ANSWERS TO CORRESPONDENTS. B. BRUCE (Camden-town): His hint about Scarpanto and Caxo or Caso in the Map of Turkey will be attended to.-DERF: Aqua ammoniæ, spirit of hartshorn; sal volatile, smelling salt, or rolatile salt of hartshorn.-AMATOR, P. S. (Limehouse): We cannot recommend any college of the kind he mentions, as they are all defective; we have found them so to our sad experience; we should be glad to see him on the subject. T. O. W. (Manchester): The rules for determining the gender of nouns in German, are contained in p. 131, vol. ii. of the P. E.-UN ELEVE (Notting-hill): See vol. ii. p. 197 et seq.-G. WRIGHT (Hull) should study the solutions of the Algebraic Problems as given in the P. E. He may teach himself Euclid, if he chooses, as may be seen by an example of this kind in our Preface to the "Self and Class Examiner in Euclid," price 3d.-H. S. See vol. ii. P. E. page 327, col. 2, near the bottom. I. T. K. (Waltham Abbey): Hyposulphite of Soda is prepared by dissolv ing sulphur in a concentrated hot solution of sulphite of soda un il the latter is saturated. The liquid, subjected to crystallization, deposits the hyposulphite in large transparent crystals. When heated, it first fuses in its water of crystallization, and by properly regulating the heat, the whole of its water may be driven off without decomposition; but if it be further heated, it is decomposed into a sulphate and sulphide. CONSTANT READER (Wye): "The first digit of a certain number exceeds the second by 4; and when the number is divided by the sum of the digits, the quotient is 7; find the number." (Swindon) should inquire at 59, High Holborn.-LABORE VINCO (Soho): His progress in Algebra does him great credit; the questions are rightly solved. DAVID: It rains is an impersonal verb.-SPEUDO: A Greek pronouncing dictionary was mentioned in our notices before; xaλenn should be pronounced cha'epce, where the cn has the rough sound of k; although the name of the letter x. chi, has the letter i attached to it, the i of the name is never to be sounded in a word where the letter x occurs; and the same remark is applicable to the names of all the letters: it is only the sound of the first letter, vowel or consonant, in the name, that is to be pronounced in any word. W. BECK (Dalston): We have seen in the Kingsland and Dalston omnibus, an advertisement relating to a Debating Club in his vicinity: we advise him to look out for it.-NAUTUS (Tipperton): We can give him no advice on the subject of becoming a Middy; but we certainly think a knowledge of navigation is indispensable.-T. K. B. (Stalybridge) will see by the solutions inserted in auswer to his question.-KEIR: Right.-G. S. (Cupar): We cannot answer his question. LITERARY NOTICES. CASSELL'S EDUCATIONAL WORKS. This work is intended to supply the people with such information relating to the study of the Bible as the POPULAR EDUCATOR has given in reference to Secular Instruction. It contains a Literary History of the Sacred Books -Accounts of their Original Text-Canonical Authority, and most Ancient Versions-The Principle and Laws of Interpretations, and the Methods of Discovering the Literal or Symbolical Meaning of Inspired WritingaIllustrations of the Geography and Natural History of Palestine-The Manners and Customs, the Laws and Worship of its People-The Antiquities of the Four Great Monarchies-The Fulfilment of Prophecy concerning them and other ancient nations-and the Fruits of modern Travel and Discovery in the East, etc. The work is written in a popular style, and is therefore specially adapted to supply Families, Sunday-school Teachers, and others, with that amount of information respecting the Holy Bible which they need to confirm and establish their own minds in the genuineness and authenticity of Holy Writ. Wherever the subject requires Pictorial Illustrations they are introduced. "To find the sine of angle, when the number of degrees is given," apply in order to meet the charges of Intidels and the subtleties of Romanists, and to Hu ton's Tables, or use the following formula: " A° 1809 J. II. FORSYTH (Lanarkshire): Be not disappointed; Hebrew will come in good time; the Greek must first be finished. JAMES ANDREWS (Birmingham): The references in the "Reading Lessons are to "Cassell's Lessons in French," parts i. and ii., price 2s. each, or the two parts bound together, in one vol. cloth, 4s. 6d. Where the part is not mentioned, as L. p. 91, the meaning is, that at page 91 of "Cassell's Lessons in French," part i, the information will be found to which reference is made; L. p. 110, part ii., means page 110 of "Cassell's Lessons in French," part ii.; and so on. Our correspondent will see that the references are to the "Lessons" as they appear in their collected form, and not as they appeared in the P. E. It would have been a toiisome and troublesome task to have adapted the references of the "Reading Lessons" to the "Lessons in French" as they originally appeared in the P. E., cxtending as they do over nearly four volumes of that work. JAQUES (Galashiels): We advise you to write to the Secretary of the Scottish Normal Schools for information; we cannot give you what you require.-1. T. O. (Oldham): We have not seen the laboratories, and so cannot advise.-BETH (York): The explanation of Church, Chapel, and Cathedral is rather a ticklish question; ask the Archbishop. Reid our Lectures on Euclid.-J. S. M. (Glasgow): The only cure for bashfulness is to rub your face with a brass candlestick!-G. S. RUTHERFORD (Maryle bone): We presume that two or three days before the examination for matriculation commences at the University of London, will be sufficient time to enter your name in the register and pay the fee. We believe that Dr. Latham's books on the English language are the best adapted for preparing you to be examined on that language.-T. C. L. (Chatham) and JOHN DAVIES (Cornwall): For books on Musical Instruments and Music generally, we recommend Messrs. Cocks and Co., New Burlington-street. The early-closing movement has our best wishes; and, if we had room, it should have our advocacy. Poisson's Treatise on Mechanics is much esteemed, and it touches on some points in Physical Astronomy. There are some smaller works, but we expect by and by to treat these subjects in an elementary manner ourselves. H. C. (Sheen) is right as to the results which would follow on the obtaining of a new charter by the University of London, such as we have proposed; there would be no limit as to age upwards from sixteen years. We don't know a book on the pronunciation of Musical Terms, but as they are almost all from the Italian, our Lessons on that language will supply the desideratum. Then as to Geographical Names, there is no harm in giving them the pronunciation of English words, generally speaking. Bordeaux being a French wors, the vowels in the second syllable should, of course, be pronounced like those in our English word Beaux; thus we say Bu; whence, we should say Bordo: but in relation to the French capital, we say both Paris and Părī, leaving out the s, in the latter pronunciation, as the French do. Mrs. SLIPSLOP (N. B.): Her remarks on the subject of the Roman notation are good, as far as they go; the Professor of Gresk under whom we stud.ed, the celebrated John Young, of the University of Glasgow, used to give us a complete account of this notation, which he began much in the same way as our correspondent; we shall keep the subject in view.-W. 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Gd. cloth, consists of a LATIN READER, adapted to "Cassell's First Lessons in Latin."-Volume II. comprises LATIN EXERCISES, price 2s. neat cloth.-Volume III. contains THE ACTS OF THE APOSTLES in the Original Greek, with copious Notes and a Lexicon, price 2s. 6d. neat cloth. ON PHYSICS, OR NATURAL PHILOSOPHY. No. XXXIII. (Continued from page 81.) EXPANSION OF SOLIDS. Kinds and Co-efficients of Expansion.-Two kinds of expansion in solids were mentioned in a former lesson, viz., Linear Expansion, or that which takes place in the direction of one dimension only; and Cubic Expansion, or that which takes place in the volume or bulk. The co-efficient of linear expansion is the elongation or increase which a unit of the length of a body takes, when its temperature is raised by 10 Centigrade from the freezing point; or, it is the increase in its length for every degree between the freezing and the boiling points of water. The co-efficient of cubic expansion is the increase which a unit of the volume of a body takes under the same circumstances. These co-efficients vary in different bodies; but for the same body there exists a simple relation between the two co-efficients, viz., that the co-efficient of cubic expansion is three times the co-efficient of linear expansion, for all ordinary purposes. Thus by multiplying or dividing by the number 3, we can always find one of these co-efficients when the other is known. To demonstrate that the preceding rule is correct for gradual expansions, suppose that a cube whose side is unity, or 1, is at 0 Centigrade. If we represent the increase which the length of a side of the cube receives in rising from 0° to 1° Centigrade by 1, its length at the latter point will be 1+, and the volume of the cube, which was 1 at the former point, will now be (1+)3 or 1+31 +372 +33. Now, the increase in length 7, is always a very small fraction, as will be seen in a subsequent table; therefore, its square and its cube 3, are in general fractions so very small, that they have no effect on the final decimal of the numbers which represent the cubic expansion. These quanties are consequently neglected in practice, and the volume of the body at 1° becomes approximately 1 + 31. order that it may not be hindered in its motion, it rests on two glass rollers. The bar Kн having been carefully measured at 0° Centigrade, and placed as shown in the cut, that is, in contact with the two rules, and the telescope being horizontal, we observe to what division it corresponds on a vertical scale AB placed at a great distance. We then replace the bar к H by a second bar longer by a given quantity, say one-tenth of an inch. The rule D being thus displaced and made to assume the position GC, imparts to the axis of the telescope a motion of rotation, and makes it take the oblique direction G B. By looking then through the telescope, we read off from the scale of deviation the quantity A B, which we shall suppose contains 180 divisions; this result being obtained, we remove the second bar and restore the first to its place; we then heat the furnace, having filled the trough with oil, a liquid which can be carried to a much higher temperature than water. In proportion as the heat increases the bar is lengthened, and the telescope is again made to take an oblique direction. The number of divisions which it indicates on the scale are then measured, say 120, and at the same time the temperature of the bath, by means of the thermometer, a temperature which we shall suppose to be 80° Centigrade. From these data, it is easy to deduce the elongation HC of the bar. For, since 180 divisions of the scale, from A to B, correspond to an elongation of the bar by one-tenth of an inch, a deviation of a single division is equivalent to an elongation of of an inch; consequently, a deviation of 120 divisions is equivalent to an elongation of 120 times 18 of an inch, that is or of an inch; or, as 180: 120:::. The length H c being thus determined, we obtain the coefficient of linear expansion-that is, the elongation which corresponds to a single degree and to a single unit of length-by dividing the elongation thus obtained, by the temperature of the bath, and by the length of the bar at 0° Centigrade-or, by the product of these quantities. If in the experiment just mentioned we had taken, for example, a bar of lead of 29 inches, we should obtain the co-efficient of the linear expansion of lead, by dividing of an inch by the product of 29 and 80; thus,; 0.000028571; and this would 15 x 29 x 80 1 The increase of the volume is therefore 31, that is, triple the | then be the linear expansion required. If this experiment be linear expansion. Determination of the Co-efficients.-MM. Lavoisier and Laplace determined the co-efficients of the linear expansion of the metals by means of an apparatus represented in fig. 174. It is composed of a copper trough placed on a stove or furnace between four blocks of stone. The two which are on the right of the cut support a horizontal axis, at the extremity of which there is a telescope; and in the middle of this axis is fixed a glass rule, which turns with it as well as the telescope. In the other two blocks are fixed two iron cross-pieces which support a second glass rule. Lastly, in the trough, there is a water or oil bath, where the bar is placed, whose co-efficient of expansion is to be measured. Fig. 175, is the representation of a section of the apparatus. G is the telescope, KH the bar, of which the two ends rest on the two glass rules F and D. The rule F being fixed, the bar can only be lengthened in the direction from к to H; and in VOL. V. made on different metals, and repeated with various temperatures between 0° and 100° Centigrade, it will be found that the co-efficient of the linear expansion of the metal between these limits is sensibly constant; that is, for the same number of degrees, the length increases constantly by the same fraction of the length which it had at 0° Centigrade. But, according to the researches of MM. Dulong and Petit, the co-efficient becomes greater between 100 and 200° Centigrade, and increases between 200° and 300° Centigrade, and so on, to the point of fusion. Tempered steel is an exception; its co-efficient decreases when its temperature passes a certain limit. The following is a table of the expansions of the most useful metals, when heated from 0° to 100° Centigrade, or from 32° to 212° Fahrenheit; that is, of the co-efficients of their linear expansion for the distance between the freezing and the boiling points of water, according to MM. Dulong and Petit, Lavoisier, and others. 111: 94 As this table is constructed for the Centigrade scale, it will be useful to show how to adapt it to the scale used in this country. By removing the decimal point in each of the numbers of the table two places to the right, these numbers will then represent the whole amount of expansion which each bar of metal undergoes when heated from 0° to 100° Centigrade, or from 32° to 212° Fahrenheit. By dividing each of these numbers by 180 (the number of degrees from 32° to 212°), the being k, the elongation corresponding to t degrees is t times k or kt for a single unit, whence it is / times kt or ktl for units of length. The length of the bar which was at 0° Centigrade, is therefore + ktl at t degrees; whence l' = 1 + ktl (1). By putting into the form of a common factor, we have l'= (1 + kt) (2). This formula will give the length l at to when the length at 0° Centigrade is known. By dividing both members of the preceding equation by ľ (1 kt), we have = (3). This formula will give the 1 + kt length at 0° Centigrade when the length at t degrees is known. By transposition in equation (1), and dividing both sides by This formula will determine the tl, we have k" — 1 tl (4). Fig. 175. D H quotients will become the co-efficients of expansion according to Fahrenheit's scale; that is, the quantities by which each bar of metal will be elongated when its temperature has risen by 1° Fahrenheit between the freezing and the boiling points of water. Thus, the co-efhcient of expansion for glass, by the Centigrade scale, is 0.000008613; therefore, glass expands 0 0008613 of its length at 0° Centigrade, when heated from that point to 100° Centigrade, or from 32° to 212° Fahrenheit; now, dividing 0.0008613 by 180, we have 0 000004785 for the co-efficient of expansion, according to Fahrenheit's scale. As it may be useful to many of our readers, we give the By denoting the volume of a body at 0° Centigrade by unity or 1, and its cubic expansion by k, the volume at t degrees will be 1+kt; but the density of a body is in the inverse ratio of the volume which it takes on expansion, we have, d ď therefore, t = whence, d'. 1+kt 1 All these formulæ and rules will apply to examples in Fahrenheit's scale, if 32° Fahrenheit be put for 0° Centigrade, 32° for t; also, if the Table of the Co-efficients of and t Expansion according to Fahrenheit's scale, be used instead of that according to the Centigrade scale. Examples. I. If a bar of iron be exactly twelve feet long at 0° Centigrade, what will be its length at 80° Centigrade, the coefficient of linear dilatation being 0 000012204 according to the Centigrade scale? = Here, by formula (2), we have l≈ 12 (1+0·000012204 × 80) 12 01171584 feet, or twelve feet and of an inch nearly. II. If a bar of iron be twelve feet long at 32° Fahrenheit, what will be its length at 176° Fahrenheit, the co-efficient of linear dilatation being 0.00000678 acccording to Fahrenheit's scale? Here, by formula (2), we have = 12 (1+0.00000678 X 144)=12-01171584 feet, or twelve feet and of an inch nearly, as before. III. If a bar of copper be fifteen feet long at 90° Centigrade, what will be its length at 0° Centigrade, the co-efficient of linear dilatation being 0.000017182 ? Here, by formula (3), we have 7 = 15 1+0-000017182 × 90 14.96685 feet, or 14 feet 11 inches nearly. Applications.-The expansion of solids presents numberless applications in the arts. The iron gratings of furnaces, for instance, should not be too accurately fastened at their extremities, but left free at one end at least; otherwise they will displace the stones of the fire-place by their expansion. If on railways the iron rails are in contact, the force of expansion will make them either become curved, or will break their chairs. When a glass vessel is heated or cooled too suddenly, Fig. 177. it breaks in pieces; because glass being a bad conductor of caloric, the sides of the vessel are irregularly heated, and consequently expand unequally, which produces the disruption of the parts. Compensation Pendulum.-The unequal expansion of different Fig. 178. metals has received an important application in the compensation pendulum. This name is given to a pendulum in which the elongation of the rod when the temperature is raised is compensated for in such a manner that the distance between the centre of suspension and the centre of oscillation remains constant, which is necessary according to the laws relating to the pendulum formerly explained, in order that its isochronism may be preserved, and that it may be employed as a clockregulator. Various methods have been proposed for this purpose; but that which is represented in fig. 177 has been generally adopted. In this method, the bob L, instead of being supported by a single rod, is supported by a series of frames, of which the vertical rods are made alternately of iron and brass. In the first frame abde, the rods ff are made of iron, and are soldered to two bars a b and c d, which, as well as the bar o i, may be made of any metal whatever. In the interior frame the two rods c c are made of brass, and are soldered to the bars oi and ed. The middle rod which supports the bob is made of iron. It is fixed only to the bar oi, and passes freely through a hole in the middle of the bar e d. This app ratus operates as follows: when the temperature rises, the iron rods ƒƒ are lengthened downwards and tend to lower the bob. The brass rods cc, on the contrary, fixed at the bottom, can only be lengthened upwards; therefore, they raise the bar oi and consequently raise the bob. By this means the bob is kept at a constant height, provided the elongation of the brass rods in the one direction be equal to the total elongation of the iron rods in the other direction. This effect is obtained by giving to the iron and brass rods such lengths in the frames as are in the inverse ratio of the co-efficients of expansion of these two metals. Another method of compensating for the elongation of the pendulum rod, is by means of compensating laminæ or bars. It consists of two bars, one of brass and one of iron soldered together, and fixed to the rod of the pendulum, as shown in fig. 178. The bar of brass, which is more expansible than the bar of iron, is placed below it. When the temperature is lowered, the rod of the pendulum is shortened, and the bob rises; but then the compensating bars become curved, as shown in fig. 179, because the brass contracts by cold more than the iron. In this manner, two metallic balls placed at the extremities of the compound bar are lowered; and if they have been properly adjusted, they establish a compensation between the points which are nearer to the centre of suspension and those which are farther from them, and thus the centre of oscillation is not displaced. If the temperature is raised, the bob descends; but the balls are raised, as shown in fig. 180, and compensation takes place by a similar operation. oxide of manganese and common salt (about equal parts by weight)-five or six table-spoonfuls will suffice for our wants; place the mixture in a Florence flask, to which a cork and bent tube have been securely adapted, add sufficient of a mixture of oil of vitriol and water (equal parts by measure) to reduce the oxide of manganese and salt to the consistence of a paste; apply heat, and proceed to collect by means of the prismatic trough as usual. A few preliminary words expressive of certain cautions to be observed in the development of this gas will not here be out of place. First of all, it is not sufficient merely to pour the dilute acid upon the mantomst he well incorporated by shaking, otherwise the flask will most probably break on the first appli- | the extent of the decomposition,-reducing it to very narrow cation of heat. The great object of well incorporating the limits-by taking care that no unnecessary amount of water powder and the fluid is to cause a wetting of the bottom and enter, and that the store bottles be of black or deep blue glass. sides of the flask. If a spirit-lamp flame be applied to dry The manipulation to be followed, in order to obviate the glass, that is to say, retained dry by the interposition of a imprisonment of water, thus to speak, with the chlorine is powder, the glass is almost certain to be ruptured. The second caution to be mentioned has reference to the danger Before finally putting aside a store bottle full of chlorine, (or inconvenience to say the least) attendant upon the escape the operator, holding it inverted, as represented in fig. 33, of chlorine, which is a gas most irritating to the lungs and air observes whether or no a layer of water (w) be lying next the passages. Not one bubble, therefore, should be allowed to stopper. If such layer be present, the stopper is rapidly escape, consequently, in addition to the bottles or jars designed abstracted and as rapidly replaced, thus allowing the chlorine to store the pure gas, the first portions which come over, and to remain, comparatively speaking, dry. I need scarcely indiwhich are necessarily mixed with atmospheric air, should be cate that by following this treatment, the chlorine becomes collected in spare bottles, placed ready on the shelf of the mixed with a bulk of atmospheric air equal in dimensions to pneumatic trough for that purpose. Our experiments, presently the bulk of the water set free: however, of two evils it is to be gone through, will require five or six bottles full of chlo- always best to choose the lesser; in the case under considerarine; half-pint wide-mouthed bottles will suffice, or even smaller tion, atmospheric air is a lesser evil than water. ones; but whatever the size, their stoppers and mouths, whilst yet dry, should be well smeared with stiff pomatum. As regards the water of the pneumatic trough, it should be-whatever certain books may say-cold. I state this pointedly, in consequence of directions very frequently given, that chlorine should be collected over warm water, in order that no portion of the gas may be absorbed. True, warm water prevents absorption of the gas, but its employment gives rise to a far more serious evil. It causes the gas to expand, to enter the receiving vessels in a rarefied condition, and finally the bottles being stoppered and allowed to grow cold, and the gas contracting, the stopper frequently becomes obstinately fixed by the agency of external atmospheric pressure. This very serious evil more than compensates for the non-absorption of the gas by hot water: nor indeed is the absorption of chlorine by cold water sufficiently great to prove inconvenient, except under the condition of the water being agitated, a condition altogether unnecessary, save and except the agitation referrible to transmission of the gas bubbles themselves. PHYSICAL AND CHEMICAL CHARACTERISTICS OF 1) Its Smell.-No specific experiment need be performed in illustration of this quality. Notwithstanding all the precautions indicated-all the care taken-most probably some will have escaped, and rendered itself manifest to the olfactory sense. At any rate, beware how you proceed to smell it deliberately, for when breathe d even considerably diluted, it gives rise to most painful sensations. (2) Its Colour.-The peculiar tint of chlorine is almost distinctive of this gas or some of its gaseous combinations. It is rendered very evident by placing as a foil, behind the bottle containing it a sheet of white paper. (3) Its Solubility in Water.-This property of chlorine has already been noticed whilst discussing the best method of collecting it; let us now direct our attention to the special demonstration of that property. For this purpose, take a halfpint bottle full of chlorine, and whilst yet inverted on the shelf of the pneumatic trough, seize it underhand thus, fig. 34, and |