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However, whether simple or compound, transitive verbs gover” an object, that is, the action of the verb falls on a noun which is hence called the object of the verb. This is a case of dependence, the noun which is the object is dependent on the verb of which, it is the object. The relation is one purely of thought, for the relation involves in the noun no change of form. With the personal pronoun there is a change of form, corresponding to the change of sense, so that the nominatives I, we, they, become as objects, or become in what is called the objective case, me, us, them. * The verb drinks may be resolved into these terms, is drink$ng, as The sick man is drinking a beverage; whence we learn that present participles have the same government as the verbs to which they belong. to Intransitive verbs, though in general incapable of an object, may take an object in a noun of kindred meaning; e.g., • Let me die the death of the righteous.”—(Numb. xxiii. 10.) “Let us run the race that is set before us.”—(Heb. xii. 1.)
Intransitives have the force of transitives also in certain idiomatic phrases; e.g., “He laughed him to scorn.”—(Matt. ix. 24.) * “we ought to look the subject fully in the face.”-Channing. “And talked the night away.”—Goldsmith. The Object. The object of a proposition variety of forms. The object also assumés several shapes. chief variations may be presented as follows:The object of a proposition may be either 1. A noun : The man drinks a beverage. 2. A pronoun : The man calls me. 3. A noun and an infinitive: The mian bids his soft remain. 4. Two now??S : He teaches his son Eatin. 5. A proposition: The man declares he is ill. If dependent on the verb, that is, if it receives the action of the verb, the noun is the object of the verb ; e.g., * Preventing fame, misfortune lends him wings. And Pompey's self his own sad story brings.”
may, as we have seen, appear in a |
THE POPULAR EDUCATOR.
| ithat is, in full, } He gave a book to his son. . So in the sentence, - He bought his son a book; the construction really is, He bought a book for his son.
You will now have the less difficulty in understanding how a sentence may be the object of a verb; as,
i The man says (that) he is ill. 'The words he is ill you will at once recognise as a sentence or statement, and a little reflection will show you that the sentence ibears to the verb says the relation of an object to its verb. The iconjunction that is merely an explanatory word, or, indeed, an -expletive. A sentence as the object of the verb may also be enlarged:* The man says he is sick and likely to die. The man says he is sick and lids beehi give/voter by the faculty for a long time.
The compound object in our model sentence will now be readily , understood, viz.,
The man drinks a beverage made of wine and water. ;In this compound object, which consists of the words in italics, analysis shows us a noun, beverage, depending on the verb drinks : ła participle, made, agreeing with beverage, and therefore conjointly
! ; with beverage dependent on drinks; a preposition, of connecting made with wine and water; a noun, water, dependent on the preposition of; a conjunction, and, connecting water with wine; and, łfinally, anothermoun, wine, connected with water and the preposition. of, and consequently standing to the preposition of and to the sentence generally in the relation held by the noun water.
I must subjoin a few words respecting the object.
Observe, then, that wine and water do not hold to drinks exactly the same relation which the words “his son Greek” holds in the above example. If so, a verb might be said to have several objects; e. g.,
* The man bequeathed money, wine, books, and land.
It is true that the nouns form the object to the verb bequeathed, but. they are a compound object made by repetition; whereas in the 'proposition *
The man taught his son Greek,
the compound object is formed by addition. And in the construc-tion which assigns to certain verbs a double object, one of thoseobjects is a person, the other is a thing. Double objects, like: single ones, may be augmented by repetition ; e. g., * The man taught his wife, his sons, and his daughters Greek. fhe man taught his son Greek, Latin, German, and French.
The position of the objectis after the verb. And the observance of this law is in English so imperative that by disregarding it you create ambiguity, if you do not change the object into the subject and the subject into the object; e.g.,
Subject. Object. The father struck the son. Subject. Object.
The son struck the father.
As an instance of ambiguity from the inversion of the object,
take this instance:— -
Which is the subject, and which the object? IJo you mean that power has praise, or that praise has powerf
When, however, the perspicuity of the sentence is not abated, the object may, for the sake of emphasis, be placed before the verb; e.g.,
“Silver and gold have I none.”—(Acts iii. 6.)
Especially with pronouns; e.g.,
“Me he restored to mine office and him he hanged.”—(Gen. xli. 13.)
You may find sentences in which one object stands before and another after the verb ; e.g.,
“Ye have the poor always with you, but me ye have not always.”— (Matt. xxvi. 11.)
Intransitive verbs have no object. The untaught are apt to confound the transitive with intransitive verbs, using the one for the
Composants and Resultants.—When several forces, such as s, P, and q, are applied to the same material point, A, fig. 4, and produce an equilibrium at that point, it is evident that the action of any one of these forces, for example s, resists the combined action of all the rest; for were the force s to act in the direction AR, contrary to its own direction, A s, it would produce the same effect as the two forces P and q, acting in the directions AF and A q. Every force which produces the same effect as a combination of any number of forces is called the resultant of such forces, and these considered in relation to their resultant, are called component forces, or composants.
: (a rod), their resultant is
into two parts, which express the intensity of the forces. Thus, in fig. 6, if
tween the directions, AP and Aq, of those forces; the reason of this is plain, namely, that the point cannot move in both Fig. 5 directions at once; and as no rea5 * *** son can be assigned why it should move in the one direction more than in the other, it must move in some intermediate direction, ‘and this direction is exactly that of the resultant of the two forces P and Q. All problems which relate to Q - the composition and resolution R of forces depend upon the following theorems, for the demonstration of which we must refer our mathematical students to the Elementary Treatises on Statics, which are to be found both, in French and English. In particular, we would mention the elegant demonstrations of M. Poisson, in his Traité de Mécanique, imitations of which have been published in English Treatises on Mechanics, by Whewell, Pratt, Earnshaw, and many others. Composition and Decomposition of Parallel Forses.—Theorem 1.— When two parallel forces are applied at the same point, their resultant is equal to their sum, when they act in the same direc
, tion, and to their difference when they act in contrary directions.
For example, if two men drag a load in parallel directions with forces respectively denoted by 20 and 15, their combined force, that is, their resultant, will be denoted by 35 if they drag in the same direction, and by 5 if they pull in opposite directions. In like manner, when a number of horses are attached to the same vehicle, and all pull in the same direction, it will beurged along the road assif it were drawn, by a single force equal to the sum of all the forces of the different animals employed. Theorem 2.--When two parallel forces, which act in the same direction, are applied at the extremities of a rigid straight line * to their sum, acts in the same direction, and its point of applieation divides the straight line which are inversely proportional to the numbers
As denote the rigid straight line, A and B its extremities, P and q, the parallel forces, A P and B Q their directions, and c the point of application of their resultant R. ; then Gr, parallel to AP or B Q, will be its direction, and P : Q :: B c : GA, that is, if
'the force P be two, three, &c., times the force Q. in magnitude,
then the part B C will be two, three, &c., times the part A C in magnitude. Whence it follows, that when the forces P and a are equal, the point of application of their resultant divides the straight line AB into two equal parts. Conversely to this proposition, any single force R applied at the point C in a given rigid straightline, A B, may be resolved into two parallel forces P and q, whose sum is equal to R, if their points of application, A and B, be in the same straight line with the point c, and if' they be so divided, that they are to one another in the inverse ratio of their distances from c.; that is, if B c : A co- : P : Q. To find the resultant of any number of parallel forces acting in the same direction, we have only to find by the preceding theorem the resultant of two of these forces, then the resultant of this resultant force and another of the given forces, and so on, until all the given forces have been compounded: The last resultant thus obtained will be a force equal to the sum of the given forces, and having the same direction; and its point of application will be determined. Composition and Resolution of Forces acting on a Single Point– If two forces, as P and Q, fig. 7, act on a single material point at A, and A P and A Q be the directions of these forces, we can determine their resultant by the following theorem. Before we enunciate this theorem, let us take on the straight lines A P and A Q, parts A B and A C having to each other the same ratio as the intensities of the forces; let us then complete the parallelogram A B D C, by drawing B D parallel to A C, and C D parallel to A B, and let us draw the diagonal A D. This figure is the parallelogram of forces, and the theorem which expresses the relation between the composants P and Q and their resultant R, is called The Theorem of the Parallelogram of Forces; viz., if any two forces acting on a material point be represented in magnitude and direction by the two adjacent sides of a parallelogram, their resultant will be represented in magnitude and direction, by the diagonal of that parallelogram which is drawn from the point where these two sides meet. Thus, in the parallelogram A B c D, if A B and A C represent in magnitude and direction any two forces P and Q, acting on a material point at A, then, will the diagonal, A D, drawn from the point A, represent in magnitude and direction the resultant R of these two forces; in other words, the direction of the resultant R of the forces P and Q, will be the straight line A R, and the resultant R will contain the unit of force as many times as the diagonal AD contains the linear unit of measurement, which was applied to the determination of the lengths of A B and A c, in order to make them represent the forces P and Q. Conversely, a single force applied to a material point may Se decomposed into two other forces applied to the same point, and having their directions in , given straight lines, that is, straight lines which shall make given angles with the direction of the resultant and with each other. For if we construct on the given straight lines a parallelogram, whose diagonal represents in magnitude and direction the given force, then its sides will represent in magnitude, and Čirection the required composants. The solution of problems relating to forces acting on a single point will be seen by the mathematical student to resolve itself into the application of trigonometry to the determination of the sides and angles of the parallelogram of forces. Thus, if P and 9 represent any two forces in numbers, and A denote the angle between their directions, then their resultant R will be represented in numbers by the following formula:—
The effects of the composition and the resolution of forces are frequently presented to our notice. For example, when a boat rowed by oars crosses a river, it does not make way in the real direction in which the oars propel it; neither does it advance in the direction of the current; but it is urged along in the direction which exactly corresponds to the resultant of the two forces which act upon it, viz., the force which puts the oars in motion and the force of the current in the river. In like manner, when several men are employed to ring a great bell each by a short rope attached to the main rope, the resultant of their united forces acts along the main rope as the line of its direction, and their individual forces form the composants, their lines of direction being that of the short ropes at which the ringers pull, in order to produce the desired effect. When any number of forces are in equilibrium about a point, any one of them may be said to be the resultant of all, the rest, but its direction, of course, is contrary to that of the balancing force ; and the resultant of any number of forces in equilibrium, is
Different Kinds of Motion.—Motion is said to be rectilinear or curvilinear according as the path described by the moveable body is a straight line or a curve; and either of these motions may be toniform or variable. Unform motion is the most simple kind of motion, and is that in which the moveable body describes equal spaces in equal times. Every momentary force produces a motion which is rectilinear and uniform, when the moveable body is not subjected to the action of any other force, and meets no resistance to its progress. Under the momentary action of a force, the moveable, when left to itself, will continue to preserve, in consequence of its inertia, the direction and the velocity which were communicated to it by the momentary action of the force. Under the continued action of forces, a moveable may likewise be made to preserve uniform motion; as in the case where the resistances opposed to the motion continually destroy the inclements of velocity which such forces tend to communicate to the moveable. We see an example of this in the motion of a train on a railway, where the motion is produced by the continued action of a certain force, but that motion is nevertheless still uniform ; this result arises from the loss of force due to the continued resistance of the air, the friction of the rails, &c., a resistance which increases as the velocity increases, and which soon establishes such an equilibrium between the moving and resisting forces, as produces the uniform motion required.
Velocity, and Law of Uniform Motion.—In uniform motion, the space described in a unit of time is called velocity.
This unit, although entirely arbitrary, is generally a second of time. From the definition of uniform motion, it is plain . that in this species of motion the velocity is constant, that is, always the same ; as, for example, in two units of the time, the space described is double, in three units triple, in four units quadruple, &c., that of the space described in one unit. This law is usually expressed by saying that in uniform motion the spaces described are proportional to the times, or in other words, the spaces described increase with the times. l
This law may be represented by a very simple formula; let v denote the velocity, t the time, and 8 the space described. Now since v denotes the space described in a unit of time, the . space described in 2, 3, 4, &c., units of time will be 20, 30, 4v, &c.; and generally, in the time t, it will be t w ; hence, we
have the formula s-t v. From this formula we have w-f.
y hence we say, that in uniform motion, the velocity is the ratio of the space described to the time employed in describing it. Variable Motion is that in which a moveable body describes unequal spaces in equal times. This species of motion may be varied in an infinite number of ways, but we shall at present only consider that in which it uniformly varies. Motion, Uniformly. Variable is that in which the spaces described in equal times constantly increase or decrease by the same quantity. In the first case, the motion is said to be wniformly accelerated; such is the motion of a falling body, when the resistance of the air is removed. In the second case the motion is said to be uniformly returded; such is the motion of a stone thrown vertically upwards from the ground. Motion uniformly varied arises from a constant force, that is, a force continually acting with the same intensity; and it is considered either as a power or a resistance, according as the motion is accelerated or retarded. Velocity, and Laws of Uniformly Accelerated Motion.—In motion uniformly accelerated, the spaces described in equal times not being equal, the velocity is no longer the space described in a unit of the time, as it is in uniform motion. In the former species of motion, we understand by the velocity at a given instant, the space which, commencing from that instant, would be uniformly described by the moveable in every second, if the action of the accelerating force were instantly to cease, that is, if the motion were to become uniform. For example, if a moveable were to acquire a velocity of 60 yards per second, after the lapse of ten seconds, during which it had proceeded with uniformly accelerated motion, and if the uniformly accelerating force were suddenly to cease its action after these 10 seconds, the moveable would, in consequence of its inertia, continue its motion uniformly at the rate of 60 yards per
On this principle, every uniformly accelerated motion, whatever may be its increments of velocity, is reduced to the two following laws:– . . -> 1st. The velocities increase proportionally to the times; that is, after a time, double, triple, quadruple, &c., any given time, the velocity acquired is double, triple: quadruple, &c., greater than that after the given time. The action of the continued force, indeed, which produces any accelerated motion, may be compared to a series of equal impulses which succeed one another at equal but infinitely small intervals of time. Now, as each of these impulses produces in each interval, a constant velocity, which is continually added to that which the moveable already possessed in the preceding interval, it follows that the velocity goes on constantly increasing by equal quantities in equal times. g 2nd. The spaces described are proportional to the squares of the times employed in describing them; that is, if, we denote the space described in 1 second by 1, the spaces described lo. 2, 3, 4, 5, &c., seconds will be denoted by 4, 9, 16, 25, &c., which are the squares of the former. o a to These laws are mathematically demonstrated in the scientific treatises on Dynamics, or the laws of motion ; when we come to treat of gravity, we shall exhibit their experimental demonstration. -> Momentum, Measure of Force.—The momentum of a body is the product of the number expressing its mass by that expres: ing its velocity. Thus, if a body moves with a velocity of 10 feet per second, and its mass is represented by 20, then its momentum is said to be 200. When a force communicates a certain velocity to a given mass, the momentum can be taken as the measure of this force. Thus, if a body moves with a velocity of 20 feet per second, and its mass is represented by 10, then its momentum is, as before, said to be 200; whence, in this case, the moveable has the same force as in the Pre: ceding case. The momentum of a body is frequently called its quantity of motion. o In mechanics, therefore, these principles are established, that, in equal masses, the forces are proportional to the velocities; and that, in equal velocities, the forces are proportional to the masses; in other words, that a force double another imparts to the same mass a double velocity; or, to double the same mass, an equal velocity. Now, let there be two forces F and f acting upon the two masses M and m, and communicating to them the velocities V and v respectively. If we suppose a third force P such that it communicates to the mass M the velocity v, we shall then have, according to the preceding principles, the following proportions :(1.) F. P :: V: v, and (2.) P : f :: M ; m: whence, F V d P M. F = 7, and F = ori Now, multiplying these two equations term by term, and cancelling the common factor P, we have
—- so ; whence
f 7???) (3.) F: f: ; Mv : my ; that is, any two forces are to each other as their momenta or the quantities of motion which they communicate to any two moveables. Thus we see that if we take for the unit of force the momentum which the unit of velocity would communicate to the unit of mass, forces may be measured by their quantity of motion. This species of measurement is equally applicable to instantaneous and to continued forces; but in the case of continued forces, we only consider the velocity which the force communicates in a second.
Forces being proportional to their momenta or quantities of
motion, it follows that for the same force the product onv is constant; that is, if the mass become twice, thrice, &c., greater, the velocity will become, twice, thrice, &c., smaller. This conclusion is drawn from proportion (3) above demonstrated; for by making F-f, we have M W = mv ; whence, it follows (Cassell’s Arithmetic, p. 101) that M: m :: v : V ; that is, the velocities communicated by the same forces to two
LESSONS IN CHEMISTRY.-No. III.
RESUMING the consideration of the metal zinc, the learner will remember that he has dissolved a portion of this metal in sulphuric acid and water; that he has evaporated this solution to dryness, and redissolved the dried mass. He will have now obtained a colourless solution of sulphate of zinc : that is to say, a solution of oxide of zinc in sulphuric acid. However, I only at the present time desire the learner to remember the single fact, that the zinc is by some means held in solution by the liquid employed, i.e. sulphuric acid and water. The exact state of its combination we need not discuss just now, this point will come under discussion hereafter. The zinc is there, and we require to obtain it, or at least satisfactory evidence of its existence; that is our proposition. How is this to be accomplished 2 A person conversant with Chemistry would almost arrive at the conclusion that zinc was present by the peculiar taste of the liquid. And indeed the sense of taste is a very valuable test: a far more precise indication, however, is afforded by hydro-sulphuric acid, or its watery solution, as we shall see. If the learner pour a little of the sulphate of zinc into a test tube; that is to say, a little glass tube of the followFig. 14 ing shape, or a wine glass, and add to this ig. 14. sulphate of zinc a portion of the hydro-sul
phuric acid solution already procured, a white powder will fall, this white powder being a combination of sulphur and zinc, and therefore called sulphuret or sulphide of zinc.
Let the reader impress upon his memory the fact that sulphuret or sulphide of zinc is white, and that it is the only metal which yields a white compound with the same agent, applied in the same manner.
If a sufficient amount of hydro-sulphuric acid solution be poured into the sulphate of zinc, all the metal will be thrown down in this condition of sulphuret or sulphide, and accordingly this process is sometimes followed in the course of analysis. The student, however, will not fail to perceive that, supposing the solution of sulphate of zinc to be very strong, a very large portion of hydro-sulphuric acid solution must be added, a treatment which would, under many circumstances, produce an inconvenient bulk of liquid., This being the case, it follows that when hydro-sulphuric acid is merely used as a test or indicator, it is commonly employed in the state or aqueous solution; when, however, it is employed as a separator, then the more convenient plan is to cause it to permeate the metalliferous fluid as a gas; this remark brings me to the consideration of the mechanical arrangement necessary to the use of this gas.
Ifamixture of oil of vitriol and water (about 1 to 6 by measure) be poured upon sulphuret of iron sulphuretted hydrogen, or sulphuric acid gas, will be liberated, as we have seen; but as thus liberated it usually carries before it little particles of liquid, i.e. sulphuric acid and water, consequently it is not well adapted to be employed as a delicate precipitating agent. To speak more precisely, the gas requires to be passed through water in Smal. bubbles, or washed, by means of an apparatus similar to that represented in fig. 15; A and B are two wide-mouthed eight or ten-ouncebottles, to each of which is adapted a cork, and each of which corks is perforated with two holes, as represented. Pre
different masses, are to one another in the inverse ratio of viously to securely fixing the cork of the vessel A, some fragments remains to be spoken of in connexion with the apparatus just ||
of sulphuret of iron are thrown in ; the bottle is then corked water is now poured into the vessel B, and the latter is also corked. It will be evident now, from the merest consideration of the various parts of this apparatus, that if a mixture of sulphuric acid and water be poured into A, all the sulphuretted hydrogen liberated will be obliged to traverse the water B before it can finally escape; in other words, it will be washed. A portion of the gas is absorbed by the water, but this matters not; the maximum of absorption is soon arrived at, and the gas comes over uninterruptedly so long as it is developed. Only one matter
described, it relates to the portion marked r. This consists of a small tube of india-rubber vulcanized by preference, and which is interposed between the two glass tubes. By this arrangement not only does a flexible joint result, but the bent glass tube admits of being removed and another placed in its stead; for, as a general rule, the same tube should not be used for testing consecutively two fluids of different compositions. most large towns, vulcanized rubber tubes of any length may be readily procured, and the operator, having become possessed of them, may cut them into lengths according to his necessities; but supposing them not procurable, the reader should be able to manufacture a substitute out of india-rubber sheet. The best material for this purpose is the rubber manufactured into sheets, but even the native bottle rubber will answer perfectly well. Supposing the artificial sheet rubber to be procured, it may be formed into tubes simply by warming it before the fire, winding it round a glass rod or tube, pressing the sides closely together, and cutting them off by a sharp pair of scissors. Thus treated the two cut edges will adhere, and a tube will result. Fig.16.
If, however, the artificias sheet rubber cannot be procured and the bottle rubber has to be substituted, the latter material requires to be boiled in water for a considerable time, in order that the necessary amount of adhesiveness may be imparted to it. Generally speaking, india-rubber tubes, thus manufactured, are strong enough for all uses to which they are applied; if additional strength be desired, it can be imparted #. first constructing one tube, then overlaying it with another, the seam of which does not correspond with the first, but is on the opposite side of the tube. The two bottles forming the compound apparatus just described, are usually attached for convenience to a slab of wood, as represented in fig. 15. The apparatus is procurable complete at the philosophical instrument shops, but I strongly recommend the young chemist to manufacture this and similar apparatus himself. eturn we now to the metal zinc. By passing a stream of hydro-sulphuric acid through it sufficiently long, the whole of the zinc will be thrown down. The operator may know when this point has been arrived at, by filtering a little of the solution from time to time, and testing the filtrate or fluid which passes through the filter. This remark leads us to another digression—the operation of filtering, so necessary to the prosecution of chemical investigations. The usual material employed by chemists, as a filtering agent, is paper. Filtering paper is of various kinds. The coarser sort is made chiefly of wool, and is of a brown colour; the finer sort resembles in its general aspect white blotting paper, which indeed may be used
as filter paper, if the true material cannot be obtained. The way to make a filter is this: first cut out the paper into the
By means of this little apparatus a filter may be rested on the edge of its corresponding glass, or removed at pleasure, with the greatest facility. Whatever is the size of the filter employed, it should be wetted with distilled water before the liquid to be filtered is poured upon it. A special apparatus is employed for wetting filters and washing precipitates collected upon them. The apparatus is of the following kind.
A thin flask slightly flattened at its base, in such a manner that it can stand without support, is furnished with a perforated cork and two tubes, as represented in the diagram, a mere casual examination of which will suffice to show that, if air be blown in through the tube A, water will emerge in a jet from the tube B, fig. 19. This jet may be so nicely regulated, that even the most delicate filter paper can be wetted without any fear of rupture.
By means of a little filter, as just described, it may easily be determined when the point corresponding with the total precipitation of zinc has been arrived at, and this operation may be considered as the type of thousands which constantly occur in the course of chemical analysis. *
Here we may, with advantage, take leave of zine for a time, and begin the consideration of another metal; not that we have nothing more to say concerning zinc, but that our future remarks will most profitably come before the reader by way of comparison. We will take up another metal, and that metal shall be manganese, a very abstruse metal in many respects. The abstruse points, however, connected with it I shall omit, merely directing the student's attention to two points-a means of obtaining it in solution, and a means of precipitating or throwing it down from this solution.
We succeeded in dissolving zinc by means of diluted sulphuric acid. We cannot readily dissolve manganese, or, more properly, commercial black oxide of manganese in this manner. Concentrated sulphuric acid, and oil of vitriol, dissolves a
portion of sit readily; but I shall have recourse to an indirect process of solution, as follows:—Rub together in a mortar two.
parts by weight of manganese, and one part by weight of salammonia. Put the mixture into a crucible of silver or platinum, if thereader possess one of these instruments; if not, into a white gallipot, and heat to dull redness over a powerful flame of gas or spirit, or a charcoal fire in preference; but a common fire will do: allow the mixture to cool, add distilled water, and filter. The filtered solution contains manganese held in solution by chlorine. How the chlorine got there, or why it