petent for the operator to have mixed it with oxygen previous | although not very correct in its results. The second method to combustion: and this is what the chemist Cavendish did. is by exhaustion, as we have seen in the instance of Cavendish's Having effected a mixture of oxygen and hydrogen, and filled Eudiometer. The third method, now to be described, is by far with this mixture a thick glass vessel, as represented in the the most usual and most important, collection by the pneuaccompanying diagram, fig. 25, and since known as Cavendish's matic trough. If a bottle be taken, filled with water, and held thus inverted over water, I need hardly say the water which it Fig. 25. contains will not escape; but if a jet of gas be liberated under the mouth of the bottle, it follows, from a consideration of some ordinary laws of hydrostatics, that gas being lighter than water, the former will ascend and the latter will descend, until ultimately the bottle becomes quite filled with gas, but empty of water. For this elegant contrivance we are indebted to the ingenuity of Dr. Priestley. In my sketch, fig. 26, I have represented a common basin as the vessel in which the bottle is inverted, and I have represented the bottle as supported by the hand. I need not say this way of proceding is inconvenient; to give full effect to the operation one requires that the bottle shall stand without support, and that the vessel shall be large-one, in fact rather like a tub than a basin; a vessel thus modified becomes the pneumatic trough. As relates to the bottle or jar in which the gas is to be collected, it will stand quite well without any support provided its mouth be sufficiently wide; if circumstances of any kind require the use of a narrow-mouthed bottle, it may be supported in dozens of ways, readily occurring to the operator. The student need not expend one penny in the purchase of a pneumatic trough, except he has to deliver public lectures, and requires display. The first wash-bowl, kitchen-tub, foot-pan, or slop-basin he can lay hands on will answer sufficiently well; and as for the support, I will now just mention one that in many cases answers even better than a shelf. It is this. Eudiometer, he then caused an electric discharge to traverse a pair of wires a b, penetrating the glass stopper 8, so that an electric spark should pass through the space by this elegant contrivance the gas was ignited, and the sides of the vessel became bedewed with moisture, which on being examined was found to be water. As the experiment adverted to will searcely be performed by any chemical novice, it would be a waste of time to describe in detail the construction and use of this beautiful instrument, I shall merely content myself, therefore, with observing that the stopper is screwed tightly down by means of a contrivance indicated in our diagram; and the foot in of brass is not permanent, but admits of being screwed off at m', and the instrument attached to this point of junction to the receiver of an air-pump. The student will easily understand, that the air originally contained in the vessel being pumped out, a vacuum will ensue, and the stop-cock e being screwed on to a vessel containing gas, the latter will rush in. The method here described is not the usual one by which vessels are filled with gas; chemists accomplish the object far more readily by what is called the pneumatic trough, to be described presently. In the experiment of Cavendish, however, water would have been inadmissible as the filling agent, and mercury scarcely more eligible. Methods of Collecting Gas.-Two methods of collecting gases have already come under our notice. Firstly, we collected hydrogen by simply inverting a tumbler over a jet, through which the gas was escaping. This method is usually called that of a displacement, and is sometimes had recourse to, the shape of a cone, the apex of which is truncated; next cut a notch in the lower or base edge of the cone, and the stand is made. The use of it will be evident from an examination of the diagram, fig. 28. The notch admits the gas delivering tube, the truncated apex delivers the gas into the bottle, which rests supported on the sides. If the student were not told of these contrivances he might think me remiss; but I want to create a feeling of independence in his mind, to impress him with the conviction, that in the majority of chemical operations involving the use of mechanical contrivances, many different methods admit of being followed, each equally good. The support just described is useful, and not inelegant, but I shall not quarrel with a student who tells me that two bricks set edgeways in a pan of water, fig. 29, furnish a support which is nearly as good. Fig. 29. 79 Compound Sentences of two Members. He will perish who loves unrighteousness. 1 2 The lark sang his matins and sank into his nest. The great fault of most books which treat of chemical manipulations is this:-they represent the apparatus which is not intrinsically best for gaining any particular result, but the apparatus which makes the prettiest engraving. This, in my The first sentence is equivalent to these two propositions :-opinion, is but a questionable benefit to the pictorial art, and a vast disadvantage to the student of chemistry. LESSONS IN ENGLISH.-No. LXXII. By JOHN R. BEARD, D.D. We have already learnt that a subject may comprise a noun or nouns standing in apposition to the principal noun; as, Principal Noun. Apposition. Victoria, Predicate. Queen of England, conquered Burmah. 1. Some one will perish. 2. The lover of unrighteousness will perish. The second sentence is equivalent to these two statements : 2. Before then the fleet had weighed anchor. This appositional clause or member proves when analysed to be a Thus what in the compound sentence stands as three members, sentence of itself; e. g., Subject. Victoria, who is Queen of England, Similar accessaries may be made to the subject, which may be called These accessaries, whether they attach to the subject or the Rel. Pron.: The man Adverbial Accessaries. The essential quality of the adverb is to declare the quality of adverbs, and pronouns:an affirmation, thus: He writes well. Principal. ACCESSARY and is refreshed. The man is refreshed But the quality of an act may be assigned by an adverbial phrase Conjunc.. The man drinks as well as by a simple adverb; e. g., Adv.: when he drinks. In number one, who is of the first person, because I is of the first person; who is of the singular number, because I is of the singular number. The effect of the relative on the verb is more clearly seen in the second instance, where an s is added to the verb, which accordingly appears as reflects. As the language is now written and spoken by the best authorities, the relative who has one change of form in the nominative, namely, in which; which is commonly applied to things. Who, however, has a genitive and an objective, as well as a nominative case, and may be declined or inflected thus : Feminine. Neuter "The malcontents made such demands as none but a tyrant could refuse."-Bolinbroke. What is a relative which performs the double function of a subject and an object, being equivalent to that which, and used in only the neuter gender; e. g., "My master wotteth not what is with me."-(Gen. xxxix. 8.) As a subject for exemplifying the doctrines laid down in regard to the structure of sentences, I shall take some sentences from Daniel Defoe, a writer of idiomatic English. Compound Sentence. "Oxford makes by much the best outward appearance of any city I have seen, being visible for several miles round on all sides in a most delightful plain; and adorned with the steeples of the several colleges and churches, which make a glorious show." Here I must premise that the form "the best outward appearance of any city," &c., is incorrect, and should have been the best outward appearance of all the cities I," &c. This compound sentence may be reduced into these simple sentences: 1. Oxford makes a very good appearance. 2. Oxford makes an appearance better than many cities. 3. I have never seen a city with a better appearance than Oxford. 4. Oxford is visible for several miles round. 5. Oxford is visible from all sides. 76. Oxford stands in a most delightful plain. 7. Oxford is adorned with the steeples of several colleges. 8. Oxford is adorned with the steeples of several churches. 9. The architectural decorations of Oxford make a glorious show. The resolution of this long sentence into the several distinct propositions which it contains, has, by showing the meaning of the several parts, prepared the way for our exhibiting the logical relations which those parts sustain to each other, thus :— Several of these parts may be analysed or explained; e. g., Number three consists of the definite article the, the superlative adjective best, the adjective outward in the positive degree, and the common noun appearance, which is the object to the verb makes. Number six presents a case of explanatory apposition, since being visible is subjoined to the subject Oxford in order to state some additional facts respecting it; number ten stands to number one in the same relation. Number twelve presents an appended relative accessary sentence of which these are the components; namely, which, a relative pronoun agreeing with its antecedent steeples; make, a verb in the indicative mood, third person, plural number, agreeing with its subject which; a, the indefinite article limiting show; glorious, an whose of which (whose) adjective qualifying show; show, a common noun dependent on or the object to the verb make. Viewed structurally, this appendage stands thus: whom Instead of whose and which we sometimes find whereof. which That, which is without any inflexional change, may be used in lieu of who or which, being applied to both persons and things; e. g., "He that reproacheth a scorner, getteth to himself shame."(Prov. ix 7. By way of applying what you have learnt, take portions of any good prose author, mark the logical relations of the sentences The word as is also used with the force of a relative after such, after you have resolved each into the simple propositions of which to many, the same; c. g., it consists, and explain by grammatical analysis (that is, "parse") the several components. In other terms, convert each of these compound sentences into simple sentences. Distribute each simple sentence into subject and predicate, distinguishing the verb (the copula) and the attribute. Next, exhibit each compound sentence in its several members, showing what are principal, what accessary, and what appended, what interposed; together with the accessaries to the subjects and objects, and the adverbial objects. Finally, give the grammatical analysis of the whole. ON PHYSICS OR NATURAL PHILOSOPHY. No. VI. LAWS OF GRAVITY; PENDULUM. (Continued from page 63.) Formule relating to Falling Bodies.-The second and third laws of falling bodies may be respectively represented by the formulæ v=gt, and sagt. For, let g be the velocity acquired at the end of a second by a body falling in a vacuum, and its velocity after t seconds; then, the velocities being proportional to the times, we have g:v:: 1:t; whence v=gt (1). Again, a body which falls during t seconds by a motion uniformly accelerated, with an initial velocity equal to zero or 0, and a final velocity equal to gt, will describe the same space as if it fell during the whole time t by a uniform motion, with a mean velocity between O and gt, that is, with the velocity gt. Now, in the latter case, the motion being uniform, the space described is equal to the product of the velocity and the time; whence, denoting this space by s, we have sgt t=gť2 (2). The demonstration of these theorems is given mathematically in treatises on Dynamics; soe Whewell's Mechanical Euclid, and other elementary works of the same description. If in the formula (2) we make t=1, we have s= }g, whence g=2s; that is, the velocity acquired at the end of a unit of time is double the space described in that unit of time. This value of g is called the measure of gravity. Thus, in the latitude of London, it has been found that a body falling near the surface of the earth, in a vacuum, describes about 16 feet in the first second of its fall; hence, the measure of gravity of London is about 32 feet; in other words, after a body has fallen 16 feet in 1 second, by the force of gravity, it would, if the attraction of the earth were removed or counteracted, continue to fall ever after with a uniform velocity of 324 feet per second. In formula (1) the velocity v is expressed in a function of the time; that is, an expression involving the number denoting the time; but we can likewise express it in a function of the space described, by eliminating t from the two formula (1) and (2). For, from the first, we have t, whence t now substi ย g v2 ; and multiplying both sides of this equation by 2g, we have 2g 2gs; and extracting the root, we have finally, v=√ 2gs; hence, we conclude that, when a body falls in a vacuum, the velocity acquired at any given instant is proportional to the square root of the height of the fall. from that centre, it follows that the intensity of gravity will increase or decrease, according as the bodies approach to, or recede from, the general level of the earth's surface. This variation, however, is not apparent in the ordinary phenomena which are observed at the surface of the globe, because, its radius being nearly 4,000 miles, the distance from the centre is sensibly the same when a body is elevated by a few hundred yards. But when the heights of bodies above the earth's surface are very considerable, gravity can no longer be considered as having the same intensity. It is necessary, therefore, to remember that the laws of falling bodies already explained are only true for heights within certain appreciable limits. 2. The second cause which modifies the intensity of gravity is the centrifugal force. A force which produces a curvilinear motion, and which gives to bodies under the influence of this motion a tendency to fly off from the axis of rotation, is called centrifugal. It is demonstrated in treatises on Rational Mechanics, that the centrifugal force is proportional to the square of the velocity of rotation; whence it follows that, under the same meridian, it increases as we approach the equator, where it reaches its maximum, because there the greatest velocity takes place. At the poles the centrifugal force is zero. At the equator, the centrifugal force is directly opposed to gravity, and is equal to of its intensity. Now 289 being the square of 17, it follows that, if the motion of rotation in the earth were 17 times slower than it is, the centrifugal force at the equator would be equal to that of gravity, and all bodies on its surface in this latitude would be on the point of being projected into space. As we proceed from the equator towards the poles, gravity is less and less affected by the centrifugal force. This happens chiefly because the centrifugal force decreases in proportion as we recede from the equator, and also because that, at the equator, the centrifugal force is directly opposite to that of gravity, whereas, in proceeding towards the poles, its direction becomes more and more inclined to that of gravity, and thus loses intensity. Thus, in fig. 15, in which PQ represents the axis of the earth, and EF the Fig. 15. 3. The intensity of gravity is also modified by the depression of the earth at the poles; for, in the vicinity, and at these points, bodies are nearer to the centre of the earth, and consequently more subject to its attraction. The formulæ v=gt, and s= gt2, having been determined by considering gravity as an accelerating force, and consequently in Measure of the Intensity of Gravity.-After the preceding cona case where motion is uniformly accelerated, they may be considerations, gravity may be considered in the same place, and in sidered as general formulæ for this kind of motion. But it must be observed, that as g denotes the acceleration of the velocity imparted in each second by the accelerating force, the value of g will vary with the intensity of the force. Causes which Modify the Intensity of Gravity.-Three causes have an effect in making the intensity of gravity vary; 1st, the clevation of the place above the ground, or general level of the earth's surface; 2nd, the centrifugal force due to the earth's rotation on her axis; 3rd, the depression of the earth's surface near the poles. 1. Since terrestrial attraction acts upon bodies as if the whole mass of the globe were collected at its centre, and this attraction ats upon them in the inverse ratio of the square of their distance cases where the heights of the fall are inconsiderable, as a constantly accelerating force; and that the measure of its intensity is the velocity imparted in one second of its fall to a body falling in a vacuum, without regard to its mass, seeing that in a vacuum all bodies fall in the same time. This velocity is represented in general by 2g: it increases from the equator to the pole, and at London it is 324 feet. The Pendulum.-The general name of pendulum is given to every solid body suspended at one point on a horizontal axis, around which it oscillates. There are two kinds of pendulum; the simple and the compound. The simple pendulum (which exists only in idea) is that which would be formed by a heavy material point suspended by a per fectly rigid rod, inextensible and without weight, at a point round which it freely oscillates. Of course this pendulum cannot be put in actual practice, because it is purely theoretical, and is employed only to determine by calculation the laws of the oscillations of the pendulum. The compound pendulum may be varied in its form in any manner whatever, but it is generally made of a metallic lens or bob, suspended by an iron or wooden rod, and moveable round a horizontal axis, such as the pendulum of a clock, the pendulum , in fig. 13 of the preceding lesson, or that exhibited in the following cut, where o is the point of suspension, and c the point of oscillation; in other words, c is the point where a simple pendulum would produce the same oscillations as the compound pendulum. Compound pendulums are suspended either on a knife-edge, on the same principle as that of balances, or by means of a thin and flexible steel spring, which is bent slightly at every oscillation. In order to explain the oscillatory motion of the pendulum, we shall first notice the simple pendulum cм, fig. 16. When the material point м is below the point of suspension c on the vertical passing through that point, the action of gravity is destroyed, or rather counteracted; but if the point be transferred to m, its weight P will be decomposed into two forces, the direction of the one being in the straight line em produced to B, and that of the other in the tangent m D to the arc mмn. The composant B is counteracted by the resistance of the point c, but the composant m D urges the material point to descend from m to M. When it reaches this point, the pendulum does not stop; for, in consequence of its inertia, it proceeds in the Fig. 16. direction M. Now, if the same construction be made at any point of the are Mn, it will be found that the gravity which asted from m to м with an accelerating force will now act from м to n with a retarding force. It will take away, there fore, successively from the moveable the velocity acquired in its descent, so that, when it reaches the point n at a height equal to that of the point m, the velocity will become zero, as it was at the latter point. Whence it follows, that the same series of phenomena will be repeated, and the pendulum will continually oscillate. In practice, this result is prevented by the resistance of the air, and the rigidity of the cord, obstacles which can never be completely annihilated in compound pen that is, that they are sensibly equal in the same time, so long as their amplitudes do not exceed a certain limit, namely 2° or 3o of the circle. Galileo was the first who established the isochronism of the small oscillations of the pendulum. It is said that, when a young man, he first made this discovery by observing the motions of a lamp suspended in the dome of the cathedral at Pisa. 2. In pendulums of the same length, the duration of the oscillations are the same, whatever be the substances of which they are composed. Thus, simple pendulums of which the material point is composed of cork, lead, or gold, perform the same number of oscillations in the same time, if they are of equal length. 3. In pendulums of unequal length, the durations of their oscillations are proportional to the square roots of their lengths. Thus, if the lengths of pendulums he respectively 4, 9, 16, &c., times that of a given pendulum, the duration of their oscillations will be respectively 2, 3, 4, &c. times that of the oscillation of the given pendulum. 4. At different places of the earth's surface, the durations of the oscillations of a pendulum of the same length are in the inverse ratio of the square roots of the intensities of gravity. 2g These laws are deduced from the formula tr√. which is derived from the application of the calculus to the motion of the simple pendulum. In this formula, t denotes the duration of an oscillation; 7, the length of the pendulum; 2g, the intensity of gravity, that is, the velocity acquired at the end of the 1st second by a body falling in a vacuum. Also, is a constant quantity which denotes the ratio of the circumference of a circle to its diameter, which is equal to 3.141592. The first two laws of the pendulum are deduced at once from the formula tV; for this formula contains the values 2g neither of the amplitude of the oscillation, nor of the density of the substance of which the pendulum is composed, the value of being independent of the values of these quantities. As to the third and fourth laws, they are also comprehended under the formula, since, in the radical expression, is the numerator, and 2g the denominator of the fraction. Length of the Compound Pendulum.-The preceding laws and formulæ are applicable also to the compound pendulum; but in this case it is necessary to define what is meant by the length of the pendulum. Every compound pendulum is formed of a heavy rod terminating in a larger or smaller mass, according to its form and purpose; now, all the different points of such a pendulum tend, according to the third law of pendulum motion, to describe their oscillations in times differing from each other, and increasing in duration in proportion to the square roots of their distances from the point of suspension. But all these points being invariably connected together, their oscillations are necessarily performed in the same time. Hence, it is evident that the motion of the points nearer to the axis of suspension is retarded, and that of the points more remote from that axis is accelerated. Between these two extremes there are some points which are neither accelerated nor retarded, and which oscillate as if they were not connected with the rest of the mass. These points being all at the same distance from the axis of suspension, form together an axis of oscillation parallel to the former; now the distance of the axis of oscillation is called the length of the compound pendu hum. Hence, the length of a compound pendulum is the same 8 the length of a simple pendulum which performs its oscillatio ns in the same time. Thus in the preceding figure of the compound pendulum, the point o is the centre or place of the axis of uspension, and op the length of the compound mass; all the points of this mass between o and c are retarded, and all the points between p and o are accelerated; but all the points at a are neither accelerated nor retarded, and therefore the point c is the centre or place of the axis of oscillation. the axis of suspension; that is, if we suspend the pendulum by The axis of oscillation possesses the property of reciprocity with its axis of oscillation, the duration of the oscillations will be the same as before; in other words, the axis of suspension wil then become the axis of oscillation. By means of this property, the length of the compound pendulum can be found experimentally. This is done by inverting the pendulum and suspending it by means of a moveable axis, which is placed, after several tries, ir such a manner that the number of oscillations performed in the |