154. When several terms on the same side of an equation are alike, they must be united in one, by the rules for reduction in addition.

EXAMPLE 2.-Reduce the equation x+5b—47—76. Here, transposing 56-4h, we have x=7b-5b+4h ; And uniting 76-56 in one term, we have x=26+4h. Ans. 155. The unknown quantity must also be transposed, whenever it is on both sides of the equation. It is not material on which side it is finally placed, though it is generally brought to the

-d-22.

A WELL-WISHER (Arsett); "Although offensive, sulphuretted hydrogen may be inhaled, when largely mixed with air, without apparent injury; and I have known it to be inhaled in large quantity, when fresh, without oroducing further harm than faintness. I have breathed a strong admixture of it with air repeatedly, and never experienced the slightest evil result. Thenard says that birds are killed by a mixture of of it in air; dogs by of it; and a horse by of it." J. C. B.-A. SOHOLAR: Nitric acid is composed of 14 parts of nitrogen and 40 parts of oxygen, or 1 proportional of nitrogen and 6 proportionals of oxygen. "It is used extensively in chemistry and the arts; for etching on copper, and as a solvent of tin to form a mordant for some of the finest dyes; in metallurgy assaving to bring the metals to their maximum oxidation; in medicine as a tonic. The nitric acid of commerce is half water, and is called double aquafortis; another kind, containing three-fourths water, is called simply aquafortis."-Gray. All of our Correspondents up to this date 16th Jan. 1854, are in error about the Four-ball Question. In the solutions we have received, the four balls DO NOT touch each other.-B. CRIMSHAW (Lambeth), should take the advice of his friends.-T. CAVE (Gee Cross): The "versed sine of a piece of cheese" is an expression that cannot be admitted into the P. E.-R. G. BRAY (Bodmin): The rule about committing all exercises to memory, must be taken cum grano salis; an author sometimes jocosely, like a doctor, prescribes more than he knows will be taken, in order that some may be taken.-T. H. Methven (Hoxton): Many thanks for his kind hints.-J. YOUNG (Huddersfield): The French Lessons are finished. "Le Civilisateur" may be had of D. Nuti, Foreign Bookseller to the Queen, 270 Strand.

H. HARTBEG (Dover): Study Latin, Greek and Hebrew in order, and in the P. E. until you can read the Scriptures in their original tongues. J. useful sciences; all arts are founded on these.-R. NURSE (Machen),: The BENTON: Mathematics, Natural Philosophy, and Chemistry are the most Lessons in English are finished.-WARIN: Received.-L. MURPHY (Queenborough): He has hinted what we intend. A ray of white light is divided in the following proportions, according to Newton and Fraunhofer respectively. Red. Orange. Fellow. Green. Blue. Prolet 108 95

45

27 27

40 27

60 46

89

109

Newton Fraunhofer 56 J. W. W. (Portsea): The honours attainable at Matriculation and Graduation in the University of London are substantial, see the P. E. vol. ii. p. 138, col. 2; and p. 215, col. 2.-A. P. T. (Cranbrook): Your trisection of an angle won't do.-CONSTANT READER (Wishiel): "The population of China has been variously computed at from 150 millions to so high a number as 360 millions-the latter of which is the native statement, issued under the imperial authority. This is considerably more than one-third of the estimated population of the globe, and would amount to an average of upwards of 280 inhabitants to the square mile." Hughes Manual of Geography.-E. MAN: See vol. ii. p. 137.—PASSAIO (Glasgow): Cassell's Arithmetic, Algebra, and Geometry, ARE NOT REPRINTS from the P. E. but works which were demanded by the readers of that work, before the lessons on these subjects could be completed; they may be read before the P. E., after the P. E., or along with the P. E. the last method being the best. Some French books are on the tapis. The Latin Lessons in the P. E. are the best; they may be followed by Zumpt's Latin Grammar by the higher students.

As to

as liable to be taken ill as other people. As to the use of the word Finis, you are right, my boy; but it is never used in books now; we only follow the multitude; but if a fellow does not know when a story is done, he has not surely attended to it while in progress; and in that case, he would be none the wiser, if we said our story is ended.

1

ANSWERS TO CORRESPONDENTS.

R. S. (Greenock): For Dr. Beard's "Latin Made Easy," you must apply to the publishers of that work, viz. Messrs. Simpkin and Marshall, London.-T. H. E.: Beza's Latin Testament.-S-L (Sunderland): We don't know.-VOLUNTARY EDUCATION (Sheffield): "Cassell's Lessons in German" are expressly stated to be a reprint from the P. E. The "Historical Educator" is intended as a substitute for the promised Lessons in History in the P. E. You will not get on well with the German, or, indeed, any language, without a dictionary; "Cassell's German Dictionary" is now publishing in numbers at 2d. each.-JUVENIS (Springfield) would have written better had he heard a good sermon; the grammar appears to be well enough.-DEUTCHE: Yes.-PLODDING GENIUS (Louth): His paper on "Perseverance in lieu of Genius," is very good; but it is capable of improvement. Let him try again, but take this new text: "Perseverance is Genius."

C. S. (Kinross): The magic lantern will be explained by-and-by under Optics. Lenses of every kind may be had in town.-SACRA ROTT (Atholl): The most common unit for measuring the earth-work of ditches is the cubic yard. The best rule is to consider the ditch, if uniform, as a prism, lying on one side, and cast up the earth-work accordingly.

G. HARPER (W. Hall): We have not seen a Geographical Pronouncing Dictionary.-A. K. R. (Edinburgh): Yes.-J. MATHESON (Glasgow): You are doing very well; go on as you have begun; finish the lessons in the P. E. first.-TYRO (Manchester): Not decided.-JOHANNES (Bradford): The rule is inaccurate; it should be, every syllable in Greek is pronounced as in English: example, tipnuns, ei-ree-nees.-A. ALISON (Liverpool) had better learn good manners before music.-J. R. (Edinburgh): Rome was not built in a day. We can't put everything into the P. E. at once. We can't recommend you books on Logic and Moral Philosophy unless we were intimate with your previous studies.

ειρήνης,

This terra is used to include-both additions and subtractions.

LITERARY NOTICES.

JOHN CASSELL'S FRENCH WORKS.

Now ready, price 4s. in stiff Wrapper, or 5s. strongly bound in cloth, the First Part complete, consisting of the French and English, of CASSELL'S FRENCH DICTIONARY: the entire work will be completed in about Twentyeight Threepenny Numbers, and will form one handsome 8vo Volume. Price 9s. 6d. bound in cloth, or the Two Divisions may be had separate. A COMPLETE MANUAL OF THE FRENCH LANGUAGE, by Professor De Lolme, just published, price 3s. neatly bound. This forms one of the most simple, practical, and complete Guides to a thorough knowledge of the French Language which has hitherto been published. The plan upon which it is conducted is admirably calculated to accomplish the proposed object. In the first place, the Grammatical Principles of the Language are clearly laid down, and, secondly, these Principles are copiously illustrated by suitable Exercises of English to be turned into Freach.

CASSELL'S LESSONS IN FRENCH, Parts I. and II., in a neat volume, price each 2s. in stiff covers, or 23. 61. neatly bound in cloth; or bound together, 4s. 6d.

A KEY TO CASSELL'S LESSONS IN FRENCII, containing Translations of all the Exercises, with numerous relerences to the Grammatical Rules, price Is. paper covers, or 1s. 6d. cloth.

A SERIES OF LESSONS IN FRENCH, on an entirely Novel and Simple Plan, by means of which a knowledge of the French Language may be acquired without the Aid of a Teacher. These Lessons first appeared in successive Numbers of The Working Man's Friend and Family Instructor." They are now reprinted in a revised form.-By special permission of H Majesty's Postmaster-General, these Lessons may be transmitted thro the Post-office, and will be sent to any Address, on the receipt of S Postage Stamps.-Price 6d, in a seat. Wrapper.

LESSONS IN MUSI C.-No. XXII.

(Continued from p. 226, Vol. IV.)

In explaining, in our two preceding lessons, the nature of the old and established notation, we have slightly anticipated the subject of the present lesson. We shall now conclude our lessons on Music for the present by elucidating the subject of "Minor Tunes." Why they are so denominated we shall explain presently. But, first, let us ask our readers to recall all that we have said

in former lessons on the "mental effect" of the note LAH (the sixth above the key-note or the minor third below), or, better still, let them recall all they have themselves observed and felt in connexion with it. Was it not always, when sung slowly, the sorrowful note? Then let us suppose ourselves trying to compose a very sorrowful tune,-should we not naturally employ this note in the most effective positions? Without composing, however, let us just recall one of the oldest tunes of this kind in existence.

a. In some tunes-chiefly those which are intended to express a mournful sentiment-the note LAH is found to predominate. It is necessarily heard both at the beginning and at the end of such tunes; and assumes almost the importance of a governing or key-note, but without changing (as soH and

YOL. IV.

b. Modern musicians, in order to give to LAH a closer resemblance to the ordinary key-note, and to direct the ear to it more decisively as the note on which the tune closes, as well as to increase the general effect of such tunes, occasionally

97