=34, per question. 2 Or, 12x+18x + x + 3x = 204, removing fractions. Whence 34x = 204, Therefore = 6, And 2x = 12, 3x 18, 4 = 4. (47.) Let x be the equal result. Then 2x, 3x, and 4x, are the parts_required. Therefore = 4; And 2x 3x=12, And 4x (48.) Let a be Then x And x 4 16 -x -- 8, 16. the stock required. 50 is the part not expended the 1st year. 50+ (x 50), the stock at the end of the 1st year. 200 3 the stock at the end of the 2nd year. Or, 32 3 4 Whence སྙ 350 Or, g* 3 350 And Or, 16 Again, x 9 ANSWERS TO CORRESPONDENTS. ACOUSTICUS (Brighton): There does appear to be some incongruity in the statement to which he refers; but in reporting the experiments or con clusions of an experimenter, we are not at liberty to shape them according to any theory that may be laid down-S. R. (Frazerburgh): In Acts xiii. 48, and 1 Cor. xvi. 15, the verb is racow, to arrange, put in o. der, draw up. dispose, appoint, assign; and in Acts xx, 13, it is diaToow, which has the same meanings, but intensively; in Ephes. ii 10, the verb is роeтoat, to prepare beforehand, to get ready. Hence the word dispose is applicable in all these places; in the first two, God is evidently the Great Disposer and Arranger of events; in the other two, men dispose or appoint themselves, but under him. A CORNISH SUBSCRIBER: Sec vol. ii. P. E. p. 332, col. 1, for the explanation of your difficulty.-J. W. (Burnley): For the largest sized maps of the world, apply to Mr. Wyld, Geographer to the Queen, Charing-cross East.A. HAWKINS (Burton-crescent): Perhaps som correspondent would kindly inform him what is the best thing to take out grease from the leaves of books.-C. R. (Ipswich): He will be gratified by Lessons on Chorography as soon as it can possibly be done -H. WOOLLEY (Ross): Received. EINE UNGELEHRTE (Westbury): We have the pleasure to inform her that a Key to the German Lessons is preparing, and that it will be published separately, like the Key to the French Lessons.-TAN (York): We have ex plained all the definitions, axioms, and postulates of Euclid long ago, and shown their bearing upon the propositions; see volumes i. and ii, of the POPULAR EDUCATOR. Plane Geometry means the Geometry of figures drawn upon a plane, as in the first Six Books of Euclid; the Geometry of Planes, means the Geometry of planes as laid down in the 11th Book of Euclid, preparatory to the Geometry of Solids, as laid down in the 11th and 12th Books. H. K. W. (Brixton): Both his poetry and prose are defective yet, and cannot be admitted into the P. E.; but he is improving. We quite agree with him as to the value of the Bible to poetical students, and as to Milton, Cowper, and Young having borrowed largely from that invaluable store. For his lines on wisdom, we substitute the following, which we have often admired for their simplicity and beauty: Prov. iii. 13-15. O happy is the man who hears For she has treasures greater far And her rewards more precious are In her right hand, she holds to view She guides the young, with innocence, According as her labours rise, DISCERE VOLO (Sherborne) must change his name into Pergere Volo; his difficulties are explained further on. Sunt mihi means there are to me, that is, I have; but this is a Latin idiom. Que at the end of words means and; as dii deæque, that is, gods and goddesses, the latter being sufficiently absurd. Ad is used emphatically for the preposition to. We cannot tell yet about the Natural History.-8. J. R. (Buckingham-street): We cannot give a decided answer about the Maps.-X. Y. Z. (Hastings): The phrase upwards of always means rather more than. W. S. FRITH (Primrose-street); His remarks on instability and want of determination in study are very good. We are glad he has got over them by perseverance, and we hope some others will follow his example.-T. T. L. (Gt. Ormond-street): There is a key to Walkinghame.-RUFUS (Westminster): We have read the excellent Report on the proposed method of supplying the Civil Service, but we have not heard what has been yet done. -J. STEVENS (Manchester): His suggestions are good.-S. D. S. (Kinross): And so are his. T. G. L. (London): His letter was sent to Dr. Jenkyn.-J. M. (Camdentown): His method of measuring a distance accesible at one extremity only, is well enough known.-W. M. K.: See our Literary Notices, and send for a list of Mr. Cassell's Publications.-R. KERSLAKE (Carlisle): Received. -J. LONGFELLOW (Glasgow): There is much truth in what he says; we must supply the deficiency as soon as possible; but we are convinced that he has got more value for his money in the P. E. than in any other publication afloat.-JAMES WARDLE (Dean Mills): Received. 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Wherever the subject requires Pictorial Illustrations they are introduced. ON PHYSICS, OR NATURAL PHILOSOPHY. No. XXXIV. (Continued from page 95.) EXPANSION OF LIQUIDS. Apparent and Absolute Expansion.-In liquids, it is only cubic expansion which is to be considered; and of this there are two kinds, apparent and absolute expansion. Apparent expansion is the increase in volume which a heated liquid assumes when it is contained in a vessel which expands less than the liquid does under the same degree of heat; as the expansion of mercury or alcohol in thermometers. The absolute expansion is the real expansion which the volume of the liquid alone undergoes. The apparent expansion of a liquid is less than the absolute expansion by the amount of the expansion of the vessel in which it is contained. The expansion of the vessel is rendered evident in the case of the thermometer, by immersing it in boiling water, provided the bulb is large and filled with coloured spirits of wine up to the half of the stem. At the instant when the bulb enters the hot water, the spirits of wine sink in the tube, which evidently arises from the expansion of the sides of the bulb; but if the latter is kept immersed, the spirits of wine become heated, and rise in the tube by a quantity equal to its absolute expansion, diminished by that of the vessel. As in the case of solids, the increase in a unit of the volume of a body when its temperature is raised from 0° to 1° Centigrade, is called the co-efficient of expansion; but then a distinction is to be made between the co-efficient of the apparent expansion and the co-efficient of absolute expansion. Various methods have been employed in order to determine these two co-efficients of expansion. The following is that employed by MM. Dulong and Petit. Co-efficient of the Absolute Expansion of Mercury.-In order to determine the co-efficient of the absolute expansion of mercury, the influence of the expansion of the vessel containing it must be avoided. MM. Dulong and Petit effected this by the application of the hydrostatic principle, that in two communicating vessels the heights of two liquids are in the inverse ratio of their densities; a principle which is independent of the diameters of the vessels, and consequently of their expansion. Their apparatus was composed of two glass tubes A and B, fig. 181, supported in a vertical position and connected by a Now let h and d be the height and the density of the mercury in the branch A, at the temperature of 0° Centigrade; and h' and d' the same quantities in the branch в, at the temperature t; then, according to the hydrostatic principle just d referred to, we have 'd' hd. But d'=1+t' by our h'-h former lesson, & being the co-efficient of the absolute expansion of mercury; therefore replacing d' by its value just referred hd to, we have l+kt=hd; whence, we find that = ht This formula shows how to find the co-efficient of the absolute expansion of mercury, when the heights h and h' of this liquid in the two tubes have been measured, and the temperature t of the bath in which the tube is immersed, are given. In the experiment of Dulong and Petit, this temperature was measured by a thermometer and capsule, as explained in the next paragraph. As to the heights and h, they were measured by means of a cathetometer (see fig. 18, vol. iv., p. 100). By this process, these experimenters found that the co-efficient of the absolute expansion of mercury, between 0° and 100° Centigrade, was 6. But they observed that this co-efficient increased with the temperature; for between 100° and 200° Centigrade the mean co-efficient was ; and between 200° and 300° Centigrade it was 30. The same phenomenon was observed in other liquids; thus we see that these bodies do not expand regularly. It was found that their expansion was more irregular the nearer that their temperates pproached those of congelation and ebullition. As to mercury, the experimenters found that its expansion was very sensibly regular between -36° and 100° Centigrade. Fig. 182. Co-efficient of the Apparent Expansion of Mercury.-The coefficient of the apparent expansion of a liquid varies with the nature of the vessel which contains it. That of mercury, in a glass vessel, was determined by MM. Dulong and Petit by means of the apparatus represented in fig. 182. It is composed of a cylindric glass reservoir or bulb, to which is cemented a capillary glass tube hent at a right angle and open at its extremity. In order to make the experiment, the instrument is weighed when empty, and also when filled with mercury at 0° Centigrade; the difference between the two weights gives the weight P of the mercury cont. ined in the apparatus. Raising it, then, to a temperature denoted by t, the mercury expands, and a certain quantity of it comes cut, which is received in a small capsule, and weighed. If the weight of the mercury which has come out be represented by P, that of the mercury which remains in the apparatus is denoted by P-p. Now, let v' be the volume of the mercury at 0°Centigrade, whose weight is P, and v the volume, also at 0° 112 P-p = v Centigrade, of the mercury which remains in the apparatus, and tion. Several processes have been employed in order to deterwhose weight is P-p. The weights of these two quantities, mine the temperature of the maximum density of water. M. which are at the same temperature, are therefore proportional Hällstrom, by weighing, in water at different temperatures, a glass ball ballasted with sand, found, taking into consideration to their volumes; that is, we have But is the expansion of the glass, that it was in water of the temperature of 401 Centigrade or 39° 38 Fahrenheit, that the ball lost exactly the volume to which v rises, when heated from the most of its weight; whence he concluded that at this tem0° to to Centigrade. Representing, therefore, the co-effi-perature the maximum density of water takes place. MM. cient of the apparent expansion of mercury by d, we Munke and Stampfer have stated the temperature of the 1 ; dt being the increase which the unit maximum density of water, at 3°.75 Centigrade, or 38-75 Fahrenheit, according to their experiments. But M. Despretz 1 + dt of the volume of mercury takes in passing from 0 to to has ascertained, by numerous experiments, that the temperature of the maximum density of water is really that of 4° Centigrade. Whence, it follows that Centigrade, as above stated. By gradually cooling a waterthermometer (that is, a thermometer with water instead of mercury) in a bath whose temperature was given by a mercurial thermometer, he found that it was at 4° Centigrade that the maximum contraction of the water in the water-thermometer took place. ย have = and consequently, we have d = p (P-p) t P- -p = 1 MM. Dulong and Petit found, in this manner, that the coefficient of the apparent expansion of mercury in glass was etto. From the data obtained by the preceding experiment, we can deduce the temperature to which the thermometer has been carried, when we know the weights P and p. For, since p in glass, we have , we find by clearing this (P - p) t equation of fractions, 6480 p = (r − p) t ; whence, t= 6480 p Co-efficient of the Expansion of Glass.-The absolute expansion of a liquid being equal to its apparent expansion plus the expansion of the vessel which contains it, we obtain the cubic expansion of glass in the preceding experiment by taking the difference between the co-efficient of the absolute expansion of mercury and that of its apparent expansion. Whence, we have the co-efficient of the cubic expansion of glass equal to 0.00002586; for M. 0480 = JAGTT 0.00002586. Regnault has found that the co-efficient of expansion varies with different kinds of glass, and even with the different forms of the vessels. For the common glass tubes used in Chemistry, he found that the co-efficient of expansion is 0 0000254. By multiplying the co-efficient of the absolute expansion of mercury for 1 Centigrade by, we obtain this co-efficient for 1° Fahrenheit; thus X95; and by multiplying by we obtain this co-efficient for 1° Reaumur; thus, 50 X =1440. The co-efficient of the absolute expansion of different liquids can be found in the same manner as that of mercury was determined; and thence by adding to it the co-efficient of the expansion of glass, the co-efficient of their apparent expansion can also be found. Correction of the Height of the Barometer.-In treating of the barometer, p. 258, col. 2, we remarked, that in order to render its indications in different places and at different seasons of the year comparable with each other, it is necessary always to refer the height of the column of mercury to a constant or fixed temperature, such as that of the freezing point of water. This correction is made in the following manner: let the height of the barometer at t° Centigrade be denoted by н, and its height at 0° Centigrade by h. Then the column of mercury being compared to a metallic rod which in being heated from 0° to to Centigrade takes the length н, we have ht 5550 H x=h+ ; whence h In this formula, the 5550 5550+t co-efficient of the absolute expansion of mercury, and not the co-efficient of its apparent expansion, must be taken, because the value of H is the same as if the glass did not expand, the height of the mercury in the barometer being independent of the diameter of the tube, and consequently of its expansion. Maximum Density of Water.-Water presents this remarkable phenomer on, that when its temperature is lowered, it only contracts as far as 49 Centigrade or 39° 2 Fahrenheit; below this point, although the lowering of the temperature continues, not only does the contraction cease, but the liquid expands even to the freezing point, which takes place, of course, at 0° Centigrade or 32° Fahrenheit; so that at 4° Centigrade, or 39° 2 Fahrenheit, water experiences its maximum of condensa LESSONS IN CHEMISTRY.-No. XXXIII. RESUMING the consideration of chlorine, we have now to Chlorine as a Supporter of Combustion.-In determining whether any medium be or be not a supporter of combustion, it is only natural that we should begin with the example of a combustible in the ordinary sense of the term. We will, therefore, take a candle or small taper mounted upon a bent wire, and furnished with disc and cork, as frequently described already, and as represented in our subjoined diagram, fig. 36. Fig. 36. Exp. Having lighted the taper, plunge it into the jar or bottle of chlorine, and observe the result. The taper burns after a fashion, but a strange sort of burning it is; only a small | denly extinguished, and the copper support will vehemently pale powerless flame appearing, whilst copious black fumes burn. are liberated on all sides. Now, why is this? Charcoal is a very combustible material under all ordinary circumstances: it is indeed the combustible par excellence of man; wherefore, then, does it not burn in our present experiment? The young chemist will perhaps jump to the conclusion, that chlorine, although a supporter of combustion, is a very bad supporter. Conclusions, however, can seldom be justly arrived at from the consideration of one isolated experiment; let us therefore try a few others. Exp. Dry a small piece of phosphorus, not larger than a pea in size; place it in a copper deflagrating ladle properly mounted, and immerse it in a jar of chlorine. These directions having been followed, the phosphorus will spontaneously burst into flame, but the flame will not possess any great illuminating power. How shall we now designate chlorine in relation to combustion, after having witnessed the evidence of our last experiment? We surely must not term it a bad supporter of combustion, seeing that it will accomplish a result quite out of the power of even oxygen gas to accomplish; namely, it will cause the spontaneous ignition of phosphorus. Exp. Procure some Dutch leaf, and hanging a few pieces of this on a properly-mounted hooked wire, as represented in fig. 37, Fig. 37. The functions of chlorine, as developed by our preceding experiments, considerably enlarge the sphere of our notions relative to combustion, and we arrive at the remarkable conclusion that, if in place of our own atmosphere of oxygen and nitrogen, we were surrounded with an atmosphere of chlorine, carbon, including charcoal, coke, and coal, would be absolutely incombustible, and carbon holding materials such as oils, fats, coal-gas, etc., would only be combustible to the extent of Fig. 38. plunge it into a jar of chlorine gas. The metallic leaf will generally take fire, again proving that under certain circumstances, and for certain bodies, chlorine is a remarkably good supporter of combustion.. Exp. Having procured some powdered antimony-real metallic antimony, not the sulphuret-throw a little of the powder into a jar of chlorine gas. Immediately the antimony will take fire. In all these cases, be careful to confine as much as possible the results of combustion, as they are very injurious when taken into the lungs. They may be confined by dexterously sliding over the mouth of the bottle or jar a greased glass plate. Exp. Our next experiment shall have reference to the curious phenomenon already noticed in the instance of the burning taper, of the development and evolution of carbonaceous fumes, but it shall manifest that phenomenon in a still higher degree. Dip a slip of bibulous or absorptive paper into oil of turpentine, then plunge it into a bottle of chlorine, and close the bottle by means of a greased glass plate. Most probably, under these circumstances, the paper will take fire, and the peculiar black carbonaceous fumes will be still more evident than before when we employed a taper. But a still more Expressive demonstration of the incombustibility of carbon in chlorine gas will be afforded by the ensuing experiment, for the performance of which we made preparations in our last their contained hydrogen. Combustion, in point of fact, is one consequence and direct evidence of intense chemical action. Without chemical action resulting in combination there can be no combustion; and inasmuch as chemical union between chlorine and carbon does not ensue, for this reason, charcoal and carbon generally are not able to burn in an atmosphere of chlorine gas. There is, however, a combination of chlorine and hydrogen, the result being hydrochloric acid gas-the gas which, when absorbed by water, constitutes the well-known muriatic acid, or spirit of salt. Hence it follows, that when we ignite a material holding both carbon and nitrogen, such for example as a taper, or oil of turpentine, and dip either thus ignited into a jar of chlorine, hydrogen is alone consumed and carbon deposited. It may be well in this place to say a few words relative to an insufficient definition formerly offered, and during many years retained, of the function of combustion, which was defined to be a rapid combination of bodies with oxygen. If this definition be accepted, then it follows that the experiments we have just performed, and the phenomena we have just witnessed, are not tho-e of combustion; indeed certain systematic writers have excluded them from the category, seeing they did not fall under the definition. Such an expulsion, however, is unphilosophical. No definition should do violence to a natural and well-established idea. Surely, then, violent chemical action, attended with the evolution of light and heat, ought to be regarded as an instance of combustion. The definition of combustion as the rapid chemical union of a body with oxygen originated in a remarkable period, of which it bears the stamp. It originated during the early part of the first or great French revolution: a period when the genius of innovation was active, and human intellect unbridled in its pride. Then it was that the chemical nomenclature of Lavoisier appeared, a nomenclature sufficiently expressive of the chemical facts then known, but totally incapable of expansion. In order, indeed, that a system of nomenclature in any science should be so, either all its facts should be well-known, or should be deducible from such simple elements, as in Geometry, |