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petont for the operator to have mixed it with oxygen previous | although not very correct in its results. The second saethod to eombustion, 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. 26, 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 in. genuity of Dr. Priestley. In my sketch, fig. 26, I haverepresented
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 pneu. matio 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, 80 that an electric spark should pass through the space s': 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 scarcely 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 en of brass is not permanent, but admits of being screwed off at m', and the instrument attached to this point of i Taking a piece of tin or iron, or other metal plate, fold it into junction to the receiver of an air-pump. The student will easily understand, that the air originally contained in the vessel
Fig. 28. 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 for 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
In great concern he ran to bear the sad tidings. a notch in the lower or base edge of the cone, and the stand is The words printed in italics form an adverbial phrase. Adverbial made. The use of it will be evident from an examination of the diagram, fig. 28. The notch admits the gas delivering phrases involve what may be called an adverbial object; thus, in tube, the truncated apex delivers the gas into the bottle, which great concern is an adverbial object. Adverbial objects may be
various ; as, rests supported on the sides. If the student were not told of these contrivances he might
1. Of time: On arriving home I hastened to bed. think me remiss; but I want to create a feeling of independence 2. Of place :
He slew his foe in the dell. in his mind, to impress him with the conviction, that in 3. Of manner: The father begged his life with many supplications. the majority of chemical operations involving the use of mechanical contrivances, many different methods admit of
An object, then, may be not only single or compound, being followed, each equally good. The support just described Single: He launched the ship; is useful, and not inelegant, but I shall not quarrel with a Compound : The waves overwhelmed the boat and the crew; student who tells me that two bricks set edgeways in a pan of water, fig. 29, furnish a support which is nearly as good. near or remote ; as,
Near : He sold his desk ;
Remote: He sold his desk to his clerk; but also adverbial, and that of three kinds, -of time, of place, of
A simple sentence is a sentence which has one subject and one affirmation or predicate ; and a compound sentence is a sentence that has more than one subject and more than one predicate. The component parts of a compound sentence are called its members. These members may be two or more; they may also each form a separate sentence:
Compound Sentences of two Members. 1
2 The great fault of most books which treat of chemical ma
He will perish who loves unrighteousness. nipulations is this :--they represent the apparatus which is
2 not intrinsically best for gaining any particular result, but the The lark sang his matins and sank into his nest. 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.
1. Some one will perish.
2. The lover of unrighteousness will perish.
The second sentence is equivalent to these two statements :LESSONS IN ENGLISH.-No. LXXII.
1. The lark sang his matins, By John R. BEARD, D.D.
2. The lark sank into his nest. COMPOUND SENTENCES.
Compound Sentences of three Members.
3 nouns standing in apposition to the principal noun; as,
1. The Queen arrived. Principal Noun. Apposition.
2. Before then the fleet had weighed anchor. Victoria, Queen of England, conquered Burmah.
3. Before then the fleet had sailed. 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.,
becomes in the analysis three individual sentences.
It is easy to see that the members may be increased almost at
The sick and all but dying man drinks water and revives. called
Compound sentences have members of two kinds, the principal Subject- Accessaries.
and the accessary. The principal member is that which enunciates
the leading thought, the accessary member is that which enunciates being Queen of England Victoria when Queen of England
the subordinate thought :-
The man drinks (and) is refreshed. These accessaries are denominated subject accessaries, because they qualify the subject. Accessaries may qualify the object namely, interposed
or appended. An accessary member is inter
The accessary member (or members) may be of two kinds, also; e. 8.,
posed when it appears in the body of a sentence, being introduced Object- Accessaries.
by a relative pronoun, a relative adverb, or a conjunction ; e. ., by her virtues. Victoria gained respect for the good laws she sanctioned.
Principal. in consequence of her birth.
INTERPOSED. who drinks
is refreshed These accessaries, whether they attach to the subject or the Rel. Pron.: The man
The man when he drinks object, may be characterised as
is refreshed Conjunc,: The man if hedrinks
is refreshed Adverbial Accessaries,
Appeided members are added by means of conjunc ons The essential quality of the adverb is to declare the quality of adverbs, and pronouns:an affirmation, thus :
APPENDED Bat the quality of an act may be assigned by an adverbial phrase Conjunc.. The man drinks
and is refreshed. as well as by a simple adverb ; e, g.,
Adv.: The man is refreshed when he drinks
qohe principal member may be expanded; e. g.,
"The malcontents made such demands as none but a tyrant could
refuse." -Bolinbroke. Principal Member Expanded.
What is a relative which performs the double function of a subThe man drinks and is refreshed.
ject and an object, being equivalent to that which, and used in only The man eats and drinks
the neuter gender ; e. g., The accessary member may also be expanded ; e. 8.,
“My master wotteth not what is with me.”—(Gen. xxxix. 8.)
As a subject for exemplifying the doctrines laid down in regard Interposed Accessary.
to the structure of sentences, I shall take some sentences from drinks
Daniel Defoe, a writer of idiomatic English.
“Oxford makes by much the best outward appearance of any Appended Accessary Expanded.
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." The man drinks (and) (is refreshed. is refreshed and strengthened.
Here I must premise that the form “ the best outward appear. Sentences may be further divided into the direct and the inverted. ance of any city,” &c., is incorrect, and should have been the A sentence is direct when the principal member precedes the best outward appearance of all the cities I,” &c. This compound accessary; e. 8.,
sentence may be reduced into these simple sentences :Direct Sentence.
1. Oxford makes a very good appearance.
2. Oxford makes an appearance better than many cities. Principal.
3. I have never seen a city with a better appearance than The man drinks (and) is refreshed.
4. Oxford is visible for several miles round. A sentence is inverted when the accessary sentence precedes the
5. Oxford is visible from all sides. principal:
6. Oxford stands in a most delightful plain. Inverted Sentence.
7. Oxford is adorned with the steeples of several colleges. Accessary. Principal.
8. Oxford is adorned with the steeples of several churches. if he drinks.
9. The architectural decorations of Oxford make a glorious show. The man is refreshed when he drinks.
The resolution of this long sentence into the several distinct should he drink.
propositions which it contains, has, by showing the meaning of the Relative pronouns are such pronouns as relate to some pre- tions which those parts sustain to each other, thus :
several parts, prepared the way for our exhibiting the logical relaceding noun, called the antecedent; that is, the foregoing word;
Logical Relations of the Sentence.
the subject to 2 Antecedent. Relative. Predicate.
makes together with 3 the predi.
cate to 1 Subject. The man who drinks water is wise.
3. the best outward appearance the object to 2 Object. The men whom he met he struck. 4, of any city
adverbial object to 2 The relative must agree with its antecedent in person, gender,
5. that I have seen
appended accessary to 2 and number; e. g.,
6. being visible
accessary to the subject 1
7. for several miles round adverbial object to 6
8. on all sides
9. in a most delightful plain 1.
read. 3 H.
10. and adorned
second accessary to 1
11. with the steeples, &c. adverbial object to 10 In number one, who is of the first person, because I is of the 12. which makes a glorious ehow appended accessary to 10 first person ; who is of the singular number, because I is of the Several of these parts may be analysed or explained; e. g., singular number. The effect of the relative on the verb is more Number three consists of the definite article the, the superlative clearly seen in the second instance, where an s is added to the verb, adjective best, the adjective outward in the positive degree, and which accordingly appears as reflects.
the common noun appearance, which is the object to the verb
makes. As the language is now written and spoken by the best authori. ties, the relative who has one change of form in the nominative,
Number six presents a case of explanatory apposition, since namely, in which ; which is commonly applied to things. Who, being visible is subjoined to the subject Oxford in order to state however, has a genitive and an objective, as well as a nominative some additional facts respecting it; number ten stands to numcase, and may be declined or inflected thus :
ber one in the same relation.
Number twelve presents an appended relative accessary sentence WHO DECLINED.
of which these are the components ; namely, which, a relative proSingular and Plural.
noun agreeing with its antecedent steeples ; make, a verb in the Masculine. Feminine. Nerder
indicative mood, third person, plural number, agreeing with its SINGULAR Nom. who
which subject which; a, the indefinite article limiting show; glorious, an Genit. whose whose of which (whose) adjective qualifying show; show, a common noun dependent on PLURAL. Object. whom whom which
or the object to the verb make, Viewed structurally, this Instead of whose and which we sometimes find whereof.
appendage stands thus :
Verb. in lieu of who or which, being applied to both persons and
Object. things ; e. g.,
Which make a glorious show. “He that reproacheth a scorner, getteth to himself shame.”- By way of applying what you have learnt, tako portions of any (Prov. ix 7.
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. 8.,
it consists, and explain by grammatical analysis (that is, “parse")
the several components. In other terms, convert each of these from that centre, it follows that the intensity of gravity will compound sentences into simple sentences. Distribute each simple increase or decrease, according as the bodies approach to, or sentence into subject and predicate, distinguishing the verb (the recede from, the general level of the earth's surface. This variacopula) and the attribute. Next, exhibit each compound tion, however, is not apparent in the ordinary phenomena which sentence in its several members, showing what are principal, what are observed at the surface of the globe, because, its radius accessary, and what appended, what interposed; together with being nearly 4,000 miles, the distance from the centre is sensibly the accessaries to the subjects and objecis, and the adverbial the same when a body is elevated by a few hundred yards. objects. Finally, give the grammatical analysis of the whole. 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 ON PHYSICS OR NATURAL PHILOSOPHY. within certain appreciable limits.
2. The second cause which modifies the intensity of gravity is No. VI.
the centrifugal force. A force which produces a curvilinear motion, LAWS OF GRAVITY; PENDULUM.
and which gives to bodies under the influence of this motion á
tendency to fly off from the axis of rotation, is called contrifugal. (Continued from page 63.)
It is demonstrated in treatises on Rational Mechanics, that the
centrifugal force is proportional to the square of the velocity of Formulæ relating to Falling Bodies. The second and third laws rotation; whence it follows that, under the same meridian, it of falling bodies may be respectively represented by the formulæ increases as we approach the equator, where it reaches its maxiv=gt, and s=>. For, let g be the velocity acquired at the end mum, because there the greatest velocity takes place. At the of a second by a body falling in a vacuum, and v its velocity poles the centrifugal force is zero. At the equator, the centrifuafter t seconds ; then, the velocities being proportional to the gal force is directly opposed to gravity, and is equal to ido of its times, we have g:v::1:t; whence r=gi (1). Again, a body intensity. Now 289 being the square of 17, it follows that, if the which falls during t seconds by a motion uniformly accelerated, motion of rotation in the earth were 17 times slower than it is, the with an initial velocity equal to zero or 0, and a final velocity centrifugal force at the equator would be equal to that of gravity, equal to gt, will describe the same space as if it fell during the and all bodies on its surface in this latitude would be on the whole time t by a uniform motion, with a mean velocity between point of being projected into space. O and gt, that is, with the velocity gt. Now, in the latter case, As we proceed from the equator towards the poles, gravity is the motion being uniform, the space described is equal to the less and less affected by the centrifugal force. This happens chiefly product of the velocity and the time; whence, denoting this space because the centrifugal force decreases in proportion as we recede by s, we have s= gtxt=€ (2).. The demonstration of from the equator, and also because that, at the equator, the centhese theorems is given mathematically in treatises on Dynamics; trifugal force is directly opposite to that of gravity, whereas, in SGB Whewell's Mechanical Euclid, and other elementary works proceeding towards the poles, its direction becomes more and of the same description.
more inclined to that of gravity, and thus loses intensity. Thus, If in the formula (2) we make t=1, we have s=19, whence in fig. 15, in which PQ represents the axis of the earth, and Er the 9=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 1611 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 1's 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 32 feet per second.
In formula (1) the velocity v is expressed in a function of the time; that is, an expression in solving the number denoting the time; but we can likewise express it in a function of the space described, by eliminating t from the two formulæ (1) and (2). For, from the first, we have t= =, whence t =
; now substi9
equator, at any point a, the centrifugal force is represented by tuting this value of tz in formula (2), we have s=$9X
the straight line A B perpendicular to the axis at K; now the force of gravity which acts in the direction of the radius CD, is
diminished by a quantity represented not by AB, but by a D, ; ;
and multiplying both sides of this equation by 29, we have which is the composant of the centrifugal force acting in the • 2g
direction A D. v=2g8; and extracting the root, w have finally, v=V 298; hence, we conclude that, when a body falls in a vacuum, the
3. The intensity of gravity is also modified by the depression velocity acquired at any given instant is proportional to the of the earth at the poles; for, in the vicinity, and at these points, square root of the height of the fall.
bodies are nearer to the centre of the earth, and consequently The formulæ v=gt, and s= } gta, having been determined by
more subject to its attraction. 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 cases where the heights of the fall are inconsiderable, as a conmust be observed, that as g denotes the acceleration of the stantly accelerating force; and that the measure of its intensity velocity imparted in each second by the accelerating force, the is the velocity imparted in one second of its fall to a body falling value of g will vary with the intensity of the force.
in a vacuum, without regard to its mass, seeing that in a vacuum Causes which Modify the Intensity of Gravity-Three causes all bodies fall in the same time. This velocity is represented in have an effect in making the intensity of gravity vary; 1st, the general by 29; it increases from the equator to the pole, and at clevation of the place above the ground, or general level of the London it is 324 feet. carth's surface; 2nd, the centrifugal force due to the earth's The Pendulum.—The general name of pendulum is given to rotation on her axis ; 3rd, the depression of the earth's surface every solid body suspended at one point on a horizontal axis, near the poles.
around which it oscillates. There are two kinds of pendulum; 1. Since terrestrial attraction acts upon bodies as if the whole tho simple and the compound. mass of the globe were colici ted at its centre, and this attraction The simple pendulum (which exists only in idea) is that which a is upon them in the inverse ratio of the square of their distance I would be formed by a heavy material point suspended by a per
fectly rigid rod, inextensible and without weight, at a point that is, that they are sensibly equal in the same time, so long as round which it freely oscillatos. Of course this pendulum cannot their amplitudes do not exceed a certain limit, namely 2 or 30 be put in actual practice, because it is purely theoretical, and is of the circle. employed only to determine by calculation the laws of the Galileo was the first who established the isochronism of the Oscillations of the pendulum.
small oscillations of the pendulum. It is said that, when a young The compound pendulum may be varied in its form in any man, he first made this discovery by observing the motions of : manner whatever, but it is generally made of a metallic lens or lamp suspended in the dome of the cathedral at Pisa. bob, suspended by an iron or wooden rod, and moveable round a 2. In pendulums of the same length, the duration of the oscillahorizontal axis, such as the pendulum of a clock, the pendulum tions are the same, whatever be the substances of which they are %, in ig: 13 of the preceding lesson, or that exhibited in the composed. Thus, simple pendulums of which the material point following cut, where o is the point of suspension, and c the point is composed of cork, lead, or gold, perform the same number of
of oscillation; in other words, c is the point oscillations in the same time, if they are of equal length.
Compound pendulums are suspended either Thus, if the lengths of pendulums he respectively 4, 9, 16, &c.,
4. At different places of the earth's surface, the durations of the In order to explain the oscillatory motion oscillations of a pendulum of the same length are in the inverse of the pendulum, we shall first notice the ratio of the square roots of the intensities of gravity. simple pendulum cm, fig. 16. When the material point m is below the point of suspen
These laws are deduced from the formula t="v", which is sion c on the vertical passing through that
2g point, the action of gravity is destroyed, or derived from the application of the calculus to the motion of the
rather counteracted; but if the point' be simple pendulum. In this formula, t denotes the duration of an C
transferred to m, its weight p will be decom- oscillation ; !, the length of the pendulum ; 29, the intensity of posed into two forces, the direction of the one gravity, that is, the velocity acquired at the end of the lst second
being in the straight line c m produced to B, by a body falling in a vacuum. Also, a is a constant quantity p--
and that of the other in the tangent m D to which denotes the ratio of the circumference of a circle to its the arc m m n. The composant m B is coun
diameter, which is equal to 3•141592. teracted by the resistance of the point c, but
The first two laws of the pendulum are deduced at once from
1 the composant m D urges the material point to descend from the formula t=rV -; for this formula contains the values a to m. When it reaches this point, the pendulum does not
2g stop; for, in consequence of its inertia, it proceeds in the neither of the amplitude of the oscillation, nor of the density of
the substance of which the pendulum is composed, the value of 1 Fig. 16.
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, 1 is the numerator, and 29 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 direction an. Now, if the same construction be made at any these two extremes there are some points which are neither point of the are an, it will be found that the gravity which accelerated nor retarded, and which oscillate as if they were not acted from m to m with an accelerating force will now act connected with the rest of the mass. These points being all at from to n with a retarding force. It will take away, there the same distance from the axis of suspension, form together an fore, successively from the
moveable the velocity acquired in axis of oscillation parallel to the former; now the distance of the its descent, so that, when it reaches the point n at å height axis of oscillation is called the length of the compound pendu hem. equal to that of the point on, the velocity will become zero, as Hence, the length of a compound
pendulum is the same it was at the latter point. Whence it follows, that the length of a simple pendulum which performs its oscillatio ns in same series of phenomena will be repeated, and the pendulum the same time. Thus in the preceding figure of the com pound will continually oscillate. In practice, this result is prevented pendulum, the point o is the centre or place of the axis of uspenby the resistance of the air, and the rigidity of the cord, obstacles sion, and op the length of the compound mass ; all the points of which can nover be completely annihilated in compound pen- this mase between 0 and c are retarded, and all the pointe dulums.
between p and o are accelerated; but all the points at a are Laws of the Oscillation of the Pendulum.—The passage of the neither accelerated nor retarded, and therefore the point o is the pendulum from one extreme position or point m to the other is n centre or place of the axis of oscillation. called an oscillation or sroing. The arc m n is called the amplitude the axis of suspension ; that is, if we suspend the penduhim by
The axis of oscillation possesses the property of reciprocity with of the oscillation ; and the longth of the simple pendulum in its axis of oscillation, the duration of the oscillations will be the the distance of the point of suspension c from the material
same as before ; in other words, the axis of suspension wil then point m.
become the axis of oscillation. By means of this property, the In treatises on Rational Mechanics, it is demonstrated that the length of the compound pendulum can be found experimentally. oscitlations of the simple pendulum are regulated by the four This is done by inverting the pendulum and suspending at by following laws.
means of a moveable axis, which is placed, after several tri de, ir 1. In the same pondulum, the small oscillations are isochronous ; / such a manner that the number of oscillations performed in the