A cathetometer or vertical measurer, as the derivation from the Greek implies, is a brass scale divided into inches and fractions of an inch, placed upon a stand which is brought exactly into the vertical position by adjusting screws at the bottom. On this scale there is placed a sliding telescope sight, exactly at right angles to the vertical, which carries a vernier capable of measuring to fractions of an inch, each one hundredth part of the former. By fixing this telescope sight successively at the points A and B, as seen in the figure, we obtain by means of the graduated scale the exact distance between these two points. Now by loading the scale-pan with weights, and again measuring the distance between the points A and B, we ascertain the amount of elongation or extension arising from the traction of the weights. By experiments conducted in this manner, it has been found so long as the limit of elasticity has not been exceeded, that the traction or extension of rods and wires is regulated by the three following laws : 1st. Metal rods and wires have their elasticity of extension perfect; that is, they resume exactly their original length as soon as the force of traction ceases. 2nd. In the same substance, and having the same diameter, the extension or elongation is proportional to the force of traction and to the length. 3rd. In rods or wires of the same length and of the same material, but of unequal diameter, the extensions or elongations are in the inverse ratio of the squares of the diameters. Both calculation and experiment prove, that when bodies are extended by traction, their volume or bulk is increased. Elasticity of Torsion. The laws of the torsion of metal wires und threads of various substances were first ascertained by M. Coulomb, a French philosopher, who died in 1806. In his researches on this subject he employed an apparatus called the balance of torsion; this is composed of a fine metallic wire or thread, fastened to a stand at its upper extremity, and stretched vertically by a weight, to the centre of which is attached a horizontal pointer or index. Below this is placed a graduated circle or dial-plate, attached to the stand by a sliding piece and tangent-screw; the centre of this circle, which is exactly under the centre of the index, is so adjusted as to be exactly under the direction of the wire or thread produced when it is in the vertical position. Now, if the index be turned round, out of its position of equilibrium, by the amount of a certain angle, which is called the angle of torsion, the force necessary to put the index in this new position is called the force of torsion. When this turning round of the index takes place, the particles of the wire or thread which were before situated in the straight line parallel to its length or axis, are now situated in a spiral round it. If the limit of elasticity has not been exceeded, the particles have a tendency to return to their original position, and this tendency is verified by their actual return to it, as soon as the force of torsion is removed; but they do not remain in this position. For, in consequence of their acquired velocity, they pass this position, and produce torsion in à contrary direction; thus the equilibrium is again disturbed, and the wire revolving now on itself, the index does not point to zero on the dial-plate until after a certain number of oscillations on both sides of this point. By means of this apparatus Coulomb proved that when the amplitudes of the oscillations do not exceed a certain number of degrees, these oscillations are regulated by the following laws: 1st. They are very sensibly isochronous, that is, performed in equal times. 2nd. In the same wire the angle of torsion is proportional to the force of torsion. 3rd. In wires of the same diameter, and with the same force of torsion, the angle of torsion is proportional to their length. 4th. In wires of the same length, and with the same force, the angle of torsion is inversely proportional to the fourth powers of the diameters. Elasticity of Flexure.-All solids cut into thin laminæ or plates, and fixed at one of their extremities, when more or less bent from their natural position, return to that position as soon as the force which bent them is removed. This property is very evident in tempered steel, caoutchouc, wood, and paper. Certain bodies can be bent only at a very small angle, unless they be extended to a very great length, or be made extremely thin. For example, glass cannot be bent unless it be formed of very thin laminæ about a foot in length, or be reduced to a very fine thread. In the latter state it becomes so flexible, that it can be formed into waving plumes, or woven into cloth. Whatever may be the species of elasticity under consideration, as we have formerly remarked, there is always a limit to its action; that is, a degree of molecular displacement beyond which the elastic bodies are fractured, or rendered incapable of reassuming their original form. Owing to several causes, this limit is variable. For instance, the elasticity of several metals is increased by hardening them; that is, by bringing their particles more closely together, as in wire-drawing, plate-rolling, or hammering. Some substances, as steel, cast iron, glass, &c., become more elastic and at the same time harder by the process of tempering, which consists in cooling a metal suddenly after it has been raised to a high tempera ture. Elasticity, on the contrary, is diminished by the process of annealing, which consists in bringing bodies to a lower temperature than that required for tempering, and then slowly cooling them. It is by this process that the elasticity of springs is graduated at pleasure. In the operation of tempering, steel and cast iron acquire a great degree of hardness, and it is chiefly for this purpose that tempering is employed. All cutting instruments are made of tempered steel. But there are some bodies upon which tempering produces an entirely opposite effect. Thus the combination of metals called tam-tam, which is composed of one part of tin to four parts of copper, becomes ductile and malleable when it is suddenly cooled; on the contrary it becomes hard and brittle like glass when slowly cooled. Sulphur exhibits the same phenomenon; when cooled slowly, it is hard and brittle; but when cooled suddenly, it becomes soft and ductile like wax; but it does not continue in this state. Glass presents a curious phenomenon of tempering in what are called Dutch tears or Prince Rupert's drops, names given to small globules of glass, in the shape of tears, which in a state of fusion are dropped into cold water. Glass being a bad conductor of heat, the central parts of these globules are still in a state of fusion when the parts in contact with the water have become solid. From this, it follows that their molecular forces being unable to resume the state of stable equilibrium, the globules become so brittle that fracture at a single point of their surface is sufficient to make them burst in pieces with a loud noise, and at once fall into powder. As glass undergoes the real process of tempering when too suddenly cooled, the brittleness of newly-made articles is diminished by annealing. them over a fire, from which they are very slowly withdrawn. Tenacity is the resistance which bodies oppose to their extension by traction. In order to determine the amount of this force in different bodies, they are formed into cylindric or prismatic rods, and subjected, in the direction of their length, to the traction of a weight of so many pounds as are sufficient to determine the force of rupture or separation of their particles. Tenacity is directly proportional to the force which produces transverse section of the rods or prisms employed in resisting the rupture, and inversely proportional to the area of the the strain. According to numerous experiments upon metals,, the force necessary to produce rupture is nearly triple of that which corresponds to the limit of elasticity. Tenacity diminishes with the duration of traction. It is found that, after a certain period, metallic and other rods give way under smaller loads than those which would produce immediate rupture; and in all cases, the resistance of bodies to traction is less than their resistance to pressure. Tenacity varies not only in different bodies, but also in those which are composed of the same matter, and in equal quantity according to their difference in form. In rods of equal sectional area, the prismatic form possesses less power of resistance than the cylindric. In a given quantity of matter, the hollow cylinder possesses a greater power of resistance than the solid cylinder; and the maximum of tenacity in the former takes place when the outer diameter is to the inner one in the ratio of 11 to 5. In the same body, the form has the same influence on the resistance to pressure that it has on the resistance to traction. Hence, a hollow cylinder, of equal matter and altitude, has a greater power of resistance to pressure than a solid one; whence it follows that the bones of animals, the feathers of birds, the stalks of grass and of a great number of plants, being hollow, present a greater resistance to rupture by pressure or traction than if they were solid, the mass of matter being the same. Woods,* Box....... Teak Fir American Pine.. num. Ductility. This is a property which many bodies possess, and it consists in their power to change their form under various degrees of pressure or traction. In some bodies, as clay and wax, a very slight force is sufficient to produce a change in their form; in others, as glass and rosin, it is necessary to add heat; but in metals, strong force is required, as in hammering, wiredenominated malleability when it is produced by the operation drawing, and laminating or reducing to plates. Ductility is of the hammer. The most malleable metal is lead; the most ductile in laminating is gold; and in wire-drawing, is platiproduce wires of this metal not exceeding the thirty-thouThe great ductility of platinum enabled Wallaston to sandth part of an inch in diameter. This was effected by covering a platinum wire of about one-hundredth of an inch in diameter with a coating of silver until the diameter of the compound wire was about of an inch in thickness; then by drawing this wire until its diameter was as fine as possible, the two metals were equally extended by the process; and lastly, by dipping the wire in nitric acid, the silver was dissolved and the platinum wire remained, exhibiting the extraordinary degree of fineness above mentioned. A thousand yards of this wire would weigh only about three-quarters of a grain; and a quantity equal in bulk to a common die would reach from London to Vienna. Tenacity, as well as elasticity, varies in the same body according to the direction in which force is applied. In wood, for example, the tenacity and elasticity are greater in the direction of the fibres than in any crossing direction. This difference is, in general, manifested in all bodies whose contexture is not the same in all directions. Yet M. Savart discovered, by means of ingenious experiments on the sonorous vibrations of bodies, that a difference in this respect existed in a number of bodies whose contexture was completely homogeneous; such as zinc, lead, brass, glass, resinous bodies, &c. He also discovered this difference in certain directions perpendicular to each other, which he called axes of stronger and weaker elasticity. M. Savart attributed this modification of these properties to a symmetrical arrangement which the particles of bodies tend always to assume when they are slowly cooled. It is of the greatest importance, in the arts of construction, to take into consideration the limits of the tenacity and compressibility of materials. In suspension-bridges, for instance, the stability of the structure chiefly depends on the tenacity of the rc is which support the road-way. The follow-bodies, but cannot be scratched by any. After the diamond ing table exhibits the weights in tons on the square inch which certain bodies can support in vertical traction before rupture, or in other words, the limit of direct cohesion or tenacity. Hardness.-This property of matter is the resistance which bodies present to scratching or abrasion by other bodies. This property is only relative, that is, a substance may be hard with reference to one body and soft with regard to another. The relative hardness then consists in this, that one body can be made to scratch or abrade another without being itself capable of being scratched or abraded by the other. The hardest of all bodies is the diamond, for it will scratch all in hardness follow the sapphire, the ruby, the rock-crystal, the flint, the stone, &c. Metals in a state of purity are generally soft. Lead can be scratched with the nail. The processes which increase their elasticity also increase their hardness; such as tempering, annealing, &c. Alloys or mixtures are harder than metals. Thus in jewellery and in coining, the hardness of gold and silver is increased by alloying them with copper. The hardness of bodies does not increase in proportion to their resistance to pressure. Glass and the diamond are much harder than wood, but they present less resistance to the blow of a hammer. The hardness of bodies is usefully employed in polishing-powders, such as emery, pumice-stone, and tripoli. The diamond, which is the hardest of all bodies, can only be ground or polished by means of a powder which is merely pulverized diamond. CASE-HARDENING is a process by which the surface of articles made of wrought iron is converted into steel. The articles to be case-hardened having been prepared in wrought iron, they are placed in an iron box in layers, in order to receive that degree of hardening on the surface which will prepare them for receiving a final polish. A layer of animal carbon (horns, hoofs, skins, or leather), at first so burned as to be capable of reduction to powder, is spread over each; the box, then carefully covered and luted with an equal mixture of clay and sand, is kept at a slight heat for half an hour, and its contents are then emptied into water. By this means, a surface of hardened steel is obtained over the whole of the article, of a thickness depending on the duration of the time in which heat has been applied. This process is particularly applicable to articles wanting external hardness and polish, as fire-irons; but it is not applicable to cutting instruments. *In the direction of their fibres. Pronounced. keeáh-ro keeái-zah English. Guelfo gwêl-fo Clear, bright Church Guida gwée-dah keeô-do Nail, I nail Seguo sê-gwo Inclosed, inclosure Quasi kwáh-zee Plump, fat Banker tahrr-keeáh-to bahn-keeê-rai Melchior The vowel i before e, when both follow the consonant c, are pronounced as though the i was not there, and the whole combination only ce. The same remark, however, made with regard to the combinations cia, cio, and ci-that in a more measured enunciation the vowel in these cases is slightly touchedholds good here also. The observation just made in the foregoing note with respect to cie is strictly applicable to the syllable gie. It is always pronounced as though the i was not there; unless slightly touched in measured pronunciation. No observation has yet been made in reference to the pronunciation of the double c (cc). This depends, as well as the pronunciation of double g (gg), on the vowel that follows the latter c. If that vowel is a, o, or u, the cc is sounded like a double k (kk) or ck. For example, bocca (bók-kah), mouth; becco (bêk-ko), beak accusare (ahk-koo-záh-rai), to accuse. If, however, that vowel which follows the latter c is e ori, the double c (cc) is sounded Igrin, grinding the teeth something like tch in the English word match, only perhaps stronger, and with vibration. On that account, I have tried to imitate the stronger sound of the cc by the letters ttch, placing the first t in the first syllable, and tch at the beginning of the second, just as I have attempted to imitate the sound of the gg by placing d in one syllable, and at the beginning of the next, in such words as paggi (páhd-jee), pages, attendants. The remark with respect to the pronunciation of the gg, however, holds good of cc; the voice must not pause too long on the t of the syllable where the first c occurs, and glide as quickly as possible to the pronunciation of the second c, which must be very much vibrated. In this way * I have explained the combination chi to be sounded like kee. When one of the five vowels follows this syllable, it is so intimately blended with the following vowel, that a kind of squeezed sound of CHI is the result, the voice sliding, as it were, from CHI to the next vowel with great rapidity. + The remark made with respect to the syllable chi, followed by any of the five vowels, is equally applicable to the syllable ghi followed by a vowel: here, likewise, the syllable ghê is, a more equal distribution of the sound tch between the two sylla as it were, squeezed, and the voice must slide into the pronunciables will be effected, which will produce the correct sound of tion of the vowels that follow ghi with great rapidity. the cc; and my imitation of that sound by ttch has no other object † The double zz, as well as the single z, may have the mild than to indicate to the reader the necessity of giving a stronger sound of the word adze (with which, by-the-bye, the ds in the word vibration to the cc. It is obvious that when cc is followed by conWindsor corresponds), or the hard sound of te in Switzerland. sonants, it must be pronounced like k, just as the single c in the According to modern orthography, the letter z is generally doubled like case must be so pronounced. For example, acclamare (ahkin the middle of words between two vowels, and the pronunciation klah-máh-rai), to elect by acclamation, to applaud; accrescere (ahkof this zz scarcely differs from that of the single z. However, krái-shai-rai), to increase, &c. When between the cc and the before diphthongs,-as, for example, ia, ie, and to,-2 must remain vowels e or the letter h is interposed, the cc is also sounded like k, single, and has always, in such a case, the sharp sound. For as well as the single c in such cases and for the same reasons, the example, ringraziare (rin-grah-tsecah-rai), to thank; pigrizia (pee-h being a mere auxiliary letter to indicate that a before e and i is grée-tseeah), idleness; inezie (ee-ne-tseeai), follies; Bonifuzio (Bonee-fáh-tseeo), Boniface. not to have the sound of itch, but of kk, as in chicchera (kík-kai-rah), a tea-cup; chiacchiera (keeáhk-keeai-rah), chit-chat. *This is the first occurrence in these lessons of the important combination gl. It has two different sounds. When it is not followed by the letter i it has the sound of gl in gland, glebe, glory, glue; and this sound can offer no difficulty. But when the combination gl is followed by the letter i and one of the vowels a, e, o, and u, it is pronounced precisely as the double (77) in the French words bouilli, fille, gresiller, grenouille, bouillon, billard, billet, brouillon, feuillu, and, generally speaking, in all those words where the W has after the vowel i a squeezed sound in the French language. They who are unacquainted with French may form a notion of this sound by separating and inverting the gl in the enunciation, i.c., by pronouncing before the g, and changing the latter into y. Only the first 7 must go to one syllable, and the second l along with the y, and with a squeezed sound to the beginning of the next, while care must be taken that the voice should glide rapidly from one syllable to the other, by which means a more equal distribution of the squeezed sound lly will be produced, and a correct pronunciation of the gl effected. An approximation to this sound may be found in the English words million, miliary, biliary, billiards, seraglio, intaglio, and oglio. The letter i, between the combination gl and the vowels a, e, o, and u, is (as well as in the combinations cia, cio, ciu, and gia, go, giu) a mere auxiliary letter, i.e., a mere soundless, written sign, to indicate that gl before a, e, o, and u is not to have the sound of gl in gland, glebe, glory, and glue, but that squeezed sound, the imitation and description of which I have here attempted. For example: vaglio (váhl-lyo), a sieve; meglio (mêl-lyo), better; Figlio (píl-lyo), I take, seize; miscuglio (mis-kóol-lyo), mixture; svegliare (zvel-lyáh-rai), to awake; togliere (tôl-lyai-rai), to take away; scegliere (shél-lyai-rai), to choose; doglia (dôl·lyah), sorrows; bigliardo (cil-lyáhrr-do), billiards; biglietto (bil-lyét-to), note, bill; imbroglione (im-brol-lyó-nai), a meddling fellow; fogliuto (fol-lyoóto), full of leaves. Egli, he, egiino, they, quegli, that one, gli (the plural of the article or the pronoun), with its numerous compositions, and gli, the final inflexion or terminational syllable of nouns and verbs, have always the squeezed sound lyee; while the mere Arllable gli, at the commencement and in the middle of words, always has the sound of gl in gland, glebe, &c. The only exception is Angli, Englishmen, pronounced áhn-glee. For example: figli (fil-lyee), sons; fogli (fôl-lyce). leaves of paper; gigli (jí-lyee), lilies: negligere (nai-gleé-jai-rai), to neglect; negligente (naiglee-jên-te), negligent; negligenza (nai-glee-jên-tsah), negligence; regligentare (nai-glee-jer-táh-rai), to neglect. ANSWERS TO CORRESPONDENTS. CIVIS (Dublin): We recommend him to take up Part I. of the French Lessons from the P. E. to follow the Lessons from the W. M. F. Part II. of the former will be ready in about three weeks.-AMBITION (Copthallcourt) will see the studies that it will be necessary for him to take up if he wishes to matriculate at the University of London, in vol. ii. of the P. E., p. 137. EIPSELLIG (Leicester): Right-CARMONEY (Belfast) will see by the solution we have inserted that his is wrong. Thanks for his other communications.-SPEUDE BRADEOS (Fetter-lane): His conjecture about the Greek extract is right; but that about the Greek lesson is wrong. There is a very considerable difference between the ancient and the modern Greek. We believe that old Homer would not be understood in his own country.-J. MILLS (Tewkesbury): His poetry is good, but not -sufficiently measured; that is, put into the proper number of syllables in each line; some lines have ten syllables, some twelve, and so on. Were we to correct it, we would begin thus: Ah, dost thou gaze upon that little child, With which earth teems throughout her wide domain. That all the powers of Mathematic lore A. RICHARDSON (Newcastle) and E. EVANS (Ashby-de-la-Zouch): We regret that we cannot give them the information they require.-W. X. (Manchester) and PARALLAX: We advise them to write to Messrs. Watkins and Hill, 5, Charing-cross, London, who will furnish them with a catalogue of their telescopes, achromatic and reflecting, with their sizes, powers, and prices. They can also have information from the same firm about magic lanterns, sliders, and diagrams or atlases of the heavens. C. B. C. (Hull) must study our Lessons in Penmanship, vol. ii., P. E.T. MUXLOW (Sheffield): Get an old copy of Barrow's Euclid (which you may at any old book-stall for is.), and you will see all the books of Euclid from the 1st to the 15th inclusive.--W. HADFIELD (Hayfield): We know of no paper in which excise vacancies are advertised.-W. J. OSBORNE (Soho): ive think that the courtesy is due to any clergyman who does not wish his sermon taken down in short-hand, to refrain from so doing; he is the best judge of the value of his own productions.-J. ADDER (Grandtully): The rule for finding the index of the quotient is this: Subtract the index of the dividend from that of the divisor, and the remainder is the index of the tion for finding the greatest common measure, there can be no difficulty at quotient; now this being done for the first term in every step of the operathe end, for the remainder will take the indices of its terms from those which correspond to them in the dividend, supposing them, of course, to be in arithmetical progression proceeding from that of the first term. T. TAIT (Glasgow) should attend to the directions given in No. 36, vol; ii.-N. P. P. should apply to the superintendent of the docks where he wishes to be admitted.-W. R. E. (Gray's-inn-road) and A SUBSCRIBER are informed that Mr. Cassell has published the very book they want," The People's Biographical Dictionary," compiled by Dr. Beard, and that it may the P. E. Lord Byron swam the Hellespont. Don't bind the "Magazine of be had at this office for 2s. 4d. in paper covers. The Atlas is progressing in Art," or any other periodical, too soon; sell your copy and buy another, taking more care next time.-J. BEWLEY (Langrigg): His verses are very good, but not up to our mark.-A TROUBLESOME SUBSCRIBER will find an article on shell-cleaning in the P. E. "Latin wards," col. 2, p. 288, vol. ii., should be "Latin words" certainly.-STUDENT OF ANGLESEA: In the pas sage "si cupis placere magistro," the "si" means only if; "cupis" means you desire, as shown by the termination "is;" ing to the Latin idiom, requires the dative "magistro," to the master, to placere," to please, accordfollow it; but we cannot literally say in English, to please to the master; yet, as to please means to give pleasure, we can say to give pleasure to the the body; but the neglect of washing the body, which is a great sin, master. Death would be the consequence of the stopping up the pores of besides being a great evil, is compensated for, in strong and healthy persons, by copious and heavy perspiration, which literally washes the body itself, be long continued with impunity.-CHEMICUS (Falkirk): Mr. Cassell is and clears the pores for a time. Still this is an unhealthy state, and cannot about to publish a work on Botany. LITERARY NOTICES. GERMAN. CASSELL'S GERMAN PRONOUNCING DICTIONARY, in Nunbers, 3d. each, or Parts, ls. each. The entire work will be issued at 8s. 6d. in strong binding. Cassell's LFSSONS IN GERMAN. Part I., price 2s. in paper covers, or 2s. 6d neat cloth. Part II. will shortly appear. CASSELL'S LESSONS IN GERMAN PRONUNCIATION. Price 1s. 6d. in paper covers, or 2s. neat cloth, will shortly be issued. CASSELL'S ECLECTIC GERMAN READER, price 2s. in paper covers, or 2s. 6d. neat cloth. CASSELL'S ELEMENTS OF ARITHMETIC (uniform with Cassell's EUCLID) is now ready, price Is. in stifl' covers, or Is. 6d, neat cloth.—KEY, 3d. ON PHYSICS OR NATURAL PHILOSOPHY— No. VIII. HYDROSTATICS. The Science of Liquids at Rest.-Hydrostatics is that part of natural philosophy which has for its object the investigation of the conditions of equilibrium in liquids, and of the pressures which they produce, either in mass, or on the sides of the vessels which contain them. The science which treats of the motion of liquids is called Hydrodynamics; and the application of its principles to the art of conveying and raising water is particularly denominated Hydraulics. This plate is furnished with a funnel-pipe at B, by which tae water is admitted into the cylinder, and with an air-tight pump-body and piston, the latter being moved up or down by means of a screw P. In the interior of the apparatus is contained a glass reservoir A, filled with the liquid whose compressibility is to be ascertained. This reservoir terminates in a bent capillary tube, the lower end of which is immersed in a mercurial bath at o. This tube is previously divided into parts of equal capacity, it having been ascertained how many of these parts the reservoir a contains; this is found by determining the weight P of the mercury contained in the reservoir A, and the weight p of the mercury contained in a certain number n of the divisions of the capillary tube; then, denotGeneral Character of Liquids. It has been already stated ing the number of the divisions of the small tube contained in the reservoir by N, we have the following proportion p : P :: p: that liquids are bodies of which the particles, in consequence: N; whence, the value of N can be easily deduced. of their extreme mobility, yield to the slightest effort made to displace them. Their fluidity, however, is not perfect; for among their particles there always exists an adherence which constitutes a greater or less degree of viscosity (stickiness). The fluidity of liquids is manifest, but in a higher degree, in the gases; the distinction between liquids and gases being, that the former possess the property of compressibility in a very slight degree, whereas the latter are highly compressible and elastic. The fluidity of liquids is shown by the facility with which they take all kinds of shapes; their small compressibility is proved by the following experiment. Compressibility of Liquids.—Subsequently to the experiment of the academicians of Florence formerly mentioned, liquids were for a long time considered to be incompressible. Afterwards, experiments were made on this subject, in England by Canton in 1761, and by Perkins in 1819; at Copenhagen, by Ersted in 1823, and again by Colladon and Sturm in 1827. From these various experiments, it has been concluded as a fact that liquids are really compressible. The apparatus employed in measuring the compressibility of liquids are called Picsometers, that is (from the Greek), Pressure-measurers. The following is a description of that of Ersted, with the improvements of M. Despretz. This piesometer, fig. 19, is composed of a very strong glass cylinder, about 33 inches Fig. 19. In the interior of the cylinder is contained a Manometer (rarity measurer) of compressed air. This is a glass tube B, closed at the upper extremity, and open at the lower extreWhen mity, which is also immersed in the mercurial bath o. the tube B is completely full of air; but when pressure is no pressure is applied to the water which fills the cylinder, applied to the water in the cylinder, by means of the screw P and the piston to which it is attached, this pressure is com municated to the mercury, which then rises in the tube в by compressing the air contained in it. A graduated scale c, placed alongside of the tube, indicates the quantity by which the volume of air is diminished; it is by means of the quantity of diminution in the volume of air that the pressure on the liquid contained in the cylinder is determined, as will be afterwards shown. In making experiments with this apparatus, the reservoir A is first filled with the liquid whose compressibility is to be found; the cylinder is then filled with water by means of the funnel-pipe R. The screw P is then turned so as to make the piston descend and produce a pressure on the water and the mercury contained in the cylinder; this pressure not only raises the mercury in the tube B, but also in the capillary tube fastened to the reservoir A, as shown in the figure. The rise of the mercury in the capillary tube shows that the liquid contained in the reservoir has diminished in volume the measure of its diminution being indicated on the tube itself, as above mentioned. In his experiments, Ersted supposed that the capacity of the reservoir remained invariable, and that the sides of it were equally acted upon by the liquid both in the interior and on the exterior. Mathematical investigation has proved that this capacity is diminished by both pressures. In their experiments, Colladon and Sturm took this change of capacity into account; and they have proved that for a pressure equal to that of the atmosphere, and at the temperature of 32° Fahrenheit, the parts of the original volume by which certain liquids were contracted, are as follows: They also observed that in the case of water and mercury, within certain limits, the diminution of volume is proportional to the pressure. Principle of Equality of Pressure.-On the supposition that liquids are incompressible and possess perfect fluidity, and are freed from the action of gravity, the following principle, called the principle of equality of pressure in every direction, universally holds good: liquids communicate in all directions, with the same intensity, the pressures applied to any point of their mass. This principle was first announced to the world by the celebrated Pascal, who died in 1662, and is sometimes called the principle of Pascal. In order to have a proper idea of this principle, suppose a vessel, fig. 20, of any shape whatever, to be filled with water, aud that in its sides at different places cylindrical openings A, B, C, D, and E are made, to which there are applied moveable pistons exactly fitting them. If to any, piston a, an external pressure be applied, say of 20 pounds this pressure is instar taneously communicated to the internal surfaces of the pistons 85 |