ON PHYSICS OR NATURAL PHILOSOPHY. No. IX. ON THE EQUILIBRIUM OF LIQUIDS. Equilibrium of a Liquid in a single Vessel.-In order that a liquid should remain in equilibrium in a vessel of any shape, the two following conditions are necessary: lat. Its surface at every point must be perpendicular to the direction of the force which attracts the particles of the liquid. 2nd. Every particle of the mass must in all directions be under the aetion of equal and contrary forces The first condition has already been considered, when treating of the influence of gravity on the direction of the free surface of a liquid. The second condition is self-evident; for, if the pressures which urged a particle in two opposite directions were not equal and contrary, it would be urged in the direction of the greater pressure, and the equilibrium would be destroyed, seeing that motion would ensue. This condition is, besides, a consequence of the principle of the equality of the pressure and reaction which every force produces when applied to a liquid. The Equilibrium of a Liquid in Vessels which communicate with one another.-When several vessels of different forms contain the same liquid and communicate with one another, equilibrium can only take place in each vessel when the preceding conditions are satisfied, and when the free surfaces of this liquid in all the veshols are situated in the same horizontal plane. Thus, let the different vessels in fig. 27, communicate with each other, and be potassa, alcohol coloured red, and oil of naphtha. When the via is shaken, the four liquids are mixed together; but when it is at rest, the mercury, which is the densest, sinks to the bottom; then above the mercury, the water will place itself; above the water, the alcohol; and above the alcohol, the oil of naphtha. Such is The water in this experiment is saturated with carbonate of the order of these bodies according to their decreasing densities. potassa, in order that it may not be mixed with the alcohol, in which this salt is not soluble. The separation of the liquids in the preceding experiment, is referable to the same cause which makes solid bodies immersed in a liquid more dense than they are, rise and float on its surface. In consequence of this principle of hydrostatics, we find that the fresh waters at the mouths of rivers float to a considerable distance above the salt water of the ocean into which they fall. For the same reason, cream, which is lighter than milk, separates from the latter by degrees and is found floating on its surface. Equilibrium of two Heterogeneous Liquids, in two Vessels which communicate with each other. When two liquids of different contained in two communicating vessels, to the conditions of densities, and incapable of chemical action on each other, are equilibrium already stated, must be added the following: that the heights of the columns of the liquids which are in equilibrium, are in the inverse ratio of their densities. In order to prove this principle by experiment, we take a bent tube, fix it on a board placed vertically, fig. 28, and pour mercury filled to a certain height with water; and suppose that a vertical layer of the liquid in the tube of communication is under our consideration. This layer cannot remain in equilibrium unless the pressures which act upon it in the directions from M towards N, and from N towards M, are equal and contrary. But we have seen in our last lesson, that these pressures are equivalent to the weight of a column of water which has for its base the layer under consideration, and for height the vertical distance of its centre of gravity from the surface of the liquid. Now if we suppose a horizontal plane M N drawn through this centre of gravity, it is plain that the equilibrium cannot take place unless the height of the liquid above this plane is the same in each vessel; therefore, the surface of the water in the different vessels must be in the same horizontal plane. into it; we then pour water into one of the branches of the tube. Now, the column of water A B pressing on the mercury at B, the level of the mercury in the tube is lowered in the branch a B, and raised in the other branch by a quantity CD; when the equilibrium takes place, if we suppose a horizontal plane B C to pass through the point в, then the column of water AB balances the column of mercury CD. Measuring the altitudes CD and a B, by means of two equally graduated scales fixed to each vertical branch of the tube, we find that the ratio of A B to CD is 13 to 1. Hence, we infer that the density of mercury is 13 times that of water; consequently the altitudes of the columns of mercury and water, above the horizontal plane, are to one another in the inverse ratio of their densities. The reason of this is plain; for as the pressures on the same horizontal plane RC are the same, the equilibrium can only be established by any column gaining in altitude what is lost in density. The preceding principle may be deduced from a very simple calculation. Let d and d be the densities of water and mercury respectively; and let h and h' be the altitudes of the columns of these liquids respectively, when they are in a state of equilibrium; and let g denote the intensity of gravity. The pressure at B, being proportional to the density of the liquid above it, to Equilibrium of Supernatant Liquids.-When several hetero- its height, and to the intensity of gravity, has for its measure the geneous liquids float above one another in the same vessel, stable product dh.g. For the same reason, the pressure at c has for its equilibrium cannot take place, unless each satisfies the conditions measure the product d'h' g. But in a state of equilibrium these already stated regarding a single liquid; and, in addition to this, pressures are equal; therefore, we have dhga'h'g; whence, unless the liquids are arranged above each other in the order of suppressing the common factor g, we have dh d'h', or d : ď their densities, that is, diminishing in their densities upwards.::h':h; which is the algebraic expression of the principle to be This condition is clearly proved by the experiment with the vial proved. of the four elements. This name is given to a long and narrow This hydrostatic principle may be employed in determining vial containing mercury, water saturated with carbonate of the density of a liquid. Thus, supposing that one of the branches VOL. IV. 87 of the tube in fig. 28, contained water, and the other ether, the respective altitudes of the liquid columns, when they balance each other, are to one another as 7 of ether to 5 of water, or as 1 to 714; whence, if the density of water be taken as unity, the density of ether is '714; and so of other liquids. APPLICATIONS OF. THE PRECEDING HYDROSTATIC PRINCIPLES. The Hydraulic Press. The principle of the quaquaversal pressure of liquids. was applied in a very important manner in the invention of the Hydraulic Press. The principle was, as we have seen, discovered by Pascal, but was first applied by Bramah. to this invention, at London, in 1796; hence, it is frequently called Bramah's press. This apparatus, by means of which enormous pressure can be produced, is composed of two cylinders or pumps A and B, fig. 29, communicating with each other, the one of very compressed by the press. The orifice o is intended, by means of a stop-cock below, to withdraw the water from the apparatus when the pressure is to be removed. Now, in consequence of the quaquaversal principle, the downward pressure of the piston A is communicated upwards to the piston B, with a force proportional to the surface of the latter, as compared with that of the former. Thus, if the surface of the piston в be 10 or 20 times greater than that of the piston a, the pressure communicated to the piston B will be 10 or 20 times greater than that of the piston A. From the piston B, the pressure is communicated by the piston-rod to the body M, which is thus compressed between the moveable plate, raised by this piston, and the fixed plate D. The figure represents a model of the hydraulic press, intended for the illustration of the principle of operation. The pump cylinders are made of glass, in order to render the action of the apparatus visible. But in actual practice, all diameter and the other of large diameter. In the small cylinder, a piston is made to move up and down by means of a lever; in its ascent, this piston draws water from the reservoir H, and thus the lower part of the body of this pump is filled. In the descent of the same piston, a valve fixed on the orifice of the pipe H, at the bottom of the body of the pump, is closed; the water driven back by the piston is forced into the body of the large pump, by a pipe communicating between the two pumps (shown in the figure by dotted lines), and terminating in a valve opening upwards. Whenever a fresh quantity of water is forced to the body of the pump B, this valve is opened; but it is Fig. 30. the cylinders of the pumps are made of strong cast-iron, on account of their being frequently subjected to enormous pressures. It is necessary also that the difference of the diameters of the cylinders be much more than that exhibited in the figure, for on this depends the great power of the machine. In some applications of the hydraulic press, pressures amounting to that of 100,000 pounds on the base of the larger piston, are frequently employed. This remarkable invention is in constant use in all cases where very great pressure is required, and where time is not an immediate object; as in packing goods, extracting juices, oils, &c. It is ends with two short tubes of glass at D and E, fig. 30. In using this apparatus it is placed horizontally on a three-legged stand or support, with the bent ends turned upwards, and coloured water is poured into the tube till it rises to a certain height in both ends in the glass tubes. As soon as the water is at rest, its level, that is, the surface of the water in these tubes, is the same; or in other words, a horizontal plane will pass through the two surfaces of the water at D and E. This instrument is employed in taking levels in surveying, that is, in determining how much one point on the ground is more elevated than another. Thus, if it were required to find how much the point в on the ground is above another point a, we place a graduated levelling staff at the point A. In the present instance, this staff is formed of two vertical wooden rods, sliding on each other in a groove, and terminated at the top by a piece of tin м, which has a mark in the middle of it. This staff being adjusted vertically at A, an observer at the level at D, directs his sight along the surface of the water at D and E, to the staff, and makes signs to his assistant who holds it, to lengthen or shorten it, until the central mark м be found in the continuation of the horizontal line D E. By measuring then the height a M, and subtracting from it the height of the level above the ground, the observer ascertains at once the difference of level between A and B, that is, how much the point B is above the point a. The following enlarged view of the water-level and levelling staff, with their adjusting apparatus, will give our students a better idea of these instruments. The figures F and G F. ing the instrument to the practice of levelling. We have seen that the differences in the vertical distances on the staff show the differences of the levels; now by the addition of these consecutive distances when the ground is ascending, and by their subtraction when it is descending, we ascertain the respective positions of any number of points on the ground with reference to any assumed horizontal plane. The level found by this instrument is only the apparent level, that is, the level which corresponds to the points contained in a plane touching the surface of the globe, supposing it perfectly spherical. The true level is that which corresponds to points equally distant from the centre of the earth. In the case of short distances, the apparent level may be taken for the true level; at the distance of one mile, the difference between them is only 8 inches; the general approximate rule for finding the difference of level between two points on the earth's surface being to square their distance in miles, and take two-thirds of this square for their difference of level in feet. Air-Level. The air-level is more sensible and more accurate than the water-level. It consists of a tube of glass, fig. 31, very than the water-level. It consists of a tube of glass, fig. 31, very slightly curved, filled with water, hermetically sealed at both ends, and containing a small bubble of air which tends always to occupy the most elevated part of it. This tube is enclosed in a metal case C D, and fixed lengthwise on a stand, which is so carefully adjusted, that when at rest on a horizontal plane, the air-bubble M is always found in the middle between two points marked on the case; and part of the case is left open, so that the oscillations of the air-bubble may be observed until it finally settles in the true horizontal position. In taking levels with this instrument, a telescope is fixed on it for the more accurate determination of the horizontal positions. The following figure L shows the H. G. I. show the level and its support, H and I two different forms of the levelling staff, The following figure K shows the mode of apply K: mode of adjusting the telescope' to the level, and the mode of bringing the air bubble to the centre of the level, and under the middle of the telescope, by means of adjusting screws. The Slope-Level, N, invented by M. Chézy, is adjusted in a similar manner. But on the right of the figure there is placed a small hole intended for the eye-piece; and on the left, a moveable sight with diaphragm, for the more accurate determination of the slopeline. To this sight there is attached a graduated vertical scale, for ascertaining the degree of the slope or inclination of any line measured on the ground, at so many inches or fractions of an | greater or less extent, below which are found two strata imperinch per yard. The stand or support for this instrument, o, is N. used also in the air-level, and similar instruments employed in surveying. 0. meable to water, as A A and BB, and having between them a permeable stratum M M. Suppose also, that the latter communicates with a more elevated stratum, through which rain water passes. This water, following the natural declivity of the ground along the permeable stratum, is found below the topographical basin which we have supposed to exist, without being able to communicate with it, in consequence of the interposition of the impermeable stratum A A. But if, in the surface of the ground, we sink a shaft which goes through this stratum, then the waters, which seek always to find their level, will rise in this shaft to greater or less height, in Fig. 32. Fountains and Artesian Wells.-Lakes, seas, fountains and rivers, are so many vessels communicating with each other, in which the waters are incessantly endeavouring to find a new level. To these may be added Artesian wells, so called because they were first discovered in the province of Artois in France. The origin of some of these wells goes back to the end of the twelfth century. At a period much earlier than that just mentioned, wells of this kind were constructed in China and Egypt. These wells are very narrow shafts sunk in the ground and of very variable depths. Their waters are generally of the nature of a continued spring or fountain. Their theory is the following: the strata of which the exterior covering of the earth is composed, are chiefly of two kinds; the one permeable to water, as sand and gravel; and the other impermeable, as clay, &c. Now, suppose that fig. 32 represents a local valley or topographical basin of LESSONS IN GREEK.-No. XIV. By JOHN R. BEARD, D.D. COMPARISON OF ADJECTIVES. Superlative (from super, above, beyond, and latus, carried) is in grammar applied to adjectives when they are in that form which signifies the greatest degree or amount of the quality described by them. The degree below, or an inferior degree of the quality, is called the comparative; and the simple state of the adjective is named the positive; thus sweet is the positive, sweet-er the comparative, and sweet-est the superlative. The Greek language has two forms of comparison. The first, and by far the most common, adds to the positive repos, τερά, τερον for the comparative, and τατος, τατη, τατον for the superlative; the second adds for the comparative iwv, īov, proportion as they communicate with a stratum of greater or less elevation. The water which supplies the Artesian wells often comes from the distance of 60 or 100 miles. Their depth varies with the localities in which they are found. The Artesian well of Grenelle in Paris, is 1,794 feet deep, and the temperature of its water is82° Fahrenheit. It yields about 660 Imperial gallons of water per minute, being one of the most abundant in supply, and oneof the deepest which have hitherto been sunk, though surpassed by that of Mondorf in Prussia, the depth of which is 2,202 feet, and the temperature of its water 93° Fahrenheit. According to the law of the increase of temperature in the terrestrial strata, it would be necessary that the depth of an Artesian well should be about 500 feet, in order that its water should be, during the whole year, of the temperature of our common baths, viz. 90o Fahrenheit, or blood-heat. Most of the adjectives of this class add the forms of or wy, oy, and for the superlative ros, corn, lotov. The ter-comparison to the stem by means of the connecting vowel • Οι ω. The connecting vowel is o when a long syllable | Ινδος, ου, ό, Indian. 18 @. nothing. is short: a long syllable is a syllable the vowel of which | Αριστείδης, ου, ό, Aristides. κουφ-ο-τερος, lighter κουφ-ο-τατος, lightest ισχυρος, strong ισχυρ-ο-τερος,stronger ισχυρ-ο-τατος,strongest λεπτος, thin λεπτ-ο-τερος, thinner λεπτο-τατος, thinnest σοφος, wise σοφ-ω-τερος, Wiser σοφ-ω-τατος, wisest εχύρος, secure εχθρ-ω-τερος, securer εχθρ-ω-τατος, securest Πατρις, ίδος, ή, one's mother | country. The English adverb of comparison, than, is represented by η (Latin quam); thus, the son is wiser than the father, is in Greek, ὁ υἱος σοφώτερος εστιν η ὁ πατηρ. Another form of comparison drops the 7, and instead, as in the previous instance, of having the same case after the n, than, as before it, puts the second noun in the genitive, as ὁ υἱος σοφώτερος του πατρος εστιν. EXERCISES.GREEK-ENGLISH. Contracted words in εος, ους, and ooς, ους, undergo contractions also in the comparative and superlative; the former Αριστείδης πτωχίστατος ην, αλλα δικαιοτατος. Οἱ Κύκλωπες blend a and @ into w, the latter assume the connecting syllable | βιαιοτατοι ησαν. Καλλιας πλουσιωτατος ην Αθηναίων. Ουδεν εσ, and blend it with the foregoing o; thus Here belong also contracted adjectives of two terminations in oυς and ovv, as ευ-νοος, ευ-νους (well disposed), ευ-νοον, ευ-νουν; comparative, ευνο-εσ-τερος, ευ-νουσ-τερος; superlative, εννο-εσ-τατος, ευ-νουσ-τατος. The ensuing four adjectives in αιος, namely, γεραιος, old, παλαιος, of old, ancient ; περαιος, belonging to the other side (of the river) ; σχολαιος, idle; take the endings τερος and τατος, without any connecting vowel, as The following four adjectives in oc, namely λαλος, talkatire, μονοφαγος, cating alone, οψοφαγος, fond of good eating, and πτωχος, poor, begging ; take is for their connecting syllable, as λαλος, λαλ-ισ- τερος, λαλ-ισ-τατος. Adjectives in ης (g. ov), after dropping the ης, take the connecting syllable iσ, as Ρ. κλεπτης, thicvish. C. κλεπτ-ισ-τερος. S. κλεπταισ-τατος So also one in ης of the third declension, namely, ψευδης, ες (g. εος, ους), false, makes ψευδιστερος ψευδέστατος. σιωπης εστι χρησιμωτερον. Σιγη ποτ' εστιν αἱρετώτερα λογου. Ουδεν εστι σοφιας τιμιωτερον. Σοφια πλουτου κτημα τιμιωτερον εστιν. Ἡ Λακεδαιμονων διαιτα ην ἁπλουστατη. Οἱ γεραιτέροι ταις των νεων τιμαις αγαλλονται. Ἡ πατρις τοις ανθρωποις φιλτατη εστιν. Οἱ Ινδοι παλαιτατον εθνος νομίζονται. Ω παιδες, εστε ήσυχαιτατοι. Οἱ Σπαρτιατικοι νεανίαι ερρωμε νέστεροι ησαν των Αθηναιων. Πολλοι των χελιδονων εισι λαλιστεροι. Οἱ δουλοι πολλακις ψευδίστατοι και κλεπτίστατοι εισιν. ENGLISH-GREEK. The father is wiser than the son. The mother is more talkative than the daughter. Virtue is the most valuable possession. Socrates was the wisest Athenian. The Athenians were wiser than the Lacedæmonians. No one of the ancient Greeks was wiser than Aristides. Men are quieter than boys. Swallows are very The Lacedæmonians were very strong, chattering. The raven is very thierish. Socrates' manner of life was very simple. Τίμιος, α, ον, hormoured, es» | Καλλιας, ου, ό, Callias, a pro per name. Δικαιος, α, ον, just. : teemed, valuable. αφηλικ-εσ-τατος. apπaу-os, robbing. Comparative, ἁρπαγισ-τερος. |