332

ment, and hoping that much good may accrue from its complete or and thanks; occasional queries of the kind he mentions may be addressed partial adoption by your students, I am, &c.-W. B.

Norwich, Feb. 3rd, 1854.

[We have inserted this letter, because we think the plan a good one, being simple and free from objections which we have had to some other plans which have been proposed. Of course the author has given us privately his name and address, a measure quite indispensable to any proposal of the same kind which we may receive.]

ANSWERS TO CORRESPONDENTS.

T. C. H. L.: We must refer you to previous remarks with regard to the
Italian Dictionary. The matter will be duly considered. With regard to the
Key in each number to the English-Italian Exercises of the previous week, it
would facilitate the progress of some earnest pupils without the aid of a
master, but at the same time further the idleness of by far the greatest
number. To satisfy their curiosity, they would compare the Key with the
exercises of the previous week, and consider themselves exempted from
the task of translating them. A living language is not learned, like a dead
one, merely for the purpose of reading, but also for the purpose of speaking
and writing; and with regard to this latter most important object, the
self-activity of the pupils must be kept up by all means in the power of a
teacher. However, a Key of all the previous English-Italian Exercises will
be given after the termination of each of the principal divisions of the
grammar, and then we think without the above-stated disadvantage.
H. PITT (Birmingham): See our answer to T. K., Clerkenwell. The
problem written out without reference to any diagram, is passably well.
Write to the Editor of the P. B. E. as you do to us.-J. D. (Birmingham):
When the chord of an arc, and the radius of the circle are given, the chord
of half the arc may be found without Trigonometry, thus: From the square
of the radius subtract the square of half the given chord, and the square
root of the remainder will be the distance of the centre of the circle from the

middle of the chord; subtract this distance from the radius, and the remainder
will be the sagitta (or distance from the middle of the chord to the middle of
the arc); add the square of this sagitta to the square of half the given
chord, and the square root of the sum will be the required chord of half
the arc.
Otherwise: subtract the square of half the chord from the
square of the radius, and extract the square root of the remainder. Sub-
tract this root from the radius, and multiply the remainder by twice the
radius; then extract the square root of the product, and it will be the
required chord of half the arc. The versed line is the difference between
the radius and the cosine. See No. 71, part 18.-J. F. TREGS (Glasgow):
Isolated is pronounced fce-o-lat-ed.

T. K. (Clerkenwell): We wish his answer to the Four Ball question
had been right; we have had many solutions, but it is not yet answered.-
UN ETUDIANT (Darlington): Most likely a Greek Dictionary, &c., will be
published.-T. F. (Holborn): The difficulty which he meets with in regard
to exercises in parsing, or any other exercises, would be met by his joining
a mutual instruction society, a thing we have often recommended. If any
six young men, or old men, or men of mixed ages, agree to meet and assist
each other, they can supply the place of a tutor among themselves: and if
any serious difficulty occurs, we are willing to become umpire. It is quite
possible to become a correct Latin scholar, or any other scholar, by dog-
gedly studying the Lessons in the P. E.; but the mutual instruction system
would greatly enlighten and shorten the process. It would even greatly
add to the power of the system, as well as to its interest and its humanity,
if the six mutual instructionists would take some ragged and destitute
juvenile delinquent from the streets, and try to instruct him and make him
a better member of society. By endeavouring to instruct such a one, they
would learn much better themselves, and they would see the human mind
expanding under culture, like a drooping plant transplanted into a new
and better soi!. Oh the pleasure of doing good! They would be amply
rewarded. Their mercy would be twice blessed; it would bless both them
that gave and them that received the precious boon. Remember" that the
Boul be without knowledge is not good."

ECOLIER (Wisbech): We shall take up the subject of Architecture again, when we can get an opening in the P. E.-J. CHILD (Tenby): Logarithms when we can get room in the P. E.-INQUIRER (Bideford): We don't think much of the books to which he refers; as to the Elementary Bodies in Chemistry, we hold in our hands a work of some value, which gives a list of 64 with their names, equivalents, &c. These, of course, will be given in order, in the Lessons in the P. E.-A. B. (Carnarvon): We do not know any College where students are admitted gratis; but what connexion this has with being a British Consul or Ambassador, we do not see!-Tom (Dublin): See our concluding Lesson on Music.-OPIFEX (Eaton Square) will find a description and drawing of the Marquois Scales, or parallel ruler, in the P. E., vol. I., p. 49, col. i, fig. 5, and line 13 from the bottom.-COQUUS (London): There is no such thing as perpetual motion inventible by man. M. GUTHRIE (Liverpool, Box W. 90) wishes an accession to a society of young men who are engaged in carrying on a manuscript magazine. As young men best understand one another, we hope this intimation will incite some unfledged geniuses to come forward and aid the good cause by their contributions. We hope, however, that these contributions will not be like those which the Professor, who used to meet his students in his own chambers finely carpeted, instead of the class-room, requested them to leave at the door.-1. GRIFFITHS (Aberystwith): See pp. 137 and 213, vol. II., P. E.; also pp. 119, 295, and 323, vol. III.; and pp. 207 et seq., U. J. CHEMISTE (Burnley): Right.-HO HYPOMENON, D. JOSEPH (Sunderland) and WM. KEYS, (Hythe): Three or four numbers will complete "Cassell's French Dictionary; and it is expected to be finished in five or six weeks.-C. L. D. (Wales) should study at any one of the affiliated colleges of the U. of London he pleases; also matriculate, and take degrees, but say nothing about his domestic concerns.-D. H. (Driffield): His important communication is under consideration.-GRATUS (Bodmin): Right,

vol. IV.

to us.-SIMPLICITAS (Wemyss): His attempt at the solution of the Mathematical questions for matriculation in the U. of L., is very fair; but a little more perseverance would have been attended with greater success.-PHILOS (London): Any one who wishes us to recommend a tutor, must give his name and address, and free us of expense in the matter.-J. WOOD (Manchester), and YOUNG MAN (Duntocher): We can't advise them.-D. R. B. (Dundee): Vol. II. of "Cassell's Classical Library" is finished.-SECULA but ingenious. As it may be new to some of our young readers, we insert RIST (Bp. Wearmouth) proposes the following question, which is very old, it: An eight-gallon cask of water is to be divided equally between two persons who have no measure of any kind, but a three-gallon cask and a five-gallon cask. How is it to be done?

MNEMONICS (Upper Stamford St.): We have never seen or heard of any permanent good resulting from the application of Mnemonics to the acquiRuddiman's old Latin example sition of Languages or the Sciences. appears to us to be the best rule: Memoria excolendo augetur, that is, "The memory is improved by exercising it."-J. C. (Salisbury): Study the Mathematics.-W. MAUNDRELL (Seven-oaks): "Borrowed a sum s for n u. What ought that sum to be?" Here, the sum u is an annuity. Now years at r per cent., to be paid off by the annual payment of a certain sum the entire sum due for an annuity remaining unpaid for a given period, Dr. Thomson, in his "Arithmetic," p. 275, shows, that in order to find compound interest being allowed on all the money thus remaining unpaid," (a1.-1) u

we must use the formulas =

values given above, and a1 =
(a,-1)'s
question, then, we have only to
process, thus: u =

100+6

n

n

100+r
100

; where s, n, and u, have the In order to solve the preceding

Example: If the sum of £7,905 16s. 4jd. reverse the formula by a simple Algebraic

30

were borrowed for 30 years, at 6 per cent., what annual sum would pay it
7905.81838.06
5.743491; therefore u =
=1.06; and a1 = ar
off in that time? Ans., £100. For £7905.8183 is the sum borrowed;
100
100: whence the answer is, £100 must be paid yearly.
=

LITERARY NOTICES.

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CASSELL'S LATIN DICTIONARY, BY J. R. BEARD, LL.D.-The public are respectfully informed that the publication of this Dictionary has comwhich will be in about Twenty-six Numbers, THREEPENOE each, or in menced, and that it will be issued regularly every week until its completion, CASSELL'S FRENCH AND ENGLISH DICTIONARY.-The FRENCH and Monthly Parts, ONE SHILLING each. Part the First is now ready; Part the Second will be ready with the Magazines for March. had, price 48., or strongly bound, 58. The ENGLISH and FRENCH portion ENGLISH portion of this important Dictionary is now completed, and may be is in the course of publication, and will be completed in about Twelve GERMAN DICTIONARY.-The GERMAN PRONOUNCING Numbers, THREEPENCE each. The entire Dictionary, forming one handsome CASSELL'S volume, will be ready with the Magazines for April, price 98. 6d. ENGLISH Portion of this Dictionary is now ready, price 58. in stiff covers, as quickly as possible, in Numbers, THRERPENCE each; and the entire or 5s. 6d. strong cloth,-The ENGLISH-GERMAN Portion will be completed Volume, strongly bound, at 9s., will shortly be issued.

is raised to the required height, the force necessary to raise it received, reacts on the water and raises it in the tube D, until by pressure on the piston continually increasing until it the piston re-descends; and in this manner, the jet continues reaches that height, and is discharged from the ascension-tube. without intermittance. In another form of the forcing-pump, there is no use made The Load of the Piston.-In the pump just described, after of the pressure of the atmosphere. The suction-tube, of course, the water has filled the suction-pipe and the barrel up to the is dispensed with, and the pump-barrel is itself immersed in mouth of the jet, the force necessary to raise the piston is equal the reservoir of water to be raised. The continuity of the jet to the weight of a column of water having for its base the of water from the ascension-pipe is obtained by the action of horizontal section of the piston, and for its height the vertical a vessel or reservoir of air, which we shall explain in the follow-distance of the orifice of the jet from the level of the water in ing description of the pump called the lift and force pump, and the reservoir from which it is drawn. Thus let it be the pressometimes the section and forcing pump, which differs but little sure of the atmosphere, & the height of the water above the from that just described, except in the application of the air-piston, and h' the height of the column of water which fills the vessel to produce continuity in the flow. This object is also suction-pipe and the lower part of the barrel. The pressure accomplished by the operation of two pumps acting alternately, above the piston is evidently H-+h, and that below the piston as in the construction of the common fire-engine. H-h', since the weight of the column h' tends to balance the pressure of the atmosphere. Now, the pressure H- tends to raise the piston; the effective resistance, therefore, is the excess of H+h, above н-h'; that is, h-rh', which was to be proved. Practical Application of Pumps.-In practice, the following rules are observed in the construction of pumps. The velocity of the piston is calculated to vary from six to nine inches per second. The area of the aperture covered by the valves is about half that of the barrel of the pump. The diameter of the suction-pipe, and of the ascension or discharge-pipe, is about two-thirds of that of the barrel of the pump. The stroke of the piston in large pumps varies from three and a half to five feet. In good pumps the loss occasioned by the time required for shutting the valves reduces the effect to about four-fifths of that produced by the piston. The following figures present different models of pistons and valves employed in the construction of pumps. Fig. 115, a piston packed with leather; fig. 116, a piston packed with hemp; fig. 117, a piston furnished with a single clack-va ve; fig. 118, a piston with a double-clack or butterfly valve; fig. 119, interior of the barrel of a pump, in the bottom of which a single clack-valve works; fig. 120, separate view of a single clack-valve; fig. 121, a conical valve.

air of the reservoir m, by the excess of pressure which it has explanation of this invention: but as it is connected with the

explanation of the forcing-pump, we repeat it here under another form, its importance demanding additional elucidation. The hydrostatic press is a beautiful application of a principle previously known for nearly two centuries, and commonly called the hydrostatic paradox; viz., that any quantity of water, however small, may be made to balance any quantity however great. The practical effect of this principle is, that when water enclosed in a vessel quite full of the liquid, is pressed by a piston at any aperture with a given force, this pressure is at once communicated to every part of the vessel of the same size as the aperture, with the same force. Mr. Bramah, by an ingenious application of the forcing-pump to an apparatus constructed on this principle, produced one of the most powerful and useful machines used in the present day. It is represented in fig. 122, where s is the piston which moves in the cylindrical

8

succession; and let us suppose that the lower extremity of
the tube g is placed between the two ajutages b and c.
1st. If we open first the ajutage b, the water runs out, its
level is lowered in the tube g, and as soon as this level reaches
that of b, the run of water is stopped. This phenomenon is
explained by the fact of the excess of inward pressure which
took place first at b; an excess which disappears when the
level of the water in the tube g is brought down to b. For,
before the water issued from b, the pressure on all points of the
horizontal stratum be was not the same. At e, it was composed
of the pressure of the atmosphere and the weight of the column
of water ge, whilst at b, the pressure was that of the atmosphere
only. But as soon as the level of the water is the same at e
and at b, there is an equilibrium, because that in the bottle
and in the tube the pressure is then the same on all points if

182.

tube f, or small barrel of the pump; p is the piston which moves in the cylinder ce', or large barrel of the pump; and at bu is the tube of communication between the two barrels of the pump. A lever of the second kind / raises the pistons, and the water in the reservoir b' is drawn into the barrel of the pumpf. When the lever is pressed downward, a valve shuts, and prevents the water from returning into the reservoir b', and forces it along the tube tbu, in order to act upon the lower extremity of the piston p, to which is attached the plate p'; ef is another plate, against which the objects to be compressed by the machine are pushed by the former. In consequence of the quaquaversal pressure of the water forced into the large barrel of the pump from the small one, the pressure of one pound on every square inch of the surface of the liquid in the latter will be communicated to every square inch of the surface of the liquid in the former. Hence, if the diameter of the piston & be one inch, and that of the piston b be ten inches, the pressure of one pound on the former will be 100 lbs. on the latter. A noble specimen of this press was exhibited in the Crystal Palace by the Bank Quay Foundry Company, Warrington; viz., that which was used for raising the Britannia Tubular Bridge. The greatest weight lifted by this press was 1,144 tons, and the quantity of water used for every lift of six feet, was 81 gallons. The internal diameter of the great cylinder was twenty-two inches, and that of the ram or piston twenty inches.

the horizontal stratum be. Thus, the pressure at 8 and at being equal to that of the atmosphere, it is easy to demonstrate that it is the same pressure which acts at any point o of the stratum be. For this purpose, let denote the pressure of the atmosphere; this force acting at b and e, is transmitted in

Fig. 193,

all directions in the interior of the bottle, according to the Mariotte's Bottle.-The bottle of Mariotte is an apparatus principle of Pascal formerly explained, and the upper side k which exhibits some remarkable examples of the pressure of resists an upward pressure equal to н-ko; for the weight of the atmosphere, and by means of which we may obtain a con- the column of water ko partially counteracts the pressure stant flow. The neck of this bottle is closed by a cork, through which is transmitted to k. Now, according to the mechanical which a glass tube passes, open at both ends; in the side of principle, that reaction is always equal and contrary to action, the the bottle there are three apertures furnished with ajutages, pressure H-ko is urged downward by the side k on the stratum 1, b, c, at right angles to the side and closed by wooden pegs. be; so that the particle of water at o, supports in reality two When the bottle and the tube are quite full of water, let us pressures, the one equal to the weight of the column of water consider the effect of opening one of the ajutages, a, b, c, inko; the other, the pressure H-ko, resulting from the reaction

of the side . The real pressure, therefore, which the particle | remembered that inasmuch as our desire is not merely to

at o supports is ko+H-ko, that is, н the pressure of the atmosphere; which it was proposed to demonstrate.

2nd. If we shut the ajutage b, and open the ajutage a, there will be no run of water; on the contrary, the air will enter the bottle by the aperture a, and the water will rise in the tube g to the level ad, when the equilibrium will be restored. For it is easy to perceive by reasoning, as in the preceding case, that the pressure is then the same at all points of the horizontal stratum a d.

discover a certain metal, but a given compound of a certain metal, we shall require not merely a test for mercury, but for that which is combined with the mercury and holds it in solution. Let us begin with a very characteristic test for soluble persalts of mercury generally-a solution of iodide of potassium. The effects of this test are most remarkable, as will be seen. Having poured a weak solution of bichloride of mercury into a test-tube or a conical glass, add to it, drop by drop, another solution of iodide of potassium, and remark the beau3rd. Let the apertures a and b be closed, and the aperture e tiful play of colours which result, also the disappearance of all be open. In this case, there will be a run of water with a con- colour, all precipitate, and the resumption of perfect transstant velocity so long as the level of the water in the bottle parency in certain states of dilution; that is to say, so soon as does not fall below the level of the lower orifice of the tube: a certain amount of test liquor has been added. It is useless for then the air would enter this orifice and fill the upper part to expatiate on changes which can be seen very much better of the bottle, where it would take the place of the water run than they can be described, but I may remark that by reversoff. In order to demonstrate that the flow of water at c is con- ing the order of experiment in testing, and adding the bichlostant, it is necessary to show that the pressure on the horizon- ride solution to the iodide of potassium solution, instead of tal stratum eh is always equal to the pressure of the atmo- adding the latter to the former, the chromatic effects will vary. phere increased by that of the column hl. Suppose, then, that Now the peculiar effects here detailed are characteristic of a in the bottle the level of the water is lowered to the stratum persalt of mercury; and the only persalt of mercury at all ad. The air which has entered the bottle supports a pressure likely to come under one's notice in a case of poisoning is the equal to H-pn. In consequence of its elasticity, the air perchloride of mercury; however, any doubt can be at once transmits this pressure to the stratum eh. Now, this stratum cleared up by the addition of the test for chlorine. Now what supports besides this; the weight of the column of water pm. is the test for chlorine? You remember, I presume, that it is Therefore, the pressure transmitted to m is in reality, pm+Hnitrate of silver-the reaction of that substance having already, —pn, or H+mn, that is, H+h. In the same manner, it under the head of "Silver," come before us. Add, then, a little would be demonstrated that this pressure is the same, when nitrate of silver solution, and a white precipitate results. But the level is lowered to eb; and so on, so long as the level is there are thousands of white precipitates; how shall we know above the orifice ; the pressure on the stratum c h is therefore what this one is? Simply by adding hartshorn (liquor ammoconstant, and so is the velocity of the flow. But as soon as the nice) to it, the white precipitate dissolves. It has been prolevel falls below the point, this pressure decreases, and con- duced, therefore, by chlorine. We have already determined sequently the velocity of the flow diminishes. Thus, we see the presence of mercury, therefore our substance must be a that the bottle of Mariotte is a means of obtaining a constant chloride of mercury. But as there are two chlorides of mercury, flow; namely, by filling it with water and opening the ajutage which is this? It cannot be the proto-chloride of mercury or aperture placed below the orifice of the tube. The because that substance is insoluble; it must, therefore, be the velocity is then proportional to the square root of the height per- or bichloride of mercury. Thus, at length, we arrive at 7h, as shown in a former lesson. the demonstration.

LESSONS IN CHEMISTRY.-No. XXII. In the course of any chemical examination, and more especially of metals, we find certain compounds demanding our especial attention. Amongst all the combinations of mercury, perhaps the bichloride, or corrosive sublimate, is that which claims our prominent notice. It is a terrible poison: its discovery and identification, when mixed with animal fluids, involve many points of chemical interest, and the manipulative processes employed in its extraction are of great beauty and delicacy.

The next test we shall employ is ether; a liquid which, by the way, is rather to be considered as a separator than a test in the ordinary acceptation of the term.

Having poured a little bichloride solution into a narrow test-tube, add to it about an equal volume of rectified ether always mean sulphuric ether), then closing the tube with (when the term "ether," without prefix, is used, chemists the thumb, agitate the tube. Proceeding thus, the ether and the bichloride solution will become intimately mixed. This mixture being effected, cork the tube (to prevent evaporation of the ether) and allow it to stand for the space of a few minutes at rest. Presently two distinct fluid layers will be recognisable; so well marked, so thoroughly individualised, that one may be readily separated from the other. The best I must premise by directing the student's attention to the means of effecting the separation is, as represented below, fig. fact of there being two chlorides of mercury-one the proto-8, by the use of a little glass instrument termed a pipette. chloride, ordinarily known as calomel; the other, bichloride, ordinarily known as corrosive sublimate: the respective compositions of which are as follow:

Fig. 8.

Hence the ratio of chlorine in these two chlorides is as one to two. Calomel may be generated in various ways. The student has already generated it by the addition of common-salt solution to proto-nitrate of mercury, and he will not fail to see, by reference to the preceding tabular exposition, that if by any process we can succeed in taking from a given weight of subÎimate half the chlorine it contains, the result will be calomel; and if we can succeed in removing the whole of its chlorine, the result will be metallic mercury.

Chemical investigation of Bichloride of Mercury in simple and omplex fluids. Taking a portion of the solution of bichloride f mercury already prepared, let us master the appearances it

The student, however, who does not possess the instrument

ffords with tests in simple solution. And here it will be may accomplish his result perfectly well by means of a glass