single sound is sufficient, but there must be two. To try it on the string as before, the length of string which makes the Fifth is 16 inches, and the length which will produce an exact Fourth below that, must be as 4 to 3, which is 21 inches, or eight-ninths of the open string. The length of string which makes the Fourth is 18 inches, and the length which will produce an exact Minor Third below that, must be as 6 to 5, which is 213 inches, or nine-tenths of the open string, being to the length in the preceding case as 81 to 80; and the length required to produce an exact Fifth below the Major Sixth, will be found to be the same. All of which may be shown more briefly by any person in the habit of the subtraction of intervals (§ 28.) For divided by make; and divided by make 10, as does also divided by And the difference between the intervals thus ascertained, is divided by which make 8. And if the consonances are taken in the octave below, the lengths of string here assigned will make concords of some kind (viz. the complements to the first concords) with the Consonances of the same name they made concords with in the first octave; the proof of which will for brevity be omitted.

3.

9

10,

32. To be able then to make just concords with the Fifth and also with the Fourth and Major Sixth, the Major Second must have two forms, or be double. And the same if any of the Consonances are in the octave below. Hence if on the finger-board which presents the Key of C, the manual of D is made double, and the sharpest of the two forms is coloured white and the other black, the Fifth (G) and Thirds (E flat and E) being at the same time coloured white, and the Fourth (F) and Sixths (A flat and A) black, the colors will point out the form to be taken to make a concord when a concord is possible.

80

33. The two sounds thus established, are called the Acute and Grave Major Second. The proportion of the lengths of strings which make them being that of 80 to 81, this is the ratio of the interval between them, and its measure is 81. This interval is called a Comma, and is of great importance in the sequel. It is eleven times what is recognised by tuners as perceptible to ordinary ears, and is consequently not a thing to be despised, though the essence of what is called tempering consists in making light of it.

34. Go next to the corresponding place at the other end of the octave; which is that of the Minor Seventh. And here it will be found by the same methods as before, that to produce an exact Fourth above ths Fourth, the length must be 13 inches, or nine-sixteenths of the open string, while to produce an exact Minor Third above the Fifth, or Fifth above the Minor Third, the length of string must be 131 inches, or five-ninths of the open string; being to the length in the other case as 80 to 81, making the interval of a Comma as before. Hence if the manual of B flat is made double and the two forms coloured black and white, the rule of colors will hold good. 35. The two sounds thus established are called the Grave and Acute Minor Seventh.

36. Go next to the place of the Major Seventh. And here it will be found by the same methods, that to produce an exact Fifth above the Major Third, or Major Third above the Fifth, the length of string must be 12 inches, or eight-fifteenths of the open string; while to produce an exact Major Sixth above the Grave Major Second, would require the length to be 122 inches, or twenty-seven fiftieths of the open string, being to the length in the other case as 81 to 80, making the interval of a Comma as before. But this last

form makes no concord with any of the Consonances; and therefore can never be demanded for such a purpose. Which joined to other reasons hereafter shown, has the effect of causing it to be in practice never wanted, and it is therefore treated henceforward as non-existent. A vast relief.

37. The sound left, will be called simply the Major Seventh. And because it makes concords with sounds previously colored white, its manual will be white.

38. Go finally to the corresponding place at the other end of the octave; which is that of the Minor Second. And here it will be found by the same methods, that to produce an exact Major Third below the Fourth, or an exact Fifth below the Minor Sixth, the length of string must be 22 inches, or fifteen-sixteenths of the open string; while to produce an exact Major Sixth below the Acute Minor Seventh, would require the length to be 22 inches, or twenty-five twenty-sevenths of the open string, being to the length in the other case as 80 to 81, making the interval of a Comma as before. But this last form makes no concord with any of the Consonances, and is therefore treated as a non-existent, as in the preceding case.

39. The sound left, will be called simply the Minor Second. And because it makes concords with sounds previously colored black, its manual will be black.

40. Ths sounds thus determined are called the Dissonances; and the intervals they make with the Key-note or the Octave are called Discords. Which does not mean that they are sounds dissonant or out of tune, (for they make concords with the Consonances, or with some of them,) but only that they are not of the kind which make what are accounted harmonious effects when sounded along with the Tonic. And they make concords with the Consonances alternately; that is to say, the white or Acute form makes concords (where a concord is possible), with the Thirds and Fifth (odd numbers), and the black or Grave with the Fourth and Sixth (even numbers), and the same if the Consonances are in the octave above or below. The Acute and Grave forms are distinguished on the music-book when desired, by the Acute' and Grave` accents drawn from the head of the note towards the right hand. The effect of an Acute or Grave mark extends throughout the bar unless contradicted; and is in other respects subject to the same rules as in the case of a Sharp or Flat.

41. The facts thus established with respect to the Dissonances, may be designated by the title of the Duplicity of the Dissonances, and are at the root of all just intonation.

42. If the places of the fourteen sounds thus determined are marked upon the string, there will be presented what is called the Canon or Just Division of the Musical String. Or this Just Division is called the Canonical Division.

Notes of Books.

History of Rome. By Titus Livius. The Third Decade, Part 1, with notes by E. R. Humphreys, L.L.D. Pp. 370. London: Longmans.

HE objects which the Annotator has mainly, but not exclusively, kept in view have been-(1.) the illustration of the historical narrative by parrellel occurrences in modern history; and (2.) the promotion of a style of translation which shall combine elegance with fidelity.

1. The historical allusions are numerous and generally speaking apposite; and if the suggestive vein which the annotation thus opens be followed up whenever the occasion offers, it will be found to lead to the most beneficial and interesting results in the mutual illustration of things, new and old. As instances of the comparisons he institutes we may cite-the sieges of Saguntum and Saragossa-the passage of the Alps by Hannibal in ancient and by Francis I. and Napoleon in modern times-the traditions connected with the battle field of Lake Trasymene, Marathon, Neerwinden, and Tewkesbury-and the use of the catapult and the turris mobilis in mediæval warfare.

2. With regard to the second object the annotator has had in view, while we fully agree with him in its importance, we must candidly express our doubts whether the means he has adopted to attain it are likely to prove successful or at all events commensurate with the labor he has bestowed upon them. Translation involves two requisites-a knowledge of the original language out of which, and a knowledge of the language into which, we translate. It is a double-edged sword, and hence its skilful use is so severe an exercise. It is in the second of these requirements that the failure generally takes place in our schools: while the proper means are employed to secure the first in the study of ancient classical writers, the corresponding means are not employed to secure the latter in the study of modern classical writers. Translation per se is not sufficiently studied, but is subordinated to mere classical scholarship: hence the common failure of Latin and Greek well understood, but most imperfectly rendered from the unskilful use of the mother tongue.

We by no means wish to disparage the labors of Dr. Humphreys for the correction of this evil, but we do not think he has gone to the root of it. In his prolegomena he lays down certain rules and modes of translation which may no doubt be true in themselves, but which do not appear to promote, but rather prevent, that pliant, easy, and versatile use of the English language, which forms the chief charm of translation. For instance, in the second rule, we are told that "the ablative absolute should be translated as marking the time of a collateral event; that is with the sign 'when' or 'while."" But surely this rule is not as universal as here stated: in such cases as re bene gesta XXIV. 20 or again rebus divinis perfectis XXIII. 14 we should be inclined to use the sign "after:" indeed the ablative absolute in these cases does not imply a strictly collateral event, but a past and subordinate event.

Again, in the thirteenth rule we are told that "forte" when joined to a verb, must be "translated by the phrase "happen' "that it may be so translated in many cases, we do not dispute: but we do not see why it "must be," and indeed in such expressions as forte accidit or forte evenit, we do not see how it could be. But if it were worth while laying down a rule for such a special point as this, it would appear necessary to do so in many other cases: for instance we should be disposed to translate the verb soleo by the adverb "generally" in such a passage as cum nubem quá sedere solita sit XXII. 30, which might be rendered "the cloud which generally rested," in preference to "the cloud that had used to rest." But in truth we do not see that these are the proper subjects for rules, or that the translation of such expressions should be cast into a stereotype mould. It is more a matter for oral correction than for written instruction: and any system which would supersede the independent exercise of taste and judgment on the part of the pupil, will defeat its own object. The specimens of translation with which Dr. Humphreys favours us are faultless, both as regards fidelity and elegance, and we trust that they may be extensively imitated: nor should we be otherwise than rejoiced to hear that our doubts as to the effect of his labors were falsified by the practical experience of teachers in the use of the work.

English Style: or a Course of Instruction for the Attainment of a Good Style of Writing, &c. By G. F. Graham, author of "English: or the Art of Composition," &c. London: Longmans.

AS Mr. Graham is the author of "English," we wish he would be so good as to write it. He discards it in the first sentence of the preface. "It would (he says) appear a paradox that, though works on the English Language are generally received with favor by the public, the study of composition should make little or no progress in our educational institutions." Now what has would to do with the author's meaning? There is nothing conditional in what he says. He means to affirm that it does appear [to be] a paradox, &c. It would appear a paradox, must be followed by words expressing the condition which "would" implies. Thus "it would appear a paradox, &c. if it were not that, so and so,' &c. here there is nothing of the kind, and Mr. Grahamn has furnished a specimen, in the first line of his work of that blunder which Goold Brown, in p. 338 of his "Grammar of Grammars," so justly denounces as the subjunctive mood used in the indicative form, and which he says "is inconsistent with any just notion of what a mood is."

Some parts of the book are useful. "The propositions" in the first chapter furnish good exercises for pupils and so do some of the subjects for composition; but we cannot honestly recommend the rest of the book. For example, the author deals with "Definitions" as if they all necessarily consisted of three parts, 1, the subject; 2, the genus; and 3, the species." In the first place this is not so; "to delay without due cause " is a good definition of "procrastinate:" and certainly there is neither species nor genus in this. Neither does Mr. Graham properly apply the terms he uses in this sentence:

subject

genus

species

(Justice) is (the virtue) (of giving to every man his due.)

Why justice is a species of the genus virtue: "giving to every man his due " is no "species:" it is simple explanation, or, in fact, it is the

66

The

Some

66

a

whole definition, virtue being mere surplusage, lugged in purely to complete the trio. He by no means simplifies grammar. He miscoins words. proud solitary," p. 123. 'Solitary" is an adjective: not a noun. times he is trifling. We think it scarcely necessary to point out that resemblance in sound will sometimes cause us to use one of these words for the others;" "lay and lie," "import and importance," "endurance and duration," &c. Small danger of this. He is in error in fancying there is any superfluity in saying "trifling minutiae of style." There are many minutiæ of style, nowise trifling, which are often ignored by Mr. Graham though not by good English writers. His great sin, however, is in giving as models of style the despatches of our great Generals and Naval Commanders of the early part of this century, from which Cobbett so effectively culled his chief examples of grammatical blunders. We certainly were not prepared for the insertion of one of these, as a worthy example, by a grammarian in the year 1857. It begins with one of the most glaring instances of bad grammar which it is possible to perpetrate.-"the enemy who I attacked." Poor Nelson little dreamt that his defective education would be so recklessly exposed. Cornish is not the dialect of the Cornish people. We were there last year, and failed in finding any one who could speak it. It is extinct. There are, of course, some good points in this book (perhaps its extracts from old English writers are the best), but it is too full of faults to be a safe book for learners.

SHORT NOTES OF BOOKS.

Statistical Book Keeping. By Fred Charles Krepp. Pp. 180. London: Longman. 1858. This book purports to be "a complete guide to those who are already acquainted with book keeping by double entry, and those who wish to substitute the statistical system." The author says in his preface that “he has endeavoured to generalize his system as much as possible, in order to enable practical book keepers to apply it easily to any case which may come before them." It is divided into "simple system," treating of "purchase, sale, settlement, control, and digest." Then follows a "book of statistics," being an epitome of all the other books during a period of ten years." This is followed by "compound system, auxiliary statistics, and special systems." The special system discusses "merchants' system, bankers' system, tradesmen's system, shipowners' system, farmers' system, and householders' system," concluding with "suggestions for the prevention of defalcations and frauds in banks, railway companies, and other concerns." The book is well got up and nicely printed.

The Sixth Annual Report of the Chaplain of the Borough Gaol, Devonport. Joseph Masters, London.-Is a well written and thoughtful pamphlet, evidencing the writer's deep and earnest interest in those social questions which are every day enlisting fresh champions. The subject of reformatories is touched upon; "the causes of crime," and "the improvement of the dwellings of the laboring classes,"- -one of the most available remedies of crime, and standing in the very threshold of all reformation-is carefully set forth and we are not surprised that the results of the labors of so zealous a clergyman, as the writer's observations show him to be, should be seen in the improved state of school and chapel, on which he modestly touches in conclusion. We bid him "God speed" in his work of usefulness, and thank him for the pleasure we have had in the perusal of his report. His practical views may be thus given in his own words :-" With the exception of the last few months (a period of the year which affords unusual temptation to boys in garden-robbing and such like offences), the juvenile prisoners have been fewer than formerly. I still entertain grave doubts as to the expediency of sending young children to gaol at all, except in cases where, by very early training, decidedly criminal habits have been contracted: and for such, a short term of imprisonment appears to me to be fraught with evil rather than otherwise. No reformation can be effected by it. Time is required for that, and when the Reformatory is not available, I respectfully suggest, that periods varying from six to twelve months be substituted in lieu of the short term. The mind soon becomes familiarised with the routine of prison life, whilst a more lengthened period is requisite to improve the tone and habits of the character." We ourselves like the prison to be part of the Reformatory buildings.