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brevity too often at the expense of clearness, — sometimes omitting matter in fact indispensable to the complete comprehension of the subject, and perhaps for the sake of introducing what is, to say the least, of doubtful value. Mr. Leonard's book is remarkably free from these faults. Where it is really necessary, he uses as many words as other authors, but very seldom where it is not. Let us take one specimen. A rule has been adopted in many of our most respectable courts of justice for computing interest when partial payments have been made. In the New York Chancery Reports, this rule is thus stated by Chancellor Kent ;
The rule for casting interest, when partial payments have been made, is to apply the payment, in the first place, to the discharge of the interest then due. If the payment exceeds the interest, the surplus goes towards discharging the principal, and the subsequent interest is to be computed on the balance of principal remaining due. If the payment be less than the interest, the surplus of interest must not be taken to augment the principal; but interest continues on the former principal until the period when the payments, taken together, exceed the interest due, and then the surplus is to be applied towards discharging the principal; and interest is to be computed on the balance, as aforesaid." Thus we find this rule in the recent Arithmetics. Mr. Leonard seems to us to have gained much and lost nothing by expressing it as follows;
“Cast the interest to the time when the money paid shall at least be equal to the interest, then discharge the interest from the money paid, subtract the excess, if any, from the principal, and cast the interest on the new principal as before, and so on."
His management of interest may be referred to as a specimen of his style. Generally the scholar carries off from common treatises no single simple rule that will really serve the purposes of business. He learns, - that is, commits to memory, - a number of half-formed ones, none of which proves available in the end, and he finally gets to performing the operations in question by a process which he owes to his own unaided common sense. The Numeration in this work, the statements of all the simple rules, and the method of proving certain operations (as multiplication), may generally be compared with corresponding portions of common treatises, much, we think, to the advantage of the former.
This is a recommendation which applies to details. A more comprehensive one is deserved by the arrangement at large. The author's study has evidently been, to make this such throughout that one subject would naturally call up another, introducing us from each to each by an obvious and pleasing gradation ; so that any article, as Fractions, Decimal Fractions, Federal Money, &c. when once discussed and explained, instead of being laid aside altogether, is made to recur practically, — not, as it were, intruding, but yet insisting upon being remembered and well understood. This merit would seem to be indispensable ; but, as we have before hinted, authors have attained to it mostly but in imperfect as well as widely-various degrees. For example, Mr. Leonard's first rule in Decimal Fractions is for changing a common fraction to a decimal. All the treatises have such a rule. It is as easily explained in one place as another. Now the position of it is important, and herein is the difference between the arrangement before us, and others which occur to our recollection. In them it is placed at the end of Decimals. Here, coming first, its principles can be employed in addition, subtraction, &c., of Decimals, which follow it. Thus the pupil has the advantage of reimpressing an important process upon his mind, at the same time that he performs an operation similar to those which occur in the actual practice of business, and so reminding him of the real utility of the rule. So, in most of the treatises, we find Federal Money placed just after Division. Of course, many rules must be given, and a long article appears. In the work before us, the subject comes after Decimals, and every operation in it is performed by reference merely to them. So, in Compound Numbers, where Fractions are to be applied to them. Mr. Leonard here has inverted the common order. In ordinary text-books, possessed too of much merit, the arrangement makes it necessary to crowd part of Compound Numbers into Fractions ; and hence follows omission as well as repetition, with a needless enlargement of the volume, and confusion of the pupil's mind. Our meaning will be understood by a reference to Reduction of Fractions, or of Decimals, in the common treatises and in Mr. Leonard's. Percentage is another case in point, and there are many more. We specify these merely as illustrations.
The form and name of that ancient stumbling-block to novices, the Rule of Three, are retained as usual. So are the old distinctions generally, which on the whole we think wise. Such a compliment to custom and habit, were it nothing more, need occasion no inconvenience. It is perfectly easy to do so, and yet thoroughly work the old processes over anew. The learner, in this book, is led on through the subject in question with a good deal of tact. Much reliance is placed on examples, to be performed by the pupil, and these are of all conceivable varieties which may be of use to him. At the same time nothing is solved by algebraic proportion ; and in this point the author agrees, so far as we recollect, with Colburn alone. The reason is clear enough. It costs the pupil more to simply state the examples in such a form, than it does to perform them without any statement at all. Nor do many persons, in actual business, make any statements in proportion, in similar cases. They work, in fact, just as it will be seen Mr. Leonard has led his learner by his right explanations to do. It is obvious to remark, that there are a vast many questions in the Rule of Three, which hardly admit of being stated in proportion at all.
This is an instance of judicious omission ; and there are many more such, though the treatise embraces, we believe, all the modern improvements in Arithmetic, which deserve to be so called. Position, Permutations, and Combinations, are among these omissions. The two last are algebraic subjects, of limited utility, and not to be explained in arithmetic. The first is wholly useless. One of our popular authors acknowledges this in his preface, though he still inserts the article in his book, apparently from mere deference to habit. Mr. Leonard would perhaps have made a good exchange, in rejecting all these Rules, had he only gained by it the insertion of Specific Gravity which is of utility, and the writing out of Mensuration, and the Mechanical Powers, without the customary mutilation. These articles contain much matter of real value, especially to young mechanics ; and, though an arithmetic is not a treatise on mechanics, we must decidedly commend the author's policy, observed in many other cases as well as this, of furnishing in his book all the matter which is really wanted by the class he writes for in actual ordinary life, and which is not to be had from other sources. Every mathematical subject of prime necessity, in fact, belongs to an arithmetic, and so does every important branch of business which contains mathematical calculation. After all, we have but the simple elements of mensuration given here. They occupy little space, though obviously applicable to surfaces and bodies so extensively, that the intelligent student can hardly fail, after making himself master of these principles, to measure correctly any thing which is likely to come in his way. So among the Mechanical Powers, we have a description of the second kind of lever as well as the first. For this a good reason exists. The second is in common use, perhaps as much so as the first. And yet we do not now remember any other instance of its finding a place in an arithmetic. So in Gauging, it is usual to give a rule for finding the capacity of a cask in ale and wine gallons only. In this treatise it may be measured in bushels, or in imperial gallons ; the latter of which, at least, is of some moment, inasmuch as this measure is exclusively used in Great Britain, and, to some extent, (like the bushel measure,) in our own country also.
Such, generally, is the practical character of the work ; and we consider it no small merit. Other illustrations of it occur to us in the excellent little department devoted to Book-Keeping, adapted to popular use, to business-forms, to the divisions of the dollar, as adopted by auctioneers, and to the account of the moneys in which the value of small articles is usually named in the various parts of the United States. These may look at first like trides ; but it is trifles like these which make up, in the aggregate, the real availability and true worth of the work. Every traveller must have learned the utility of the statements last named, — not to say every reader of newspapers. Probably the least indispensable part of the work is the article on Foreign Measures, Weights, and Moneys, being chiefly intended for one class, the merchants ; but it is obvious, that a remark like that just made respecting domestic information equally applies, as regards these other matters, to every person who would consult foreign histories, or travels, or even a common journal.
The leading recommendations of Mr. Leonard's book, then, are its simplicity, clearness, and practical character. More can scarcely be said in favor of such a work. We ought, however, to mention, that not a few cases occur of the correction of long-established errors, especially in the form of rules, some of which, popular as they have been and still are, must frequently be productive of most incorrect and inconvenient results. A striking instance of this kind will be found in Mensuration. At the same time, the book, doubtless, is not perfect itself. We have detected a few errors in the answers here and there, and there are some cases, where the author has relaxed a little from his rigorous principle of making things perfectly plain to the most indifferent understanding. For example ; “Per cent. is a contraction of the Latin per centum, which signifies per hundred.” But these are trivial things, easily corrected in another edition.
7.- The Characters of Schiller ; by Mrs. Ellet. Boston:
Otis, Broaders, & Company. 1839. 12mo. pp. 296.
This is a volume of a very interesting character. It shows a fine literary taste, and very considerable attainments ; and the subject of it, to wit, the genius of Schiller as displayed in his dramatic characters, is one of great and daily increasing interest to the lovers of German literature. There is no controversy in the minds of men, in regard to Schiller. On all hands he is acknowledged to be a poet of a very high, if not of the highest order ; and the warmth and honesty of his heart, which shine out in his writings, are acknowledged with an equally harmonious consent. In this respect, his fate is widely different from that of his great contemporary, Goethe, whose indifference to the stirring interests of the age is daily operating to diminish his fame, and to weaken the love with which his memory is regarded.
As a dramatic author, Schiller had several great faults. He had but little power in depicting, or rather in representing, men as men, -- as living beings, - with the foibles and virtues which mark them in actual life. His characters, it is said, are almost all ideal, which means, that they are not real; that they are compounded of qualities in such proportions as are not found among men. They are not human beings, but only personifications of those qualities ; and the sentiments they are made to utter, are not such as men would actually utter under the given circumstances, but such as the poet himself feels in contemplation of the imaginary scene. It is this which makes Schiller so preëminently what the Germans call a subjective poet. Now it is plain, that the dramatic characters of such a poet open but few questions for criticism to decide. The aim of each character is distinctly seen at once. We are not obliged to ponder upon it, as we do in deciding on the merits of a character of real life. We know at once what the poet means by it, provided we comprehend the import of his language. There are no hidden motives influencing conduct ; no half-betrayed idiosyncrasies, which are to be traced out by a long and scrutinizing comparison of words, and hints, and actions. When we read a play of Shakspeare, we are strongly persuaded of its reality ; his men and women come and go, talk and act, exhibit one or another part of their characters, just as we have seen men and women do every day of our lives ; and, when the action or the sentiment rises into the tragical VOL. XLIX. - NO. 104.