ANSWERS TO CORRESPONDENTS. CHEMISTRY. The first of the long-wished-for Lessons in Chemistry will appear in our next number. This subject will be treated in a very popular manner; so that all our students will be taught to make experiments for themselves in the cheapest possible manner. This notice should, through the recommendations of our present subscribers, add greatly to their number: and we hope that by our united efforts, this number may soon be doubled.

W. O.: We have not seen the books.-M. H. (Salkingham): The only thing we know of likely to suit her purpose, is "Diagrams in Wood" to illustrate the Gower-street Edition of Euclid. Solid Geometry, Book I. The set of 9 in a box. 78. 6d. Or "Geometrical Solids" to illustrate Reiner's Lessons on Form, &c., the set in a box 98. Sold by Taylor and Walton (now Maberly), Upper Gower-street. We fear that she is not likely to get Plane Diagrams in wood to illustrate any of the Six Books of Euclid, even in London; but if so, perhaps some kind correspondent would inform us on her behalf, and we doubt not many others.

J. W. (Dundee) has made most encouraging progress in his German studies. We should hardly have thought it possible for him to write so good a German letter as he has sent us in so short a time as six months. Though not without fault, it does him great credit. He cannot do better than keep the great names he mentions constantly before his mind. If he will only persevere as he has begun, he may hope for much success. He is right in thinking the pronunciation of German easier for an Englishman than that of French, and we trust he will derive benefit from the study of our lessons on that subject. A thorough knowledge of Latin is not absolutely indispensable, though highly desirable, as a qualification for the study of modern languages. -Student of the P. B. E. (Hull) is anticipated; it may be useful to mention, for the sake of our readers, that the table of the number of books, chapters, verses, words, and letters in the Bible, is to be found in a little book called the "Companion to the Bible," published by the "Religious Tract Society," St. Paul's Church-yard, London.

GEO. BEVAN: Many thanks for his trouble.-W. E. WILLIAMS (Merthyr Tydvill): See col. 1, p. 192, vol. I.-KENNETH (Halifax): The lines are defective in spelling and rhyme; otherwise, they are pretty fair.-GLASG. ABERDON. Mutual instruction Societies have existed in Aberdeenshire for some years past. By a little inquiry, he will find what he wants. We agree with our correspondent when he says that "debating and mutual improvement societies do not make their existence sufficiently known in public; and that, go where you may, they appear to act like the Egyptian priesthood, which scrupulously and systematically kept what knowledge it possessed within a very select circle. We add, that there is something suspicious in this practice; and we hope, for the sake of the world at large, and that of their own honest intentions in particular, that such societies will hereafter court publicity ELDON (Reading): Well-done, treading in the footsteps of many, you request of us an English Dictionary. The largest and oldest house in London is engaged on this very thing; but when will it appear? that is the question.-J. Mc. C. (Ochiltree), will find a reference in another part of our answers to correspondents which will satisfy him.-J. WILLIAMS (Hirwaun): We know as little of the population of Hirwaun as of Timbuctoo. The sacred books of the Hindoos are pure rubbish, and were written very long after the books of Moses.

DAVID JONES (Chelsea): Is right.-UN GARÇON (Knock Down, Tedbury): What he suggests is the very thing we are going to do.-R. H. (Paddington): We suspected the trick; but we shall keep our eye on the gentleman; thanks for his hint.-T. C. L. and G. ARCHBOLD: Received.-W. H. C. (Colne), is right; thanks.-W. B. BREEDON: Ego men baptizo humas en hudati, true that I dip you repeatedly in water; to this, the corresponding FIGURATIVE sentence being, but he shall imbue you with the Holy Spirit, even with fire. Here, baptizo en is taken in the advanced and figurative sense of limbue with, for I dip frequently in, that is, in order to imbue with.JESSE WAIN: Mathematics.-H. G. (Manchester): If any one wants our opinion of a book, they must send us a copy. Is it reasonable that we should either buy or borrow?-L. JONES (City): We recommend the Lessons on Phonetic Short-hand which have appeared in the P. E. as best adapted for self-instruction, and Webster's Johnson's Dictionary for general purposes.A. G. (Greenacres Moor): Answered before.-G. FORT (Colne): Put the emphasis on the accented syllables: Planta'genet; Biledulge rid, which should be Belad-el-djeʼrid.-G. H. E. (Malton): See the letter on certificates of merit in our correspondence.-ALPHA (Blackfriars-road): See a notice on the duties of a Reporter in the P. E.-R. HOUSE (Bristol): Many thanks for his note.

Tом THUM (Perthshire): His way is right, and the other entirely wrong; this is our dictum; but we have neither time nor space for our reasons.-W. HARTLEY (Skipton): Should begin at Lessons in English No. I. page 150, vol. I, and continue to study carefully every lesson after this till the last. He will then be very different from what he is now.-JOHN O'CONNELL (Cappoquin): It is not easy to decide whether the writers of the reign of Queen Elizabeth or those of Queen Anne rendered a greater service to the Literary and Scientific World. We should vote for those of the latter; but the influence of those writers who lived between these two reigns, appears to us to have been the greatest.-G. GROCUT, (Lubenham): Most likely his solution of Taylor's problem is correct in itself; but it is not done according to the prescribed mode.-E. SMITH (Stoke Newington): The degrees of A. M., L.L.B. and L.L.D. can be taken at the University of London, and at appointed intervals. The price of the calendar of the University is 48.-A TAR (St. Columb): Norie's Navigation is the best for general purposes. We cannot say when this subject will come up in the P. E.GEORGE SLOSs (Auchinleck), and T. E. (Newcastle): May be correct in their own way, but they have not taken up the question as intended. They should look at the solution of X plus Y.-JOHN ROY (Stonehaven): His method of solution is, we believe, correct; but not sufficiently worked out.-J. PARKER (Norfolk): A. SAMPSON and C. BERTRAM (Ellangowan):

Received.

A number of correspondents have written to us asserting that the statement concerning the number of books, chapters, verses, &c., in the Bible, sent to us by J. Biggar, is not quite correct. We shall have no controversy on the matter; but we refer all whom it may concern, to a book called "Companion to the Bible," published by the "Religious Tract Society," as an authority, which we presume will settle the question.

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IMPORTANT ANNOUNCEMENT TO OUR LATIN STUDENTS.— With a view fully to carry out the object of the POPULAR EDUCATOR as a means of educating the people, it is our intention shortly to commence the publication of a series of works on Classical Literature, to be entitled CASSELL'S CLASSICAL LIBRARY. This series will contain the productions of the most eminent Classical Authors, with other works calculated to assist in the acquisition of a general knowledge of the languages and literature of ancient Greece and Rome-the whole published at such a moderate price as to place them within the reach of all. A number consisting of twenty-eight pages, crown octavo, printed on the same paper as the fine edition of the POPULAR EDUCATOR, will appear every week, price twopence. The first number will be published on the first of August, and will contain the commencement of a Latin Reader, prepared for the use of beginners. Among the reading lessons, of which this work will consist, will be found easy and amusing Fables, Mythological Legends, Anecdotes of Eminent Men, an Epitome of the His tory of Rome from the earliest time to the Emperors, and a useful chapter on the Geography of the Nations of Antiquity. These will be accompanied by a Dictionary of all the Latin Words, explanatory Notes, and Grammatical References; the whole forming, when complete, a cheap and convenient Introduction to Latin Literature. It will consist of ten numbers, and cases for binding will be issued at sixpence each. This work will be followed by Latin Exercises, intended to ground the student in the Syntax of the language, and thus prepare him for entering with advantage upon the study of more difficult authors. CASSELL'S LATIN DICTIONARY is preparing for the press, and will be published uniformly with Cassell's French Dictionary, in Weekly Numbers, at 3d. each, and in Monthly Parts, price 1s.

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and thus saved the trouble of multiplication or division; and which when multiplied or divided, indicated the powers or the roots of the same, and thus saved the labour of raising powers and extracting roots. This, however, will be best understood by examples: Let us take two series, the one arithmetical and the other geometrical, corresponding to each other, as follows:

1. Arithmetical series, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9,

10, 11, 12. or Logarithms. 2. Geometrical series, or common numbers. 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096.

contains within itself the represented products of all numbers whatever by each other, provided we were enabled to divide and subdivide the distances between the numbers marked on the sides, left and right, top and bottom, to an indefinite extent; this division and subdivision being carried on, according to a proper scale, from the logarithms of the intermediate numbers. To illustrate this remark by an example: suppose we wanted the product of 51 and 47 from the table. Taking rather more than of the distance between 5 and 6 at the bottom, to denote 51, and rather more than of the distance between 4 and 5, at the left-hand side, to denote 47, Here, if you add any two numbers or logarithms in the first and drawing straight lines from these points to complete the series as 4 and 7, their sum 11, will indicate the product of the rectangle in the table, we find that they meet in a point close two numbers which they indicate in the second series; for to the diagonal marked 24; now as tens multiplied by tens under 11 you have the number 2,048, which is the product of produce hundreds, the product of 51 by 47 must be nearly 24 the indicated numbers 16 and 128. Again, if you subtract the hundreds; the student will of course find the actual product number or logarithm 6 from the number or logarithm 11 in the to be 2,397 instead of 2,400. This approximation to the truth first series, their difference 5 will indicate the quotient of the two is valuable in a thousand practical cases in actual life, and will numbers which they indicate in the second series; for, under 5, tend greatly to assist mechanics and others who require to you have the number 32, which is the quotient of the indicated know the product of any two numbers as nearly and as numbers 2,048 and 64. Next, if you take any number in the quickly as possible. Let us take another example: suppose first series as 3, and multiply it by 2, the index of the square, you will have 6 for the product; but 6 in this series stands looking at the table, we see that 50 multiplied by 50, would we wish to multiply 49 by itself; here 49 is nearly 50, and on above 64 in the second; therefore 64 is the square of 8, because 3 stands above 8 in the second series. Lastly, if you take 9 in plainly give 2,500, as 25 is found on the diagonal line in which the first series, and divide it by 3, the denominator of the the sides of the square of 5 meet; now parallel to this diagonal index of the cube root, you will have 3 for the quotient; the distance of 49 on the left-hand side and at the bottom, we have that of 24 very close to it, and mentally guessing but 3 stands above 8 in the second series; therefore 8 is the between the numbers 4 and 5 as before, we find that the eye cube root of 512, because 9 stands above 512 in the same would lead us to place the meeting of the sides of the square series. This subject is of course capable of much greater of 49 in the diagonal marked 24; hence we infer that the extension; but we must pause here to explain our new Multi-product of 49 multiplied by itself is nearly 24 hundreds; the plication Table.

In this table the logarithms of the numbers placed along the left-hand side from bottom to top are represented by the straight lines or distances along that side from 1 to 10; that is, the distance from 1 to 2 is the logarithm of 2 in the Neperian system, measured numerically from a diagonal scale of equal parts; the distance from 1 to 3 is the logarithm of 3 in the same system, measured from the same scale; and so on. In like manner, the logarithms of the numbers placed along the bottom from left to right, are represented by the straight lines or distances along the bottom from 1 to 10. The products of any two numbers of which the one is taken from those placed along the left-hand side, and the other from those placed along the bottom, will be found thus: look for the corner of the rectangle (which is a square, when the numbers are equal) in which those lines meet which are perpendicularly drawn from the points where the numbers are placed, at the left-hand side and at the bottom of the table; having found this corner, then look along the diagonal which is drawn through it, and either at the one end or at the other, you will find the number which is the product of the two given numbers. For example, suppose that you wished to multiply 3 by 4, if you run your eye along the straight line drawn perpendicularly from the point marked 3 at the left-hand side of the table, till it meets the straight line drawn from the point marked 4 at the bottom, you will find that these straight lines meet in a diagonal, which has the number 12 at each end of it; therefore, 12 is the product of the two numbers 3 and 4. In like manner, if you wish to know the product of the number 5 multiplied by itself, you will find that the perpendiculars drawn from the points marked 5 at the left-hand side and at the bottom, meet in a diagonal which has the number 25 at each end of it; therefore 25 is the product of 5 multiplied by 5, or the square of the number 5. In this way, the products of all numbers from 1 to 10 by each other, can be found by immediate inspection of the table.

Some persons, after reading the preceding remarks, will perhaps say, "Well, all this is very ingenious, but what is the use of it? In a common multiplication table from 1 to 10, we have the same results put down in a much simpler form, and in a way which most people can understand very much better!" True: we do not deny the fact; and it is well that such is the case; but in this Geometrical Abacus, we have here exhibited by lines the relations which exist among numbers; thus we speak both to the eye and to the mind. Besides, we have other advantages in this table which the common multiplication table does not possess. This table

actual product of 49 by 49 being 2,401 instead of 2,400.

This table will also serve the purposes of division, the raising of powers, and the extracting of roots. In performing division, look for the dividend at the extremity of one of the diagonals in the table, and for the divisor at the left-hand side; then from the point where the perpendicular drawn from the divisor meets the diagonal drawn from the dividend, you will find a perpendicular drawn to the bottom, and at its extremity will be found the quotient. For example, suppose you wish to divide 28 by 7; looking for the diagonal marked 28, you will find the perpendicular drawn from 7 at the left hand-side meets it at a point from which there is a perpendicular drawn to the bottom, and this terminates at 4; therefore, 4 is the quotient. To extract the square root of a number: look for the given number at the extremity of a diagonal; then look for the middle point of this diagonal, and the perpendicular drawn from it to the left-hand side or to the bottom will lead to the root required. Thus, to find the square root of 16; look for the number 16 at the extremity of a diagonal, and from its middle point you will see two perpendiculars, one drawn to the left-hand side leading to 4, and another drawn to the bottom leading also to 4; therefore, 4 is the square root of 16. If there be no perpendiculars drawn from the middle point, imagine them to be drawn, or draw them with a pencil, and they will enable you to guess the square root very nearly. Thus, to find the square root of 30; look for the middle point, and suppose perpendiculars to be drawn from it to the left hand side or to the bottom; you will then find that they will meet these in a point exactly between 5 and 6; therefore, the square root of 30 is nearly 5; but this square root found more exactly by calculation, is 5.477 &c. To take another example; let it be required to find the square root of 2. Here taking the middle point of the diagonal marked 2, you find that the perpendiculars would fall exactly between 1 and 2, thus indicating that the square of 2 is nearly 1; the calculated root, however, is 1.414 &c.

It may perhaps be inquired by the ingenious student, why in these examples, as well as in the former ones in multiplication where the factors consisted of units and tens, we have only approximate answers; whereas, in the case of factors consisting of units only, the answers are complete? The reason is this, that the table would require to be subdivided according to a certain law, namely, that the differences between the logarithms of successive numbers are constant; but the differences between the numbers themselves are variable; and therefore, these differences are not strictly proportional to each other. This law will be best understood by examining the following

table of the Neperian or Hyperbolic Logarithms of numbers And now one word for the consolation of those readers who from 1 to 10 inclusive, with their differences.

ignorant of chemistry, as he might fancy, for, strictly speaking, no person is totally ignorant of chemistry; how, by what process of reasoning, experiment, or induction, would the conclusion be arrived at, that the metal in question was zinc ?

Why it is evident that in all investigations, whether chemical or otherwise, we determine what a thing is, by comparing it with other things, and learning what it is not. We may not possibly be conscious of such being the order of reasoning, but the order exists nevertheless. In the matter of zinc, then, the investigator would have pursued some such sort of reasoning as this: The substance is a white metal, hence it is neither copper nor gold. It is not a soft metal, hence it can neither be lead nor tin. To this extent, common sense or the unconscious reasoning faculty of most persons would readily have gone, but not much farther. Perhaps some investigating mind more acute than its fellows, might have fancied a resemblance between zinc in its brittle form, and steel, and desirous of testing the correctness of his supposition, might have bethought himself of trying upon the unknown metal the effect of an ordinary fire.

He would have found that the substance will melt under this trial, whereas steel would not have melted; hence the material in question could not have been steel. The inquirer who should have had recourse to this mode of investigation, would have performed a chemical operation; he would have acted the part of a veritable chemist, fire being one of the chief agents which chemistry employs in distinguishing one material from another, in separating one from another or more, in combining materials so as to imitate the productions of nature, or even advancing, if the expression may be used without presumption, before nature, and bringing compounds into existence which had never hitherto been formed. Now it would scarcely be untrue to say that chemistry presents us with at least a thousand different characteristics, by which zinc might be individualized from every other substance,―might be separated from a thousand or ten thousand others,-might be recognised under any of the numerous forms which it is capable of assuming,-even if it should come before us in a transparent state! The tyro in chemistry perhaps ejaculates with surprise :-How can a metal be rendered transparent? Nothing more easy, nothing more common than this. There does not exist a metal which cannot be dissolved, forming a transparent solution; surely the student will concede, that, under these conditions, the metal is rendered transparent.

acts by undeviating laws; these laws it is the aim of science to interpret. If the zinc have vanished from the mixture of oil of vitriol and water it must have vanished under the form of a gas. Had the student proposed to himself for solution the general question, whether any metal could become a gas and escape? the question would have been rational; the supposition involved would moreover have been correct, inasmuch as certain metals can assume the form of gas; nay even flint can assume the form of gas; but so far as our present investigations are concerned the zinc has not vanished, it is in the solution. Although invisible and in the solution, we will hereafter, in the next lesson, find it; meantime at present we will let it rest. During the course of this lesson the student has not been required to use any chemical instrument properly so called, a wine glass and a jug having been the only instruments employed. In the course of the next lesson certain instruments however will be needed, and instructions for making these intruments will be given meantime let the student provide himself with the following materials:

1. A roll of brimstone.

2. A thick wire or thin bar of iron.

3. A small rat's-tail file, and three-square file. 4. A quarter of a pound of the kind of glass tube termed quilled. 5. A florence oil flask.

6. A few sound corks.

7. Two four ounce phial bottles, and

8. A piece of india-rubber tube, about one fourth of an inch in diameter and eight or ten inches long.

The last article may be readily procured at the tobacconist's shop, being now frequently employed as a flexible tobaccopipe tube.

With these preliminary directions, I shall now take leave of my pupils for the present. Those who like to be very industrious may accurately fit about three inches of tobacco-pipe shank to one of the corks, as shown in the diagram; may repeat the operation on a second cork; and finally may adapt accurately, air-tightly, one cork to one of the four-ounce phials, the other to the florence flask. I have said may do this, had I said may do it if they can, the expression would have more correctly

But we will now render zinc transparent. It will be neces-represented my opinions. The fact is that the accusary to do this as a preliminary to future investigations. Take rate air-tight adjustment of corks, so frequently therefore about one part of oil of vitriol by measure, pour it necessary in chemical experiments, is not so selfinto an earthenware jug, and pour upon it about six measures evident an affair as many people suppose. The of water distilled, by preference; if not readily obtainable, rain fitting of a cork to a florence flask, or a tobacco-pipe shank to water. Remark the great heat developed during this mixture; a cork nearly air-tight, is no difficult matter, but nearly airthis circumstance has no reference to anything we are about tight will not do for our purpose, the adjustment must be accujust now, it relates to something connected with the philoso-rate-perfect. If therefore the chemical novice succeeds in phy of heat, involving a point to be discussed hereafter. Re- accomplishing this wihout the instruction to be conveyed in the mark the circumstance, however; it is a striking and impor- next lesson, he is permitted to take some little credit to him self.

tant phenomenon. Pour now the mixture of oil of vitriol and water into a wine glass, in order that the changes about to ensue may be readily seen. Throw in a portion of the zinc, and a little more, and a little more, until it is no longer dissolved. Possibly, however, notwithstanding all care, a little excess of oil of vitriol may be employed. This matters not, as we shall take means to dissipate the excess hereafter.

The amount of oil of vitriol used need not be more than a tea-spoonful, it must not however be measured by a tea-spoon. Remark now what a commotion ensues, observe the bubbles which arise, notice their smell. They are evidently bubbles of a gas. What is that gas? This will be subject of inquiry hereafter. The subject at present under investigation is zinc, let us therefore pay attention to it solely. The zinc rapidly dissolves,-dissappears, becomes transparent, and thus the general proposition that a metal can be rendered by combination transparent, nay even invisible, is proved.

But a novice in chemistry may fancy the zinc is no longer present. Without knowing exactly where it can have gone, the young chemical beginner may suspect it is not there; that it has vanished by some supernatural agency. Banish at once the term, banish the idea, banish them at once and for ever from your mind and vocabulary. Chemistry recognises no supernatural agencies; chemistry is based upon the conviction justified by the accumulated experience of ages, that nature

"

Fomerly, in ceremonious addresses, the words Dere (old gen. plural of ter, that person) and Ihre (old gen. plural of er, hel were used instead of Guer (your) and Ihr (her); as, Ihro Majestät, her majesty, &c.

Euer was formerly written ewer, and the syllable Ew. as an abbreviation is used in address to persors of high rank, with the verb in the plural. Ex. Ew. Majestät haben befohlen, your majesty has ordered.