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Notes AND REFERENCES.-A. L. S. 60, R.5.--.grand, grown and the co-efficients of these tums are
up.-c. from courir; L. part ii., p 81.--. from roir; L. part 8 X 7 28 x 6
il., p. 110.-c. bien faite, well shaped.--|. quel jarret ferme, achat

56 X 5
1,8,

70 X 4 28, = 56,

70, a firm step.--g. from devenir; L. part ii., p. 88.--\. se complaire,

3

=56

5
to almire himself-i. tout de bon, in good earnest.--;. en somme, 56 X 3 28 X 2 8 X 1
finally, k. L. S. 6, R. 1.

= 28,

7 Whence, the complete expansion of a y to the eighth

power, is LESSONS IN ALGEBRA,No. XII.

(4--4)5 = 8.try + 28.x852 562°43 + 70.«*yl — 56x”y

+ 28x2y6 - Exy + y. (Continuerl from page 116.)

Er. 6. Expand (m + n)?. Here we have, by the same rules, In our Lesson in Algebra, No. xi. page 381, vol. 16., te

(un + ac)? =mtinen + 21m°2 + 35m). + 35111". + 21

more to imns +17.
proposed some Examples for Practice in involution by means of
the Binoinial Theorem. We now proceed to give the solutions

Ec. 7. Expand (a + b). Here we have a tab) =
of these examples by that theorem,

29 + 9a 5+ 36a7b2 + 8420 + 126a' + 126a11 + Stirl

+ 36a-87 +9abe + .
Exc. 1. Expand (x + y)? Here, according to the Binomial
Theorem, rules 1, and 11. p. 383, the signs and indices of the

Er. 8. Expand (r + y). Here the answer is
quantities of each term of the expansion will be the follow- 2:10 + 10y + 45.790+ 120374) +- 210.yl + 252.r*y + 210
ing:

zky at 120 x"yi to 45.7'y to 10.ry! +. ***, toy, + xy, ty.

E'. 9. Expand (x -- y)13. IIere the answer is Next, according to the theorem, rules in, and w. p. 383, the -13 13./2y + 78.x117? 256x:20,3 + 715.1"y! - 1287.8 + co-efficients of the successive terns will be the following:

1716.5 7 + 1716.xoyi + 1287.1999 · 715r4y + 286. * ylio 3 X 2 3 X 1

- 78x"yll + 13xyl2 -- 313. 1, 3, =3,

1; 2

Ex. 10, Expand (a - b). Here the answer is Whence, by combining these results, we have the complete ai --- 7ab + 21ab? 3õulbs to 35alt - 21a-b3 +70:26 - . expansion, or third power of x + y, as follows:

Er. 11. Expand (a + b). Here the answer is (x + y)} = 33 to 3.x"y + 3xy2 + 43.

a“ + 8076 + 28ab2 + 560°/3 +70ab! + 56u2b5 + 28.1?+

Sabi +64 Ex. 2. Expand (+) Here, as before, the signs and indices of the quantities in each tern of the expansion will be the Er. 12. Expand (2 +/). llere, treating the number 2 first tullowing:

as if it were a letter, we have by the rule a', toob, + , +ahl, +64

(2 + x) = 2 + 5.243 + 10.20.20 +10-2?x+- 5.2.r' + r), Next, the co-efficients of the successive terins will be the where the point or dot is employed as the sign of multiplicafollowing:

tion. Now, by raising the number 2 to the powers indica ed

by the indices, and multiplying these powers by the co-vill4 X 3 6 X 2 1, 4,

cients, we have for the answer,

(2 + x) = 52 + 80x + 804x + 40.29 + 10++. Whence by combining these results, we have the complete Er. 13. Expand (a - bx toc)}. Ilere, by putting ~ -- box expansion, or fourth power of a + b, as follows :

=d, we have (a + b) =a + 40%) + 6a?l2 to 40b3 + bl.

(a - bx + r) = (a + c) == + 3dl-c +- 3110 otc, by the

rule,
Er. 3. Expand (a - b). Here, as before, the signs and
indices of ille quantities in each term of the expansion will be

Now, restoring the value of d, we have
the following:

(a - bx + c)=(a - 1.7) ot 3c (a - bx)2 + 36(-- but)

+03
(4%, - a'b, ta'b, abi, tall, -- abs, +7.

But, (-- 17): = 23. 3a (4x) + 3a(b) (b.x)
Next, the co-efficients of the successive terins will be

3a-v,+ 3abbed;
6 x 5 15 X 4 20 X 3

15 x 2

Also, (a --tr) =a? 2abr +0, 1, 6, - 16,

= 15,

Anil 301

b) = 314c Cuber to bed";
6
And 3c (11
br) = 344?

3.14;
6 X 1

Now, collecting all the terms thus obtuined, we have = 6, 51.

(a bx + 0)3 = a. 3a bi to 3a5.2.2--- bx + 31°c -- Babce

+3620x! + 3ac 3le'i to.
Whence, as before, the complete expansion, or sixth power
of a + b, is

E... 11. Expand (a + 3bc)! Here the answer is

(a + 3he) = a + 30-(316) + 34(316) + (3bc) Q6 6a’b + 15a6b2 ~ 20 a 13 + 15 a-b! · Gabi + 16.

= a + 9a-bc + 27abet270 c!. Ex. 4. Expand (+9). Here the signs and indices of the Ex. 15. Expand (2ab -- 2)! Here the answer is quantities are

(2ab-3) = (2ab) - 42cm) + 6(2) 4(27)x+ x3, + rty, to 334, +*y', + xy", + y.

=16a16

320 6x + 24002 Sabas taka And the co-efficients of these terms are

Ex. 16. Expand (4ab + 50°). Here we have 5 X 4 10 X 3 10 X 2 5 X 1

(tab + 5c = (40%) + 2(1ab) (56") + (50)
1, 5, -= 10,

= 10,
--- 5,
=1.

= 16a-be to udabe: 1.250,
5

Ec. 17. Expand (3x
Whence the complete expansion of x +y to the fifth power,

by). Here we have
is

(3x – 6y) = (3.r) 3(3.x)? (64) +- 3 3x) (6y). - (Oy)!

27.03 (c + y) = x + bry + 10.x2y + 10x+y3 + 6xy + yo.

1623-y + 324.cy --- 216y.

Ex. 18. Expand (5a + 3d)3. Here the answer is Er. 5. Expand (x - y)”. Here, the signs and indices of (5a + 31)3 = (5a)3 + 3459)2 (34) + 3(5a) (32)2 + (30)" tne quantities are

= 125a3 + 2254d + 135ad2 + 27d3. * 26, -ty, trefy, yo, + sigtry', + *?y, - xy', +y;

• 11. WOOLLEY (Ross) correctly solved 13 of these exerciscs

1;

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2

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171

2y =

internal imaginations of the human soul, of all the other languages, SOLUTIONS TO ALGEBRAIC QUERIES. ancient or modern, living or dead, that have since adorned our

earth. Now, it is such a language as this we all stand in need of, Solution to the Algebraic Problem p. 61, ro'. v. By JAMES Hione, in this world of sin and imperfections; and to our alter the Bloxwich.

discovery of it, there!ore, should we bend our earnest minds: it is

to be lamented that we retain so little of the original goodness o. Let x and y be the two numbers, then by the question we our progenitor, and why should any refuse to seek for and obtain have

what he may? Nay, but let us each and all press on with the ay = 22 — 3*, (1.)

most assiduous, agonizing diligence, and we are sure to be amply 32 + y = 20 33, (2.)

repaid; for what arails our pains, or wherein should they be By multiplying boih members of (1.) by x + y, cancelling accounted of, if, when we have mastered the glorious object of our and transposing, we have

desires, we have then achieved the noblest performance that the 2xy = x3 — yo, (3.)

human inind is capable of here below, where even the best tbings By equating the values of 13 - 7, found in (2.) and (3.), we

are verily only shadows when compared to the never-failing enjoy

inents of a better world? have 2xy = x + y (4.)

Secondly. The fact that the Irish is the oldest living language, By adding the corresponding members of (1.) and (4.), and is incideru reason why it ought to get the preference with every dividing by 2x, we have

I will not now insist on the duty which devolves upon us Chris. x=y2 + ly, (5.)

tians to labour for the conversion of the Jews, but if I may be By substituting this value of x in (1.), cancelling, reducing, allowed to take a comparison from hence, I would say that the and dividing by y’, we have

reasons why we should prefer the Irish are analogous to those that y = ; whence y=175.

ought to induce us to strive for the return of the seed of Abraham By substituting these values of y: and y, in (5.) we have

to the fold of their true Shepherd. x=+5.

For, let me ask, why has God preserved the seed of Israel unmixed with other races of men and why are they yet a

distinct people ? Will anybody attempt to affirm that it is By J. K., Lancaster.

for the purpose of making them to be universally de-pised,

and in order that they might be an everlasting disgrace? Not so. - vo, (19)

And why has the Irish been preserved from the beginning in like *+1 = x3 y?, (2.)

manner? And why does it yet exist a pure and living language, By multiplying (1.) by (x + y) we have

preserved unadulicrated in our little corner of the great dwelling xy(x + y) = x3 – xy2 + x’y 48, (3.)

house of the hunian family? Is not this a sure, earnest plodze and By subtracting (3.) from (2.), member by member, and sepa- scal, that it is yet to flourish, spread abroad its branches, and

rating the right-hand member of the remainder into therewith cover the earth as the waters do the seas? Ilence, Mr. factors, we have

Editor, you will admit of its superlative clain.

As an Irishman, I, too, am proud of its primeral antiquity, for 2? + y2 — xy(x + y) = xy(y x), (4.) By adding the members of (1.) and (i.) crosswise, and trans- these I shall not aitempt to perplex you just now. Horever, this

which I think I could produce good circumstantial proofs; but with posing, we have

is not because that being so complicated you could noi well make 222 = xy(2y + 1),

them out, but because I have one or two topics more to touch upon, y(y + 1)

and should therefore be afraid of trespassing too much on your ;

patience by lengthening a letter which is perhaps already too long.

I will only add on this head, that I am myself very anxious to learn By substituting this value of x in (1.) and dividing both sides Irish, as are also numerous others of your readers on this side by y, we have

the chem.cl, and I give you my word that if you commence it, and

go on with your wonted vigour and perspicuity, you will obtain 2y + 1 (

lasting honour in tliis "Sister land." I am not, of course, altogether 4

a novice at it, having been a pretty apt chap at picking up word, By reducing this, and removing denominators, we liave

and improving my knowledge of them by perusing Ncilson's

Hi! Grammar,” and “ John O'Daly's Primer," a little book 4y + 2 = 4y + 4y +1-4,

which, by the way, I think you could not too warmly recommend. Or 4 j = 5; whence y = 15,

I am now going to propose one or two questions. llave you 5+5

published your second Arithmetic yet? I have made myself well

acquainted with your first, and am looking out anxiously for the 4

other.

Would you kindly inform me how tlie Log rizlinis for those Nos.

betrveen 1 and 10, eic, are found, as I could not make it out in ally CORRESPONDENCE.

work upon them which I have seen? If anything to the point is
said in ihe P. E. I should like to know the page. Why did you

not give us some instructions in Laud-surreying? Wiil you siorily
THE IRISH TONGUE.

commence Mensuration ? I like very niuch your “Lectures ont Sir,–If I mistake not, you promised on a former occasion to

Euclid,” only they are too" fer and fur belwcen." - Ever yours, etc.,

A LOVER OF IRISI. commence, in your renowned educational sheets, a series of lessons om

[ het in das blockteads

' might obtain a tolerably good acquaintance by his good circumstantial proofs, " we have no doubt that oue hebt ihat truly original, independeut, luncompounded, and a ten readers, like ourselves, being open to conviction, would auxiou." sonu tungls melodious language. Now, ulichongnu i do not wish desire to have a series of lessons such as he wishes for. el ter understand by what I'ain just"going to rematk, that your are we to do, when we have numerous students praying is 10

am bold to inform you that this language por esessies polainas alive them crebrand others imploring us to give them weish, and the Greek and Latin themselves, Caticlate coCaspire to non deve estar craslicand the grebrew in point of antiquity: We renember a scoich corting this view of the subject phich it cam endeavouring to re- lightander endeavouring to prove to us that the Galic was tlie eneo hilo four notice , you will vermit me, sir, te vay becere you language spoken in Paradise, because the name for

an egg in what hans, otro if oxy reasons for making the above allegationes and tongue is me hatural Sound which a man makes in sucking eggs; of It is universally admitted that the Almighty created our first father of his physiog. when he uttered it, and the comment we made upon

will observe, that it is the angelsi perfect of deza tangiarela course, we can't even spell it, but we well recollect the appearance Adam, boly, püre, and perfect; and forasmuch as He could not it at the time, viz. that he must be right, for there were no egythat the language which Adam used was simply and absolutely perfect and complete in all its parts. You may be convinced that it

that Eve must have taughi us all. possessed qualities the most to be admired--the most compre- at present to permit us to touch it. As to the Logarithms of larg benaiye simplicity, and the most admirable adaptation to the nuinbers, let him consult pp. 47, 60, and 61, vol. v. of the P. E.;

Our second Arithmetic is in demand, but our hands are too full

Whence x =

29 1 = 120+12

-1;

And 2 =

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but we shall touch upon Logarithms again, in our future Lessons

Then fondly to her bosom pressed in Algebra. Some instructions in Land-surveying have been given

My little form, and said, in vol. 1. of the P. E., see pp. 204 and 228 ; and in Mensuration,

Oh, Willie dear, remember me,

When I'm among the dead.
see pp. 172, 173, and 174 of the same volume, Euclid is coming
faster now.)

But, mother dear, you will not die,

And thus your Willie leave?
MANUSCRIPT MAGAZINES.

That you shall soon be called away
SIR, --For some time past I have been studying English Gram-

I can't, and won't believe.
mar, and I think the more I study the less progress I make. Per-

Bat, ah! one month had scarce gone by, haps the reason I do not make any progress is, the want of some

When she was near her grave; one to assist me. If five or six of the female students of the P. E.

Oh! how my little heart did wish would agree to study Dr. Beard's Lessons in English, on the same

That I her life could save. plan as your correspondent T. J. proposes in No. 105, I should be

But, ah! that wish was all in vain, very happy to join them. And you know if there was any thing we

For soon she went to rest; did not understand we might apply to you for instruction. What do

And I shall never see her more, you think, Sir ? Would it not be a good way to obtain a correct

Till I am with the blest. knowledge of our own language? I wish (if it would not be too

'Tis now some twelve months since I've seen much trouble) ihat you will mention it in the P. E., as perhaps it

The place I used to roam;
would induce some one to come forward and act as conductress.

But now I'm going back again
I am afraid I am giving you a large amount of trouble, but my

To our old house at home.
desire to know more of my own language is great; and not having

But, ah! what pleasure can be there?
any one to assist me my difficulty seems double.

No mother will I find;
Do you think I need study penmanship any more ?-I am, etc.,

But strangers now must welcome me,
A VILLAGE GIRL.

And some may be unkind,
Barrowden, Rutland, 24th May, 1854.

There's but one spell that draws me there,
It is my mother's tomb;
I'll visit that, and then depart

From our old house at home.
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The First Three

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spheroïdal state of liquids, it is supposed that the liquid gloON PHYSICS, OR NATURAL PHILOSOPHY. bule is supported at a distance from the vessel by the tension

of the vapour which is produced at its surface, so that the No. XXXVIII.

liquid not being heated by contact, but only by radiation, is

converted into vapour very slowly; and the more so, because (Continued front page 160.)

water being diathermous to rays emitted from an intense

source, the greater part of the radiant caloric traverses it CALEFACTION.

without heating it. M. Boutigny considers that the cause

which hinders the liquid from wetting the metal is a repulsive
Spheroidal State.- When liquids are poured on incandescent force which is generated between the liquid and the heated
metallic substances, they present remarkable phenomena, body; a force which becomes greater in proportion as the
which were first observed by Leidenfrost, about a century ago, I temperature of the latter becomes more elevated. This hypo-
and which have been since studied by some philosophers. It thesis agrees with the following observation made by Mr.
is to M. Boutigny d'Evreux, however, that we owe the know- Perkins. A stop-cock having been placed on a steam boiler
ledge of certain curious and important facts on this subject. below the level of the water within it, the liquid would not
It has been long known that when drops of water are thrown run out by the stop-cock, when opened, if the sides of the
upon red-hot iron plates, they assume a globular form, and boiler were raised io a very high temperature, although the
employ less time in vaporising in proportion to the degree of interior pressure was very great; but if the temperature of
heat attaizied by the plates. This property, which has been the sides was lowered, the liquid would rush out with con-
carefully studied by M. Boutigny, is called by him calefaction; siderable force.
and the bodies found in such a state are said to be in the

In accordance with the results of these curious researches
spheroidal state. If a capsule (a small cup) made of silver or

on the spheroïdal state of liquids, M. Boutigny has latterly platinum, of considerable thickness, be powerfully heated, and connected the phenomena of calefaction with facts formerly a few drops of water be dropped into it by means of a pipette, deemed incredible, and which now-a-days are fully substanit is observed that the liquid does not spread itself, nor wet tiated. It had been asserted that men ran bare-foot upon the capsule, as it does at the ordinary temperature ; but that melted metal in an incandescent state, plunged their hands it assumes the form of a flattened globule. In this state the into melted lead, etc. Coupling these assertions with the water takes a rapid gyratory motion at the bottom of the stories of trial by fire, and incombustible men, he was desirous capsule, and not only does it refuse to enter into ebullition, of verifying these phenomena. After some unsatisfactory but it vaporises fifty times more slowly than if it were in the efforts, he found that in founderies some workmen, more hardy boiling state. Moreover, the capsule be cooled, there will than others, passed their fingers into incandescent cast metal; happen an instant when it is not sufficiently hot to preserve and some ran bare-foot upon a trough of melted iron which the water in the spheroïdal state; its sides are then wetted by had just issued from the furnace, etc. He himself passed one the liquid, and suddenly a violent ebullition takes place. hand right through a stream of red-hot iron about a quarter

All liquids may assume the spheroïdal state, and the tem of an inch broad, and dipped his other hand into a vessel full perature of the capsule in which the phenomenon is produced of incandescent metal of the same description. He repeated is more elevated in proportion as the boiling point of the liquid this trial at the Mint in Paris, and plunged his hand, without is higher. Thus in the case of water, the capsule must be hurt, into a mass of silver in a state of complete fusion. M. Bouheated to, at least, 200° Cent. or 3920 Fahr.; and in that of tigny considers that there is no contact between the hand and alcohol to 134o Cent, or 273o.2 Fahr. M. Boutigny has the metal; the perspiration with which the epidermis or observed that the temperature of liquids in the spheroïdal under-skin is always more or less impregnated, passing into State is always lower than that of their state of ebullition, as the spheroïdal state, reflects, without absorption, the radiant in the following examples :

heat proceeding from the melted mass, and does not heat it Liquids.

enough to throw it into a state of ebullition. Whatever may
Spheroïdal Temperature.

be the explanation of these facts, well authenticated now, they
Water
950.5 Cent. or 2030.9 Fahr.

completely account for the reality of the frequent success of
Alcohol

75 5
167 9

the trials by fire, in the days of ignorance and barbarism.
34

93.2 Sulphurous Acid (liquid) 10:5

13 •1

DENSITY OF VAPOURS. Notwithstanding this reduction of temperature in the By the Density of a Vapour is meant the ratio between the spheroïdal state, the temperature of the vapour produced by weight of a certain volume of that vapour and the weight of the liquids in this state is equal to the temperature of the the same volume of air, at an equal temperature and pressure. capsule; whence it follows that this vapour is not produced Two methods have been followed in the determination of the in the mass of the liquid. This property of liquids, by which density of vapours; the first, employed by Gay-Lussac, is they preserve a lower temperature than that of their ebulli- applicable to liquids which enter into the state of ebullition tion, has led M. Boutigny to the discovery of a remarkable below 100° Cent. or a little above it; the second, adopted by experiment, that of the congelation of water in an incan- M. Dumas, may be employed in the case of temperatures descent capsule. He heated a platinum capsule to a white which may rise to about 400° Cent. or 752° Fahr. The appaheat

, and poured into it some drops of anhydrous sulphurous ratus of Gay-Lussac is represented in fig. 198. acid. This liquid, which boils at -10° Cent. or 14° Fahr., . It is composed of a cast-iron vessel filled with mercury, in behaves in the capsule like water; that is, its temperature which a glass cylinder, m, is immersed; the latter is kiled pburous acid, a small quantity of water, the latter, being cooled by a thermometer

, T. In the interior of the cylinder is a by the acid, is instantly frozen ; and 'the capsule being still graduated bell-shaped glass, c, which is at first filled with red-bot

, we take out of it, to our great surprise, a piece of mercury. In experimenting with this apparatus, the liquid In the spheroïdal state there is no contact between the sented at a, on the left of the figure ; this bubble being then Liquid and the heated body. M. Boutigny proved this by the hermetically sealed, it is weighed; and by subtracting from placed it perfectly horizontal; he then poured on it'some weight of the liquid it contains. The bulb is then introduced depes of water coloured black, and this liquid passed into the into the glass c, and the apparatus is gradually heated until opheroïdal state : next, he placed the flame of a candle at a the water in the cylinder reaches a temperature higher by distinctly visible, for some time, bet ween the spheroid of water would enter into the state of ebullition. The bubble then bept at a small distance from the plate, or that it made its tension of the vapour into which it is converted, the mercury Tibrations so rapid that the eye could not distinguish them.

pary that the bubble be so small as to allow of all the liquid

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VOL. Y.

introduced into it being converted into vapour. This conver: moment when the jet of vapour stops, which takes place wher. sion completely takes place when the bath, having reached all the liquid is vaporised, the tapering point of the deck is the temperature of ebullition which belongs to the liquid hermetically sealed, the temperature of the bath and the enclosed in the bubble, the level of the mercury is still a height of the barometer being noted at that instant. Lastly, little higher in the interior of the glass than on the exterior, This, indeed, shows that there is none of the liquid remaining

Fig. 199. unvaporised; otherwise, the interior level would be a little lower than the exterior level. We are, therefore, sure that the weight of the liquid which was in the bubble, exactly

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Fig. 198.

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when the globe is cooled and carefully wiped, it is weighed again, and the weight, p', thus obtained, represents the weight of the vapour it contains plus the weight of the glass, minus the weight of the air displaced. To obtain the weight of the vapour, therefore, we mus: subtract from the weight r' the weight of the glass, and add to the remainder the weight of the air displaced, which will be easily done after the volume of the globe has been found. To determine this, the neck of the globe is immersed in the mercury, and its extremity is

there broken off with a pair of small pincers. As the vapour represents the weight of the vapour which is formed in the is condensed, there is a vacuum created in the globe; and the glass c. As to the volume of this vapour, it is ascertained by mercury rushes into it by the pressure of the atmosphere, and means of the graduated scale on the glass. We have only completely fills it, if all the air has been forced out of it. now to calculate the weight of a volume of air equal to that Then by pouring into a graduated vessel, the mercury which of the vapour, and to divide the weight of the vapour by that fills the globe, we determine its volume at the ordinary temof the air ; the quotient is the density or the specific gravity perature. By calculation we easily deduce from this, the required.

volume of the vapour at the temperature of the ba:h, and con. The process which we have thus described is not applicable sequently the volume of the vapour at the same temperature: to liquids whose boiling

points exceed 150° or 1600 Cent., that Having ascertained by this process, as well as by that of is, 3020 or 320° Fahr. The reason is, that in order to raise Gay-Lussac, the knowledge of the weight of a certain yolume the oil with which the cylinder is filled to these temperatures, of vapour, 'at a determinate temperature and pressure, the the mercury, in the vessel must be heated to a degree con- density of the vapour may be ascertained by calculation. If siderably higher, a degree at which it produces yapour from any air remains in the globe, it will not be completely filled the mercury which it would be dangerous to inhale. Besides, with the mercury; but the volume of mercury introduced in the graduated glass vessel, the tension of the mercurial will still represent the volume of the vapour. The following vapour would increase that of the vapour which is the subject table shows the densities of some vapours as compared with of experiment, and would thereby become a source of error in that of air, at temperatures a little higher than that of the the result,

boiling points of the liquids from which they are generated :The following process, invented by M. Dumas, can be employed at any temperature up to that at which the glass would

Table of the Densities of Vapours. become soft and flexible, that is, about 400° Cent, or 752° Fahr. The apparatus is composed of a hollow glass glohe, , with a

Vapours.

Densities. tapering neck, fig. 199, and capable of holding about a pint of

Common air

1.0000 water. This globe is completely dried within and without,

Vapour of water

0.6235 and weighed when it contains air only, which gives r the

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alcohol

1.6138 weight of the glass. The liquid to be vaporised is then intro

do. sulphuric ether

2.6860 duced at the tapering point, and the globe is next immersed

do. sulphuret of carbon 2.6447 in a water-bath saturated with salt, or in a bath of neat's-foot

essence of turpentine 5:0130 oil, or of D'Arcet's alloy, according to the temperature of the

mercury

6-9760 ebullition of the liquid contained in the globe. In order to

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8.7160 keep the latter in the bath, there is fixed on one of the handles of the pot or vessel which contains it, an iron rod which is Problem 1. To find the density of a vapour when the weight furnished with a sliding support of the same metal. The of the vapour in grains, its volume in cubic inches, its terapez support carries two rings, between which the globe is placed, rature in Centigrade degrees, the height of the barometer, and as shown in the ligure. On the other handle is fixed a rod of the height of the mercury in the bell-shaped glass are given. the same kind, which carries a thermometer, D. The globe and the thermometer being immersed in the bath, the latter is in cubic inches, tits temperature in Centigrade degrees, 1 the

Let p denote the weight of the vapour in grains, v its

volume heated a little beyond the boiling point of the liquid in the height of the barometer in inches, and a the height of the globe ; then the vapour, as it issues

through the extremity of mercury in the glass vessel also in inches ; it is required to the neck, drives out the air in the apparatus ; and, at the Bind D the density of the vapour.

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