And thundering and floundering. And gleaming and streaming and steaming and beaming, And thumping and flumping and bumping and jumping, And so never ending, but always descending, PHONETIC SHORTHAND. Edinburgh, 13, South Charlotte-street, May 29th, 1854. DEAR SIR,-The contents of the shorthand letter you sent me are such a pleasing tribute to the value of the P.E. and to the simplicity of the system of Stenography which I communicated, that I have taken the trouble to transcribe the whole for your inspection. The translation is verbatim—not a word or character has been passed undeciphered. In answering the letter, you should recommend a larger scale of writing, and a more exact attention to the relative sizes of the characters. The writing is beautifully executed. It is, considering the time spent in learning the system, a marvel of neatness and accuracy. Should you publish the letter in extenso, you can tell your readers that the writing occupied but half a page of small note paper, or exactly thirteen square inches. I wish you would let your correspondents know that the system is now published with improvements, and that the Vocabulary of Logograms is in progress in accordance with the new Alphabetic basis. It will, however, be some months yet before the work is published. My professional engagements leave me but little time, and the Shorthand has often to give place to more pressing matters during the little leisure I have. I was very much pleased to see the letter of the Railway Policeman last week. If you give me his address, I will send him a copy of the Pop. Stenography.-Yours, very truly, R. Wallace, Esq., Dalston. ALEX. MELVILLE BELL. The following is the Letter referred to by Mr. Bell : Gibraltar, 4th May, 1854. SIR,-Having hitherto been a subscriber for the POPULAR and BIBLICAL EDUCATOR, the former I feel convinced is a work that cannot be too fully appreciated amongst all classes of people; being, in fact, notwithstanding the rapid march of intellect and civilization of which England may boast, a wonder of the age. I have read and studied several lessons on different subjects attentively, for the express purpose, not only of learning from its pages myself, but of endeavouring to find out that its foundation is laid down with such a systematic principle, that all who wish to avail themselves of the opportunity of acquiring knowledge may do so, by applying their mind studiously and industriously to any part of it; and in which, I feel called to announce from my humble position in life, that it surpasses any work hitherto published. I felt very much puzzled when I commenced upon the French Lessons, owing, no doubt, to my entire ignorance of foreign languages at the time. However, I relinquished the French for a time, and made an effort to learn the Spanish language (which I have attained tolerably well for the time I applied myself to it), considering that it would facilitate the study of other languages; but it does not, further than, perhaps, giving me a knowledge of a foreign articulation, so that I felt nearly as much puzzled afterwards as before; and I would have been entirely so, had I not kept the first lesson brooding in my mind during the short time that I left it off. As I could not shake off the puzzling difficulty that had become seated in my mind, which was as though it urged me to apply my mind industriously to the task that I might surmount it, I took up the book again, and after three hours close study, I felt convinced that I could overcome it; I then did the same the two following days, which almost set my mind at ease, as I saw the difficulty vanish, and the leading principle of the articulation was impressed on my mind; so that, on the fourth day I committed four lessons to memory, besides feeling a confidence within me that my pronunciation was very nearly correct, as far as it could be attained from books alone. Feeling somewhat elated at the progress I had made, I went and paid a visit to some friends of mine who knew French, and spoke a few sentences extemporarily, besides reading a little to them, an effort by which each of them was astonished; in fact, one of them said I spoke the same as any Frenchman that ever he heard speak, as far as I was acquainted with it. I have no doubt but I can attain it in six weeks for ordinary conversation. But as I do not wish to hold any correspondence at present with regard to the French language, etc., except in Phonetic Shorthand, which I wish to become properly acquainted with, as it is a ready means for corresponding with those who know it; if you will favour me by your assistance, as I am one who is labouring under difficulties to acquire knowledge, I shall feel much obliged to you, and will always endeavour to show something meritorious for the pages of the POPULAR EDUCATOR, that I hope will encourage many young men to spend their leisure hours in a similar manner, and banish ignorance from their path. I have not applied my studies to the Phonetic Shorthand more than THREE WEEKS, that is, AN HOUR EACH DAY for that period, and as I think that I have made good progress in that time, I have purposely written this letter in the Phonetic style for your inspection, and I hope that you will have the kindness to let me know if it is correct, and sufficiently abbreviated for general reporting. I also wish you to send me a small treatise containing a more extensive vocabulary of Logograms, besides a few examples of speeches, sermons, etc., written in the Phonetic system, so sufficiently abbreviated that I could be able to take down a verbatim speech or sermon. I will give the order for the treatise to Mr. Hooper, the ironmonger. Hoping that you will forward an answer along with it, as it will much oblige, yours, respectfully, etc. JOSEPH INESON. The In Two Parts:-1. French and English; 2. English and French. French Department carefully edited by Professor DE LOLME, and the English Department by Professor WALLACE and H. BRIDGEMAN, Esq. In one large handsome Octavo Volume, price 98. 6d. strongly bound. QUELLE. Price 28. each in paper covers, or 23. 6d. bound in cloth. The CASSELL'S LESSONS IN FRENCH. Parts I. and II.-By Professor FASTwo Parts bound in One Volume, price 43. 6d. the Exercises. Price 1s. paper covers, or 1s. 6d. cloth. LOLME. Price 3s. neatly bound. A SERIES OF LESSONS IN FRENCH, on an entirely Novel and Simple Plan. Reprinted in a revised form from "The Working Man's Friend." Price 6d., by post 7d. Nearly 30,000 copies of this work have been sold. Now Ready, CASSELL'S GERMAN PRONOUNCING DICTIONARY: paper covers, or 2s. 6d. in cloth. Two Parts bound together, price 4. 6d. CASSELL'S LESSONS IN GERMAN PRONUNCIATION: consisting of easy Extracts from German Writers. Price 1s. paper covers, or 1s. 6d. cloth, CASSELL'S LATIN DICTIONARY. In Two Parts:-1. Latin and English: 2. English and Latin. BY J. R. BEARD, D.D., and C. BEARD, B.A. In Weekly Numbers, 3d. each, and Monthly Parts, 1s. The First Three Monthly Parts are now ready, as also the First Thirteen Numbers. ON PHYSICS, OR NATURAL PHILOSOPHY. No. XXXIX. (Continued from page 175.) HYGROMETRY. THE object of the science of Hygrometry (moisture-measuring), is to determine the quantity of the vapour of water contained in a determinate volume of air, or in the atmosphere. This quantity is very variable; but the air is seldom saturated with the vapour of water in our climate; and it is never completely free of that vapour; for, if we expose hygrometric substances to the action of the air, these substances absorb the vapour of water at all times. By hygrometric substances here, we mean those which have a great affinity for water, as chloride of calcium, sulphuric acid, etc. Hygrometric State.-The air not being in general saturated with vapour, the hygrometric state, or the fraction of saturation of the air, is the ratio of the actual quantity of the vapour of water which it does contain, to the quantity which it would contain if it were saturated, the temperature being the same in both cases. Now Mariotte's law applies to vapours not saturated as well as to gases; whence, it follows, that at an equal temperature and volume, the weight of the vapour in a space not saturated, increases with the pressure, and consequently with the tension of that vapour. We may, therefore, instead of the ratio of the quantities of vapour, substitute that of the corresponding elastic forces; consequently, the hygrometric state of the air may be defined as the ratio of the elastic force of the vapour of water which it contains, to the elastic force of the vapour which it would contain, at the same temperature, if it were saturated. As a consequence of this second definition, it is important to observe, that when the temperature varies, the air may contain the same quantity of vapour, and yet not be in the same hygrometric state. Thus, when the temperature is elevated, the elastic force of the vapour which the air would contain in the state of saturation increases more rapidly than the elastic force of the vapour which actually exists in the air, and then the ratio of these forces, that is, the hygrometric state, becomes less. The weight of the vapour contained in a given volume of air may be deduced from its hygrometric state, as will be shown at the conclusion of this lesson. Hygrometric Instruments.—Instruments employed to determine the hygrometric state of the air, are called Hygrometers. Many instruments of this kind have been invented; but they may be classed under four principal kinds. Chemical hygrometers, absorption hygrometers, condensation hygrometers, and psychrometers. The latter kind is founded on the rapidity of the vaporisation of water in air. Chemical Hygrometers.-Every substance which possesses a great affinity for water is a chemical hygrometer. A substance of this kind, such as chloride of calcium, is introduced into a U-shaped tube; this tube is then put into communication with an exhauster, filled with water, like the vessel a, fig. 202. As soon as the water is allowed to run out of the exhauster, the air rushes into it, through the tube which contains the desiccating substance, and all the vapour which the air contains is absorbed by this substance. If, therefore, the tube and its contents be weighed both before and after the experiment, the increase of the latter weight gives the quantity of the vapour of water contained in a volume of air equal to that of the exhauster. From this weight, we can then deduce, by calculation, the hygrometric state of the air. This process is the most exact, but it is not sufficiently simple for meteorological observations. Absorption Hygrometers.-Organic substances which lengthen when they become humid, and shorten when they become dry, are called absorption hygrometers. Several hygrometers of this kind have been invented. The one most employed in practice, is that called the hair hygrometer or Saussure's hygrometer, from the name of the inventor. This instrument is composed of a brass frame, fig. 200, on which a hair e is stretched, after having been freed from its natural grease by immersion in water containing one-hundredth part of its weight of sub-carbonate of soda. If the hair be not thus purified, it will absorb very little vapour, and its lengthening will VOL. V. be very small; but when it is freed from all greasy matter, it rapidly lengthens in passing from a state of dryness to a state of humidity. The hair c is supported at its upper end by a catch a, fastened by a screw d. This catch is raised or lowered by means of a screw b, to which the nut is fixed. If the hair be knotted, a torsion will arise, which will render its lengthening irregular. At the lower end, it is wound on a pulley o, to which it is fixed. This pulley has two grooves, on one of which the hair is fastened; and on the other, in a direction contrary to that of the hair, is fixed a silk thread, which supports a small weight p. The axis of the pulley carries a small index, which moves over a graduated scale. When the hair is shortened, the traction which it exerts raises the index; when it lengthens, the weight p causes the index to descend. To graduate the scale, that point is marked 0° where at the ordinary temperature, the index stands in perfectly dry air; and that point is marked 100° where it stands in air completely saturated with vapour; the interval is then divided into 100 equal parts, which are the degrees of the hygrometer. The zero, or point of extreme dryness, is determined by placing the hygrometer under a bell-glass, in which the air is dried by enclosing with it substances having a great affinity for water, as chloride of calcium, or calcined carbonate of potassa. The air of the bell-glass loses its humidity, and consequently the hair shortens and causes the pulley and the index to move round, but very slowly. At the end of fifteen or twenty days only, does the index become stationary, which indicates that the air of the glass is completely dried. On the scale, 0° is then marked at the point where the index stands. The point of extreme humidity is obtained by removing the desiccating substances from the bell glass, and wetting its sides with distilled water. This liquid, by its vaporisation, soon saturates the air of the glass, and the hair rapidly lengthens. The small weight suspended by the silk thread, and wound on the pulley in a direction contrary to that of the hair, now causes the index to turn round in a direction opposite to that of zero. In less than two hours, it becomes stationary; and the point where the index stands, is marked 100°. According to Saussure, a hair stretched by a weight of about five grains is lengthened, between 0° and 100°, by of its length. Hair of a light or flaxen colour is that which lengthens in the most regular manner. The expansion which the hair undergoes by the variations of temperature are neglected, because it has been observed that for a difference of 33° Centigrade or 91°4 Fahrenheit, the lengthening of the hair does not alter the index more than of a degree on the hygrometer. This small expansion being omitted, it is observed that whatever may be the temperature, the index of the hygrometer returns exactly to 0° in air perfectly dry, and to 100° in saturated air. The fixity of the latter point shows that in saturated air, the air always absorbs the same quantity of water, whatever may be its tem. 117 TABLE OF HYGROMETRIC STATES OF THE AIR, TEMPERATURE OF 50° FAHRENHEIT. bulb A is about two-thirds full of ether, in which is immersed a small thermometer enclosed in the tube. The two bulbs and the tube are completely freed from air, by boiling the ether in sealing the latter, when the vapour of the ether has driven out the bulb a, while the bulb B is still open, and then hermetically all the air; thus the tube and the bulb B contain only the vapour of ether. The bulb is then covered with muslin, and ether is made to fall on it drop by drop. This liquid, by its evaporation, cools the bulb and condenses the vapour in its interior. The interior tension is then diminished, the ether of the bulb A immediately gives out new vapour, which is then condensed in the same manner in the other bulb; and so on. Now in proportion as the liquid is thus distilled fr m the lower bulb into the upper bulb, the ether in the former is cooled; and at the moment when the air, which is in contact with the bulb ▲, and which is cooled with it, reaches the temperature at which the vapour of the water contained in it is sufficient to saturate it, this vapour is condensed and deposited on the bulb, a, in the form of dew, a ring of it surrounding the surface of the liquid. It is there, in fact, that the cooling, arising from the evaporation, is especially produced. The interior thermometer, at this instant, indicates the temperature of the dew-point, that is, the temperature of the surrounding air. In order to obtain this point to a greater degree of approximation, we observe the temperature at the instant when the deposited vapour disappears on being again heated, and we take the mean between this temperature and that at which it was deposited. It is advisable, that during this experiment, the hygrometer should be placed in a current of air, as in an open window, so that the evaporation of the ether on the muslin may take place with greater rapidity. Lastly, in order to render the deposition of the dew more visible, the bulb A is commonly made of glass coloured black. As to the temperature of the air, it is noted by means of a thermometer placed on the stand of the apparatus. The hygrometer of Daniell having thus shown the temperature at which the A 0.257 0.500 air would be saturated, it is now required to deduce from it water. The tube E does not communicate with the exhauster; the hygrometric state of the air. For this purpose, we observe it contains only a thermometer intended to show the tempethat in a free space which contains a mixture of air and vapour rature of the air. Under this arrangement, some ether is at the atmospheric pressure, when the temperature is lowered, poured into the tube D, until it is about half-full, and then the elastic force of the vapour remains constant until the point the stop-cock of the exhauster is opened; the water in the of saturation. In fact, the elastic force of the mixture is equal latter escapes, and the air in the tube D is rarefied. In conto the sum of the elastic forces of each fluid, as formerly sequence of the atmospheric pressure, the air then enters by explained; now while the air is cooling, its tension remains the tube A; but as this air can only enter into the tube D and the same, for it increases as much by the diminution of its into the exhauster, by passing through the ether, it vaporises volume, as it decreases by the reduction of its temperature. a part of this liquid, and thus cools it sooner in proportion as The tension of the vapour must, therefore, also remain the flow is more rapid. When the process of cooling reaches invariable, since the elastic force of the mixture necessarily the point at which dew is deposited, as in the hygrometer of remains the same as that of the pressure of the atmosphere, Daniell, the thermometer T then indicates the corresponding after the process of cooling, as it was before. Consequently, temperature, and we have the elements necessary for deterwhen the air is cooled, the tension of the vapour which it con- mining the hygrometric state. In this instrument, the whole tains remains constant until the point of saturation; and at mass of ether is at the same temperature, in consequence of this point, this tension is the same as it was before the cooling the agitation of the current of air; besides, the observations commenced. According to this principle, if we look in the table are made at a distance by means of a telescope, and thus of elastic forces formerly given, p. for the tension f corre- every cause of error is avoided. sponding to the dew-point, this tension will be precisely that Hygroscopes.-Apparatus which merely indicate that there is possessed by the vapour of the water which is in the air at the more or less vapour of water in the air, without showing the moment of the experiment. If, therefore, we look in the same quantity, are called hygroscopes. They are constructed of table for the tension F of the vapour saturated, at the tempe- various sorts; the most in use are those made in the form of rature of the air, the quotient of the tension f divided by the little men whose heads are covered or uncovered with a hood, tension F will represent the hygrometric state of the air. For according as the air is more or less humid. These instruments example, the temperature of the air being 15 Centigrade, are constructed on the property which twisted cords and cat suppose that the thermometer of the bulb a marked 50 Centi- gut possess of untwisting by the action of humidity, and of grade at the moment when the dew was deposited; then look-twisting more by that of drought. Their indications are ing in the table of elastic forces p. 144 for tensions correspond- obtained by fixing to the figure a small piece of cat-gut by one ing to 5° and 15° Centigrade we find f equal to 0-257 inches of its extremities, and by attaching its other extremity to a and F equal to 0.500 inches, therefore =0.514, is the moveable piece. These hygroscopes are slow in their motions; that is, their indications are always behind the actual hygroratio of f to F, or the hygrometrie state of the air. The hygro- metric state of the air, and their sensibility is very small. meter of Daniell is liable to several causes of error: 1st, the The Psychrometer.-The psychrometer (cold measure, from the evaporation of the bulb A only cooling the liquid at the surface, Greek), invented by Professor August, enables us to ascertain the thermometer immersed in it cannot give exactly the tem- the tension of the vapour contained in the atmosphere, perature of the dew-point; 2nd, the observer standing near the dew-point, the point at which the atmosphere would be the apparatus, modifies the state of the surrounding air, as saturated, and the absolute weight of the vapour contained in well as the temperature. any particular volume of air. This instrument consists of two very delicate thermometers, whose degrees exactly correspond with each other, and are divided into fifths or tenths of degrees, the scales ranging from about -25° Centigrade or -13° Fahrenheit.o 40° Centigrade or 104° Fahrenheit. These thermometers are vertically fixed in a frame, at the distance of about three inches from each other. The bulb of the one is covered with muslin, which is kept continually moistened by means of a cotton thread attached to it, the other end of the thread being kept in a vessel or cup full of distilled water; the bulb of the other is kept dry. As the water imbibed by the muslin surrounding the one bulb evaporates, the mercury in the thermometer begins to sink, and the drier that the air is, the more rapid will be the evaporation, and the more sensible the descent of the mercury. When the air around the bulb is saturated with moisture, the mercury will become stationary, and the point at which it rests will be the dew-point or condensation-point. The greater that the difference is between the heights of the two thermometers, the more dry must be the state of the air, and the further is the vapour it contains from being at its maximum density. The difference between the heights of the two thermometers will be zero, if they are placed in an atmosphere containing aqueous vapour at its greatest density. From the degrees of heat shown by the two thermometers, the elastic force of the vapour in the air, and its amount per cent., can be determined. M. Regnault has invented a condensation hygrometer which avoids the causes of error in that of Daniell. This apparatus is composed of two thin polished silver cups of about two inches in height and one inch in diameter, fig. 202. Fig. 202. In these cups are Axed two glass tubes D and E. Each of them contains a very sensible thermometer fastened by means of a cork. The cork of the tube D, is traversed by a tube A open at both ends and immersed in the cup to the bottom. The tube is also put in communication, by means of the bottom of the stand and a leaden pipe, with an exhauster & full of The humidity or hygrometric state of the air varies at all hours, we might indeed say, at all minutes of the day. It is at its maximum before sun-rise, and at its minimum in the middle of the day. It varies in the different months of the year. In December, the air is the most humid; and in July and August, the most dry; yet, it can be proved that in these two latter months the air contains the greatest quantity of the vapour of water in consequence of the evaporation of the running and stagnant water on the earth's surface being more active. On the sea-coasts, the air, other things being equal, is more humid than in the interior of the continent. In the steppes, deserts, and pampas, the greatest known dryness prevails. On mountains, the air has sometimes an extraordinary dryness; but at a mean, it is more humid there than in the plains. The relative humidity varies with the wind; hence, we have dry winds and moist winds. In the middle of Germany, the driest wind is the east; the most humid, the north. These winds change their character in the different seasons of the year. In winter, the east is the most humid, and the west the driest. In summer, on the contrary, the west is the most humid, and the east the driest. These differences affect the temperature of the winds; the most humid are the coldest. LESSONS IN ALGEBRA.-No. XVII. (Continued from page 170.) SIMPLE EQUATIONS. TWO UNKNOWN QUANTITIES. In our former Lessons on Simple Equations, we gave the rules for solving those which contain only one unknown quality; and, with the exception of one or two, the whole Centenary of Problems were solved by means of these rules. We proceed now to show how to resolve equations which contain two unknown quantities. Cases indeed frequently occur, in which two unknown quan tities are necessarily introduced into the same calculation. Ex. Suppose the following equations are given, viz. :— (1.)x+y=14, (2.) x — y = 2, Here, if y be transposed in each, they will become 1.) x=14-y Now, the first member of each of the equations is x, and the second member of each is equal to x. But according to the Axiom that quantities which are respectively equal to another quantity, are equal to each other; therefore we have 2+y=14-y; whence, y = 6. Lastly, by substituting the value of y in the 1st equation, we have x+6=14; and ∞ = 8. Therefore, 8 and 6 are the values of x and y. In solving the preceding problem, it will be observed that we first found the value of the unknown quantity x, in each (quation; and then, by making one of the expressions denoting the value of x, equal to the other, we formed a new equation, which contained only the other unknown quantity y. This process is called extermination or elimination. In the resolution of equations, there are three methods of extermination, viz. by comparison, by substitution, and by addition and subtraction. Prob. 5. Given 4x the values of x and y. Prob. 6. Given 5x+8=7y, and 5y+32=7x; to find the values of x and y. Ans. 11 and 9. Prob. 7. To find two numbers such, that their sum shall be 24; and the greater shall be equal to five times the less. Here, let be the greater; and y the less. -2y= 20, and 4x+2y= 100; to find Ans. 15 and 20. From this equation, by separating the left hand member into Case I. To exterminate one of the two unknown quantities by factors, we have comparison. RULE.-Find the value of one of the unknown quantities in each of the equations, and form a new equation by making one of these values equal to the other. Find the value of the unknown quantity in this equation, by the rules formerly given. Then substitute this value of the one unknown quantity in either of the other equations, and resolving it by the same rules, the other unknown quantity will be found. Prob. 1. Given x+y= 36, and x values of x and y. Transposingy in the first equation, y= 12; to find the gives Transposing y in the second equation,,, Transposing, etc., Substituting the value of y, y x36 12y36 Hence, 24 and 12 are the values required. Prob. 3. Given 4x+y=43, and 5x+2y= 56; to find the values of x and y. Ans. 10 and 3. Prob. 4. Given 4x -2y= 16, and 6x 9y; to find the values of x and y. Ans. 6 and 4. The rule given above may be generally applied for the extermination of unknown quantities. But there are cases in which other methods will be found more expeditious. Prob. 10. Given hy, and ax + bxy2; to find the values of x and y. As in the first of these equations, x is equal to hy, we may in the second equation substitute this value of x for x itself. The second equation will then become, ahy + bhy = y2. The equality of the two sides is not affected by this alteration, because we only change one quantity z for another which is equal to it. By this means we obtain an equation which contains only one unknown quantity. Whence, y=ah bh, and x = ah2 + bh2. This process is called extermination by substitution. Case II. To exterminate an unknown quantity by su stitution. |