of Algebra With Exercises by Drs. Fisher and Schwatt of the University of Pennsylvania, has just appeared. The authors are both among the first mathematicians of this country, and are also splendid teachers. They have given more time and care to the preparation of this book than is usually given to elementary texts. As a result, one finds in the book a remarkably clear and logical development of the subject. The book contains many desirable, even necessary features, not usually found in books for beginners. In the Introductory Chapter on General Number the extension of the number system is made in an admirable way. The idea of positive and negative number is brought out in such a manner that no student can fail to appreciate it. In the second chapter the fundamental operations with algebraic numbers are considered. The fundamental laws of algebra are fully treated and the law of signs proved in an interesting manner. The distinction is clearly made between + and as signs of operation and as signs of quantity. In the advanced treatment of multiplication and division and in factoring much emphasis is justly placed upon type-forms. The early application of factoring to the solution of equations is worthy of note. The introduction to the solution of problems in Chapter V is especially valuable. The treatment of inequalities, irrationals and imaginaries is unusually good, the treatment of irrationals being the first really satisfactory discussion that has appeared in an elementary text. The problems have been selected with care. The gradation and variety is very noticeable. The book, as a whole, is unified and will surely hold the interest of the student from the opening chapter to the end of the book. THE RAND-MCNALLY ARITHMETICS. This is a two-book series with an accompanying Manual. The books are written by that able educator, Dr. E. C. Hewett, of Illinois. The Primary Arithmetic has considerable space devoted to oral work. This leads by easy stages to real number. There are many helpful suggestions to teachers and the book will certainly prove interesting to the pupils. The Practical Arithmetic seems to justify its title. Much of the rubbish so common in arithmetics is not found in here. Accuracy in operation, clear insight into the fundamentals, and development of principles are the things greatly emphasized. The problems are of a very practical character. The whole subject of arithmetic is remarkably well unified. As an illustration, in percentage neither cases nor formulæ are given. The subject is developed as the direct application of the fundmental operations. The Manual will be a great help not only in the use of these books, but in the rational teaching of any text of arithmetic. The various subjects are treated in a thoroughly scientific as well as pedagogical way. This series of books is worthy the careful consideration of every one who is interested in the progress of the subject of arithmetic. HORNBROOK'S PRIMARY ARITHMETIC. The purpose of the book is well stated in the preface. "The progress of a beginner in arithmetic is of a desirable kind when it involves a succession of insights into the relations of numbers and an increase of expertness in dealing with them." This little book places due emphasis upon the number-system. Counting is fundamental, counting by 10's, by 5's, by 2's. Frequent use is made of number tables, and in this way the child is greatly helped in his understanding of the number-system. The work of the second, third and fourth years is covered in a most excellent way. The choice of problems and exercises is especially good. Helpful suggestions to the teacher are of frequent occurrence. The book is neat and attractive in appearance and is published by the American Book Company. LECTURE ON ELEMENTARY MATHE- By Joseph Louis Lagrange. Translated by Thomas The Leçons élémentaires sur les mathematiques of Lagrange have long been regarded as the highest type of elementary expositions on account of their originality and elegance. These lectures were delivered in 1795 at the Ecole Normale, an institution which had its origin in the French Revolution, and which has had a very great influence in shaping the practical tendencies in modern education. Coming from one of the greatest mathematicians of modern times, they are unique in character; filled with historical references, philosophical remarks, and practical suggestions, they cannot help having stimulating influence. This book contains in addition to the original five lectures, a very interesting biographical sketch of Lagrange and an appendix on the "Origin of Algebra." The lectures are entitled: I.-On Arithmetic, and in particular fractions and logarithms; II.-On the Operations of Arithmetic; III.-On Algebra, particularly the resolution of of Equations of the Third and Fourth degrees; IV. On the resolution of Numerical Equations; and V. On the employment of curves in the Solution of Problems. I cannot mention in this brief review all the subjects considered in these lectures, but their general character will best be shown by a consideration of one of the subjects, taken up in the first lecture; viz., the relation of the process of measuring one magnitude by another, to the process of finding the greatest common divisor, to continued fractions, and to certain series. This relation, it seems to me, is a very striking one and is here brought out in a very striking manner. Let it be required, for example, to find the ratio of one line, to another; i. e., to measure one line by another regarded as the measure, but which is not divided into sinaller parts. The most obvious method is as follows: Apply the measure to the proposed length and let it be contained three times, say, with a remainder. Since the remainder is less than the measure, it can be applied an integral number of times, say two, to the measure, with a remainder. Apply this remainder to the preceding remainder, which is contained four times, say, with a remainder. This process is to be repeated until a remainder is found which is contained in the preceding remainder an integral number of times, which must happen if the lines are commensurable, or the process must be carried out indefinitely, if they are incommensurable. Suppose by this process the successive remainders are contained in the preceding remainders five, two, and three times, the last being exact, then the ratio of the given lines is expressed by the continued fraction: different remainders and not to the different quotients. Consider now the series of fractions, 1, 1, 162, 122 13561 1,4, each fraction being obtained by dropping part of the continued fraction thus: 7=3+}, 3+1 2 ++, etc., the last being the value of the continued fraction. The fractions preceding the last are alternately smaller and larger than the last, and possess the remarkable property of approaching the last in value in such a way that no other fraction can approach it more nearly unless its denominator is greater than the product of the denominator of the given fraction and the denominator of the following fraction. Thus no fraction can approach 22 more nearly than unless its denominator be greater than 9X47. The above series of fractions possess the interesting property that the difference between any two consective fractions is a fraction whose numerator is a unity and whose denominator is the product of the denominators of those fractions. This leads to another expression for the ratio between two magnitudes. Thus, in the example above: 356 1227 + 1237=1+1=2x9 + 1 I am sure no teacher of arithmetic could read these two lectures without having his conception of arithmetic enlarged, and without feeling a renewed interest in the subject. This would certainly be of the greatest value in his teaching. The lectures on algebra are elementary in character, and would be of the greatest value to all teachers of algebra in high schools; indeed, they could be read without difficulty by students who have had the ordinary high-school course in algebra, and would form a valuable supplement to such a course. This work will certainly prove very beneficial to all interested in elementary mathematics, and I am sure all such will feel grateful to the translator and publishers for their excellent English edition of these classic lectures. [The Open Court Publishing Company, Chicago.] UNIVERSITY OF PENNSYLVANIA. JOHN B. FAught. MEETING OF TOWN AND CITY SUPERINTENDENTS. The ninth annual meeting of Indiana's town and city superintendents held its sessions at Indianapolis November 10, 11 and 12. Over two hundred members were enrolled, the attendance being larger than usual. An interesting program was presented and discussed with spirit. The committee on course of study made its final report, which was adopted and recommended as a basis in forming courses of study throughout the state. So satisfactory was this report that the association appointed a committee to prepare a high school course. The State Board of Education reported that it had engaged Professor S. H. Clark of Chicago University, to revise the 3d, 4th and 5th readers. Considerable difference of opinion prevailed in regard to the excellence of the present series of text-books. The arithmetics were especially condemned, and the slight difference in price of the series commented upon; while the first and second readers received a fair share of criticism. Superintendent Geeting in this connection made the remarkable statement that more money was expended for first and second readers than for all the other readers, the spellers, the arithmetics and the geographies combined. The most interesting and thoughtful discussion of the association turned upon the relation of Industrial Training, Sloyd and the Kindergarten to the public schools. There seemed to be an awakening all along the line to the importance of these departments of education. Superintendent Wiley urged the enactment of a law extending the operation of Industrial Training. He believed a better correlation of studies and an elimination of certain elements of the curriculum would make the introduction of such work quite feasible. Superintendent Goss argued that Manual Training was especially needed in the cities for its reactionary force, and its chemical power to combat the evils of the street. It should go, he contended, to the seventh and eighth and even to the lower grades of the public schools. Sloyd was shown to be of Swedish origin and to signify dexterity of hand. The argument for Sloyd resembled that for Industrial Training. One speaker thought it had an influence to teach pupils "to work and not to get out of work." It Superintendent Millis made an earnest plea for the Kindergarten. He thought that the Kindergarten needed the supervision of the public schools and that the schools would profit greatly from the mere enthusiasm of kindergarten teachers. was felt that the school was under obligation to give the pupil the greatest amount of training at the earliest period-an obligation which the Kindergarten could well discharge. These three topics might have been discussed to advantage in one paper, their mutual relations and limitations presented and their point of adaptation to the public schools argued. "How to Get and Keep the Boys in High School" drew out much discussion, the question of athletics especially provoking debate. Superintendent McDaniels' paper on "The Province of the High School Principal" was well written and thoughtful. The leading ideas advanced were that the high school principal should be his pupils' confidential advisor, and that he should keep in sympathetic touch with the lower grades. Superintendent Snyder's "Objections to Departmental Work" lay chiefly in the pupil's loss of responsibility to teacher and the teacher's deprivation of close, personal relation to pupil. The sessions closed with a forcible paper on "Number as Ratio" and a desultory discussion on the "Compulsory School Law," "Semi-Annual Promotions" and "Grade Meetings." H. S. SCHELL. THE LANTERN THAT GIVES THE TRUE LIGHT. While the modern magic lantern is in no sense whatever a lantern, it will, doubtless, always retain the name. Within the last ten years it has been greatly developed, being no longer a toy or curiosity box, but a genuinely scientific instrument; as much so in its way as the microscope or telescope. The more pretentious but well-known word stereopticon designates two or more magic lanters of a high grade used together and registering accurately on the same screen; the stereopticon produces the dissolving effects which so fascinate a miscellaneous audience, making many pictures appear as though they were a series and leaving no blank gaps between. Still the plain single lantern is infinitely better than none, and to the ownership of one of these any family may aspire which is rich enough to buy a cheap sewing machine. In schools of any and every grade and size the magic lantern should be found, as a matter of course; it is in itself a teacher of great range and efficiency. In having placed their superb line of lanterns, with a practically unlimited stock of slides, within easy reach of schools of all degrees, the manufacturers, Messrs. J. B. Colt & Co., of New York, certainly deserve well of all instructors. They will be happy to correspond with you on the subject, and to supply any information relating to it. In a matter like this it will be well to act on impulse and write them at once. EDUCATIONAL INFORMATION. Lafayette Day was successfully observed in the public schools of Ashland, Ky. President A. H. Yoder of Vincennes reports a good year thus far at Vincennes University. Professor Melson C. Marshall is enjoying his third year as principal at Kent, Ind. Miss Myrtle D. Ogden is his assistant. President J. H. Smart of Purdue University is in California seeking restored health. He has a leave of absence for six months. Favorable reports are made of Superintendent Johnson's work at Franklin, Ind. Large attendance, harmony and interest are some of the indications. Alfred Bayliss, one of the editors of Child-Study Monthly, was elected state superintendent of Illinois November 8th. This promises well for the schools of that state. E. L. Kellogg & Co. announce a reduction in the price of their excellent School Journal from $2.50 to $2.00. This will be recognized as a low price for an illustrated weekly paper. Purdue University monograph No. 5 is on "Yeasts and their properties." No. 6 is on "Bread making." In both there is quite a fund of scientific information practically applied. The teachers of Ashland, Ky., have organized a reading circle. Herbert Spencer and current events are the present subjects of study. They have been joined by some of the county teachers. Miss Margaret Williams is supervisor of music at Hillsboro, Ill., this year. She has succeeded in arousing great interest among both pupils and patrons. She is quite a success as a special teacher of music. Samples of the Perry Pictures as advertised on another page of this issue have reached us, and they can not be too highly praised. The marvel is that such artistic material can be furnished at so small a price. The Southeastern Ohio Teachers' Association met in Ironton, October 28-29. The neighboring state of Kentucky was ably represented on the program by Superintendents Leech of Catlettsburg, and Crabbe of Ashland. The Kentucky Educational Association will hold its annual session at Louisville, December 27-29. The program prepared assures an interesting and profitable meeting. Superintendent E. H. Mark of the Louisville schools is president of the association. Superintendent M. W. Deputy of the Jennings county schools announces his expectation of bringing "all the trustees and teachers in the county to the State Association at Indianapolis." What a gathering we should have if all superintendents would do likewise. THE EDUCATOR has great pleasure in recommending the products of the Health Food Co., at Battle Creek, Mich. This notice is voluntary and wholly unsolicited by that company. Moreover, it is based upon the principle that the proof of the pudding is in the eating. Send for their catalogue. The Indiana State Normal School Alumni Association will tender an informal reception to all alumni and to all other persons who have at any time been students in the school, at Indianapolis, on Wednesday evening, December 28, immediately after the annual lecture. The place of the reception will be announced later. The Atlantic Monthly promises a wealth of the best reading for the coming year. Without losing any of its high character as the exponent of the best things in American literature, the Atlantic has come to see that this best stands very close to the best in education. Development in this direction is giving it a peculiar value to teachers everywhere. To Professor Tharp of Roll, Ind., we are indebted for an interesting report of Arbor Day observance in Washington township, Blackford county. The unique feature was a joint meeting of all the districts at the center of the township. The results are seen in the improvement and beautifying of school grounds. Much of the credit belongs to Trustee Virgil H. Alexander. The Parke County Teachers' Association held its eighteenth annual meeting at Rockville, on Friday and Saturday, November 25-26. The instructors were Miss Mary E. Moran of the State Normal, who treated the subject of reading and literature; and Professor E. H. Lindley of Indiana University, whose subject was Psychology. The work of the instructors was highly appreciated. A number of good papers were presented by home teachers. A profitable meeting is reported. Mr. George Wilson was chairman. AMONG THE NEW BOOKS. It is rare, indeed, nowadays to find lying right in our midst a fallow field with soil so fertile as that which Mr. Frank Stockton has turned over with such success in Buccaneers and Pirates of Our Coasts. It is so obvious, too, that Mr. Stockton was just the man who should tell what there is to say about such a subject. The great wonder is that he did not say it before, so evident is it that he has the genuine pirate spirit. "When I was a boy," he begins, "I strongly desired to be a pirate. .. I had a great desire to become what might be called a marine Robin Hood. I would take from the rich and give to the poor; I would run my long, low, black craft by the side of the merchantman, and when I had loaded my vessel with the rich stuffs and golden ingots which composed her cargo, I would sail away to some poor village, and make its inhabitants prosperous and happy for the rest of their lives by a judicious distribution of my booty." It is easy to see how such largeness of soul would have its influence in idealizing some of the "Brethren of the Coast," whose adventures are described. However, the portrayals are not one-sided, but faithful rather to the history into which they are woven. It is interesting just at this time to notice that piracy was one of the natural products of the monstrous Spanish exactions in the seventeenth century. The stories are not usually connected except as they all deal with the same class, but they make, nevertheless, fine reading for boys, both young and old. [The Macmillan Co., $1.50.] One of the most helpful books for teachers in the study of Shakespeare is the little book recently issued by the Doubleday & McClure Company of New York, and entitled How to Study Shakespeare. The author is William H. Fleming, and the book is fortunate in possessing an introduction by the eminent Shakespeare teacher and student, Dr. W. J. Rolfe. While the book is of great value, as suggested, for teachers, it seems that the purpose in preparing it was mainly to |