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ong time yet the patience of (he calculator will have to «upply the imperfections of analysis." The method employed by liaron Damoiseau is very nearly identical with that suggested by Lagrange. It will be remembered, when hinting at the method pursued by Clairaut in this difficult subject, we pointed out that there was a difference between computing the perturbations of a comet and those of a planet, though the effect is produced by the same cause in both cases. In planetary perturbations it is possible to integrate the differential variations of each of the elements of the orbit, but, in the cose of a comet, the eccentricity is so large, and the inclination to the ecliptic varies to infinity, that it is not possible to develop the disturbing function in a series arranged according to the nscending powers of these quantities, and we must forego the advantage of having, as a means of determining the inequalities of comets, formula;, which, as in the case of planets, embrace an indefinite number of revolutions, and need only numerical substitutions to give the sought-for results. In order to integrate the differential formula) of the elements of the disturbed orbit, recourse must be had to a method of approximation, known to astronomers as the method of mechanical quadrature». This method consists of dividing the curve described by the comet into small portions, in which the alterations produced by the disturbing forces on each element of the orbit can be computed. Suitable formulai provide the calculator with the means of computing from these disturbed segments the total variation of the elements in the interval comprised between the two extremities of the are of the trajectory that is being considered. I5y these means the astronomer knows the alteration of the elliptic elements of the orbit between two consecutivo passages of porihilion. Of course, since the only object is to divide the path of the comet into small segments, this can be effected either by equal portions of time or equal portions of arc of eccentric anomaly. In either case, the amount of interval is left to the discretion of the calculator. The method of mechanical quadratures must be adopted while the comet is pursuing that portion of its path near the Sun, but for the parts distant from the Sun an approximate solution is obtained by supposing the mass of the Sun and planets collected at their centre of gravity, and Lagrange gave expressions by the quadration of which the process is made accurate. He demonstrated also that without considerable error, expressions may bo found for these laet-meutioned terms which will be integrable.*

Damoiseau hoe applied the method of quadratures throughout for e¡jual intervals of eccentric anomaly, and computed the effect of Jupiter, Saturn, and Uranus only, from 1682 to 1835. Subsequently he calculated the disturbing effect of the Earth. In the first half of the first revolution he appears to have employed the elements deduced from the observations of 1682, and in the latter half the elements deduced from the observations of 1759. In the second revolution the elements are altered for every 30° of eccentric anomaly.

source of perturbation, without regard to the numerical labour, and for the masterly manner in which the whole of the vast work is conducted," is undoubtedly that of Professor Kosenberger. "So complete," remarks the present Astronomer Royal, "are the whole of these computations, that if names were taken not from the discoveries of these bodies, or from those who conjecture their identity, but from those who from accurate calculation on an uniform system, combine the whole of our information relating to them, we should call this body not Halley's, but Rosenberger's." He first, and with the greatest care, computed the elements of the orbit from all the observations that were made at the apparition in 1682. Similarly, the observations of 1759 were discussed, and from the method adopted, very great accuracy was obtained for the discussion of the next period, from 1759 to 1835. The perturbations of all the planets (Neptune, at that date, remained to to discovered) wero computed with great precision, with the exception of about 00° of eccentric anomaly, when the position of Jupiter was such as to produce great disturbance, and which could not be calculated with the same admirable degree of precision without a more accurate knowledge ofthe comet's orbit. For theseCO°ofeccentricanomaly, Rosenberger assumed Damoiseau's results, and the general effect of perturbation is very accurately determined. Nor did Rosenberger forget the effect of such a medium as Professor Encke liad demonstrated to exist. He computed that the effect of such medium would be to accelerate the return of the comet by about a week. The Earth hastend the perihelion passage 15} days, Veuus about 5 J days, and Mercury and Mars together nearly ono day. Including all tho perturbations, Rosenberger concluded the nearest approach to the Sun would take place on November, 3d. 19h., Paris time. Neglecting the amount of acceleration, duo to the existence of the ethereal medium, the time of perihelion was expected at November, lid. Oh. Paris time.

But one more effort to determine the elements of tho appearance in 1835, remains to be mentioned, that of Dr. Lehmann, which, though in some respecte inferior to that of Rosenberger, yet demands very great praise. The distinguishing characteristic of the investigation lies in the fact that the computer has carried back the effect of perturbation to the apparit-on in 1G07, adopting the method of quadratures by equal intervals of time. This additional labour was undertaken to detect, if possible, the effect of a resisting medium. The predicted time of reappearance was by this cnlculation later than in any other—viz., Nov. 2(5. The cause of the discrepancy is most likely to be found in the fact that the elements were not changed sufficiently often in computing the perturbations between 1759 and 1835 ; the frequency of the change, as we pointed out, is entirely at the option of the computer.

The excitement that was experienced in 1759, at the approaching return of this comet, was as nothing compared to the anxiety that was felt in 1835, to effect early observations of it. In

going over the paper, as it lies before us, the arguments in favour of its discovery seem very small, and Dr. Olbers must have been guided rather by what ho hoped than what he thought.

Aided by a powerful instrument, and the transparent atmosphere of Italy, Father Du шоп с bel, of the Collegio Romano, detected the expected comet on the morning of the 6th of August, close to the computed place, the error amounting to about seven minutes of arc in Right Ascension, and seventeen minutes of declination. (To such of our renders who have no idea of space measured on the sky, we may say that that distance is rather more than a semi-diameter of the moon.) Rapidly the attention of other observers was еэпcentrated on the welcome visitor, and observations were showered in from all parts of Europe, Sir James South and Captain Smyth representing English activity on this subject. The reduction of the observations shows the lGth November to have been the day when the distance of the comet from tho Sun was the least, so that the predictions of Rosenbergen were but 5 days in error, a degree of approximation that can be appreciated only by those who have been engaged in computations of that long and delicate nature. The Royal Astronomical Society of England rewarded the talented mathematician with their gold medal as an acknowledgment of his eminent services.

The comet continued visible till the 22nd of November, when its near approach to the Sun rendered observation impossible. On the 30th of December, on passing from the Sun, Kreil,oí Milan, succeeded in obtaining a view of it, bat the southern declination soon rendered it impossible for European observers to continue their observations. At the Cape of Good Hope, Sir John Ilerschel and Sir Thomas Maclear prosecuted their investigation of its path among the stars, till the middle of May, when it was finally lost sight of, till it shall appear again in 1911, when this generation shall have passed away, and its children be anticipating the infirmities of age.

(Го br /¡oaeiuded nert *tek.)

SCIENCE FOR ТПЕ ГОСШ.

Вт The Rev. E. Kehsan, Clongow*» ¡college. (Continued from page Si.)

THE definition being thus briefly explained, it remains to see how it contains the IJ. and III. part of the treatise on mechanics.

I. Force may be prevented from having its effects by another force. Thus in Fig. 1, the force which would cause the weight A to fall, may be counteracted by an equal weight В at the opposite end of the cord. There is then produced what is called equilibrium.

II. Force may be allowed to have its effect entirely, or, more or lass modified. Let the weight В be removed, A falls to the ground with

These alterations do not appear to be sufficiently I jann'arv 1835, Dr. Olbers published a paper in

which ho expressed hie opinion that the comet would be visible in the spring of that year. 11 is conclusions are based upon facts drawn from the experience of previous returns, assuming that tho comet has sustained uo sensible diminution of its mass. The last observation ofthe comet in 1759

frequent. As the result of Damoiseau's calcula tious, he predicted the return of the comet to perihelion on the Uh of November, 1835, at 8h. P.M., Paris mean time.

Some years later a seoond attempt io determine the perihelion passage was made by Ponte

coulant. In narrating the history of the*calcula- | WM ,.ffäcted 1)y MeS8ier, when its distance from tions of this comet in a chronological order, we tho Sun wa$ ab()ut ,.os_ nnd from the ealth vi2 should have mentioned that Burckhardt com- (the Klirthv (iistaBce from the Sun being regarded putedwith admirable precision the elements of ' Mnily) Olbers remarked that about the bethe orbit from Flamstced's observations in 1C82, imli '0t March, the comet's distance from the and Messier s in 1759. From these elements Sun and the Earth woald be nearly the same Pontccoulant endeavoured to determine the path , _ 378 But м the ligüt 0f »heavenly body, not of tho ellipse that would be described in 183o. I ,

It would be to lengthen out this paper to ■' ,., _. . .- , .„ /d i,„:„„

in,. .. г и ..*_ self luminous, is proportioned to (K being

length, to pursue the course of ionte- ''

tedious length, to

coulant in his elaborate calculation. His method is that of L'igrangp, adapting quadratures throughout. The result to which his final calculations led him was that the comet might he expected to approach nearest the Sun on November, 12d. 17h. Paris mean time, or about a week later than the epoch assigned by Damoiseau.

But the investigation on which is bestowed the greatest care, and the one " that is most remarkable itir tho extraordinary completeness of its detail, for tho pains taken to include every possible

r Memoir Hoy. lat. Soc., Vol. IV.

R'D»

tho Badius Vector, and D being the distance from the Earth) the comet in the beginning of March would be about 30 times less bright than when it was last seen by Messier, and, consequently, the probability of its being seen, small in the same proportion. Nevertheless, Dr. Olbers urges on astronomers the necessity of continual and careful sweeping to attempt to discover it, and to aid in its detection, computed two ephemcrides on the assumption of its perihelion passage taking place at the let and 11th of November. This paper gives somo idea of the anxiety i that was felt at its approach, for on carefully

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the full force acting upon it. Let В he replaced by a small weight; A now falls more slowly. Id both cases there ie produced what is universally called motion.

III. Force may be allowed to have its effect for a short time, to be overcomo in its turn by the f>rco which it at first overpowered. _ In Fig. II. is represented a coiled spring with a weight attached. The weight beiug raised and let gently fall, at first the spring is stretched beyond its position of rest, dotted coil; then the force of tho fall being exhausted, the coijls of the

st, » -«.,4inr, A »um the weight ! Rives to many bodies a fixed determined form, -gbf recover'that jK^^rnTM.7jMnÍ by what i. ¿led crystalUsation. -This subject

has its own place in chemistry.

III. Impenetrability signifies the impossibility of two bodies occupying the same space at one and the same time. This is the strict, but not the ordinary notion. When a nail is driven into a block of wood, it is said to penetrate the wood. Such is not true; the wood particles are only pushed aside. The wood does not exist in the space occupied by the iron. In the Fig. 3 there is no water in the space occupied by the immersed body A.

But of the three states the impenetrability of the gaseous is the most remarkable, and may be shown moBtdistinetly

{¿lb. sud again the spring recovers inj ruing continues until the force of the nrst Ы1 is worn out, by causes to be seen later. Here is produced vibration.

The laws of I. are called the equilibrium ; or in one word, Statics ¡ of IL, the laws of motion or Dmamie«; of III., the laws of vibration ; which might be entitled Palmotics. This third point, in practice, chiefly regards acoustics (sound), as shall be explained.

The three conditions of force, аз above, are to be found in the solid, liquid, and gaseous state, giving new divisions; statics of solids or Statics; statics of liquids, Hydrostatics; statics of gases, Pneumatics; dynamics of solids, or Dynamics; dynamics of liquids, Hydrodynamics ; dynamics of gases, Pneumatics; palmotics (acoustics) of solids, liquids, gases

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in the study of mechanical principle to have a good notion of

They

the many properties which bodies possess may be divided into two classes, essential and accidental. To those which are more importaut amongst them, will be applied the form laid down in the explanation of the.word study—i. e., their laws,' proofs and explanation shall be studied.

Section I.

Essential Pboferties or Mattes. These may be taken singly or in groups, as they are more or less important. Though these latter may not require details of laws, they may have applications important or interesting.

§ 1. Extesbiojt, Fiofbe, Impexetbamlitt. I. Extension is the occupying of space by length, breadth, and depth. A body cannot be imagined to exist without these.

Application I.—Rules, Measures.—What these are is sufficiently understood from daily ex- ex perience, and from treatises of arithmetic with which the student is supposed to be familiar. They are, in short, conventional means of representing portions of space. Any abstract discussion of this, or similar subjects, has no place in an elementary series of mechanics.

Application II,—Hednced Space.—By this is understood the proportional representation of a large space by a much smaller; as.'.for example, when several miles of the country are represented by as many inches on a map. And hero it is mort important to remark that the greater the difference (the greater the reduotion) the more «art must the instrument be; a very small portion of an inch may cause great error.

Sub-Application.—Heavenly Space.—The great extent of the Heavens, which is represented by very small space in our observing instruments, makes it imperative that the greatest exactitude be obtained when there is question of declaring ab»olnte space, otherwise errors of even millions of miles may be admitted.

Application Ill. —Pyramids.—Recent researches of Piazzi Smyth, have confirmed the opinion of Mr. John Taylor, of London, that the Great Pyramid of Egypt was constructed with the design of fixing a system of measures for the human race. The Hebrew measures, and those of many countries, are found to have been established upon this system.

H. Figuro signifies shape, form. Besides the countless figures which art can produce, Nature

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to the eye. Fig. 4 Fia

rep resents a glass re-
ceiver inverted, and
forced down into a
vessel of water. Not-
withstanding the ten-
uity of the air, the
water cannot pass up
into the receiver, to
any great height.
The air cannot be
pushed aside, it re-
sists ; it may be forced
into the smaller com-
pass; ityields slightly,
as a whole, to the ex-
ternal pressure of -
the water, and lots

in a quantity varying with the height of the water in the outer vessel. A candle floated nnon the water helps to make the inside level more apparent. Were it not then for this making place, the smallest pin could not be forced into a solid, or into the small recipient filled with a liquid or the gas.

§ II.—Divisibility.

Matter can be reduced to smaller and smaller dimensions. The delicacy of the instrument seems to be the only limit. What is possible beyond this point is of no importance in mechanics. The question is left then to chemical and speculative philosophy. Divisibili ty of

space serves to introduce a some

what important

instrument. Application I.

—The Vernier.

—The vernier,

named after its

inventor, Pierre

Vernier (died

1637), is a mea

sure which,

without sub-divisions, shows

certain fractional parts of a

given divided

space exactly, or

as near as may

be required; to

be brief and clear, a few points 1. Construction.—A measure

10

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is made, shorter by one division than a certain portion of the given space. This portion is determined by taking divisions, as manyas there are units in the denominator, of the required fractional parts. The shorter length, divided into as many parts as there are units in the same denominator, constitutes the venier. Example: Let it be required to show lOths of a division of the rule A В, Fig. 5. The vernier J is made 9 divisions long, and

1 divided into 10 parts. In the same 'way, if —

20

1

— be required, the vernier will be 1929 30

divisions long, and divided into 20 30 parts. In 1

the most general form — representing any fracn

tional division, the vernier will be n — 1 part in length, and divided into » parts.

II. Principies.—From the construction it is

evident that each division of the vernier is

shorter by the fractional part than a division of

the given pace. In the example the vernier

1 111

divisions are— , could be — or shorter

10 20 30 n

than those of the rule A B. Consequently, if when laid upon the rule, any division of the vernier correspond to a division of the rule, the divisions of the rule towards its zero will show 1, 2, 3 « fractional parts of its own divisions -, or, in short, the figure of the vernier, which corresponds, tells the fractional parts. Should no lino correspond, the nearest correspondence is taken, and the fractions estimated as before, either within or beyond the limit. The error, in plus or minus, must be less than the fraction for which the vernier is constructed; therefore, by more and more exact vernier, the possibility of error can be reduced as circumstances may require. In many ordinary measurings one millimetre more or less would be of no consequence; in many phy

1 sical experiments — of a millimetre must be 10

1 1 shown; in astronomy —, — may be absolutely

20 30 ! indispensable.

III. Practical use.—Let it be required to measure the bar A С (Fig. 6) so as to be within an

1 error of — mm. The division being taken to

10 represent mm, the rule shows that the bar is 4 »im plus the, bit (a J). This bit the vernier will measure. Its zero is placed against the end of the bar, and some line of correspondence looked for. In the figure, the 3rd division of the vernier

3 corresponds. The space « S is therefore — mm

10 long. For each division of the rule from я to a

i is — mm longer than the divisions of the ver10

1 2

nier, or in another way d e = — mm, f g = — 10 10

3 b a = — 10 Now, suppose the bar \ of a 10th mm shorter.

Here is the greatest possible error; i of — mm

10 too much or too little. Circumstances determine which to take. Other methods of applying the vernier may be met with, but these return in principle to the one explained.

IV. Sorts.—Verniers are of two sorts, straight and curved. These latter are used for the fractional parts of the divisions on a circle. Fig. VIL, A B are of circle V vernier. This form is sometimes called the Nonius, from the name of the inventor, a native of Portugal.

V. Limit.—Delicacy of division is the only bar to indefinito vernier division. Practically,

1

— »tire is the ordinary limit. Beyond this point 50 there is danger of confusion. With greet care

1

— mm can be produced. To read these very 100

fine divisions, and observe the correspondence, a microscope is used.

Sub-application.—Cathctometer.—The object of ¿hie instrument, invented by Dulong and Petit, and perfected by Gauibcy and Pouillet, who named it, is'to measure, by means of the vernier, the difference of level, of two points in the same, or different vertical. In its essentials, the Cttthetomcter, is a vertical rule of brass, divided into millimetercs. Along the rule elides a telescope, in the inside of which, in a fixed place, are tho very fine threads crossing at right angles a Fig. 8. The slide which carries the telescope is provided with a delicate vernier, by

1 which — mm can be measured. For the

50 details, Fig. 8 A, a heavy foot of metal, provided with spirit levels, S S' (to be explained later) and screens for raising or lowering tho foot, ne tho

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scope, has B spirit level L, and is brought to exact level by the screw D. The ,i¡,je E nBg ап opening at О, through which the divisions of the rule are s?en; and along which is the vernier V ; M. its microscope, to be moved as required. To the slide E a second slide F is connected by a screw II. This file F can be tightened to the rule by the screw K. For use, the slides E and F are drawn up by hand until the crossing point of the telescope threads items to be more or less on a line with the first surface. By the screw К the slide F is fixed, and by the "screw H the slide E is gently raised until the crossing point

* О il/ n вт ill part of the pillar is seen. + The cap and greater part of the steel pillar are с oocoaled by the rule, which must »how/all front.

is in exact coincidence with the surface. The position of the vernier zero is noted accurately. The second surface is examined with the same precaution; and the difference of the vernier zero in the two positions represents the difference of level desired.

"man, in his Cours de Physique de l'Ecole Polytechnique, considers the cathetometer so very useful an instrument that he goes at some length into the conditions requisite for good action. These would be here out of place, as introducing unknown subjects. The same may be said once for all, as regards omissions of details of instruments and machines hereafter; as much as possible, all points not yet explained to the student, will be kept out of view until their own principles have been studied. Though this method may not be agreeable to a general reader, it is of immense advantage to one who is only entering upon scientific study. For thus each point receives his undivided attention, its principles are more quickly studied and understood; that weariness caused by¡ frequent divergence into, and forced return from various trains of thought, is avoided ; and, above all, the danger of mere superficial knowledge is almost completely guarded against. It then is a source of pleasure when the course has been completed, to review instruments, machines and combinations of machines, as a whole. Each part shows itself with its principles clearly present to the mind and not as another element, to increase the general confusion of ideas, so commonly conse quent on mere general reading.

{To be continued.)

ON THE DRESSING OF LEAD ORES.

A PAPER was read on this subject before the Institution of Civil Engineers on the 5lh inst. by Mr. T. Sopwith, Jun., M. Inst CE.

This communication was limited to a description of some works the author had had occasion recently to establish in Spain for the dressing of lead ores, as B general account of the present state of such operations in England could not be satisfactorily given in a single paper. Moreover, as regarded this branch of mechanical engineering, Germany was in advance of England. By dressing was to be understood the art of obtaining from the raw material extracted from the mine, called house or mine stuff, the pure ore it contained, to the rejection of the impurities with which it was associated. Bouse might be said to yield, in an ordinary way, from 5 per cent, to 25 per cent, of galena, which when pure had a specific gravity of 775, and produced 86 per cent, of metallic lead. The lead ores of commerce were usually dressed to a tenour of from 74 per cent, to 78 per cent., though argentiferous ores were frequently delivered with two lower percentage. All galena was mixed with silver ; but the term argentiferous was only applied to that in which there was upwards of 12oz. of silver per ton. In dressing, the principle applied was that of separating the lead ores by means of their readier gravitation. This operation was easy or difficult according as the accompanying impurities were of greater or less specific gravity.

At the works referred to, about 350 tons of lead ore were prepared per month. There were two dressing floors, the higher and the lower. On the former manual labour was principally employed. On the lower floor the stuff was treated which required to be passed through the crushing mill ; and it was more particularly this machinery and method that it was the purpose of this paper to describe. On the higher floors from 200 tons to 220 tons per month were prepared, or twothirds of the entire quantity. Two systems of paying the miners were adopted in mineral mines; one, by " tribute " or " bingtale," where the men w. re paid in proportion to the amount of clean ore the mine stuff excavated by them produced; the other, " tutwork " or " fathomtale,"where they were paid by measurement. The adoption of the former system introduced complication, and more expense in the dressing operations than the latter.

The author, in describing the various machines, and the quantities of work they could deal with fixed as a standard the richness of mine stuff treated at about 12 per cent, (by weight), equal to work which would be known in the North of England ns producing 2\ binge per shift.''

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The washing operations commenced 1/ turni njj a stream of water into the "teams "containing the "house," which was raked out by a man on to a grate, and there hand-picked. The author used two grates, the higher one with spaces of 1 inch, and the lower one of 1 inch, in preference to one grate with spaces \ inch wide, as usually employed. The stuff passed through the second grate into a stirring trunk, where a partial separation of the coarser particles from sludge and slime was effected. The coarser particles were of a size convenient for botching, and the common botching tub could treat from 8 to 15 tons of stuff per day. Between the waste, which was wheeled away, and the pure ore, there was an intermediate layer of what was called " chatter," consisting of particle« mixe 1 with ore which could not be separated without further sub-division. This was effected by means of a crushing mill. In England from 25 tons to 30 tens was a fair day's work to pass over one grate. The author found, by the use of two grates, that 40 tons could be passed, without any increase of labour, at a cost of about 2s. 6d. per ton of clean ore produced.

The ore which passed through the coarse wire bottom of the botching sieve accumulated at the bottom of the tub, and was called "smiddum." This was rendered fit for market by further preparation in the plain buddle. The sludge deposited in the trunks attached to each grate was prepared in a round buddle. A separation having first been made of hard lumps.small stones, or chips of wood, Ac, the sludge was delivered at the centre of the buddle accompanied with water. The bottom being inclined outwards about 1 in 10, the particles were carried by the water in that direction :the heaviest and richest being deposited nearest the centre. The buddle described was larger in diameter, and treated nearly four times mere stuff than that usually employed. The water on leaving the sludge trunk carried with it a certain amount of slime, which was deposited in pits, and was subsequently treated in a machine called the Brunton's Cloth, the action of which was described, as also of the dolly tub, by which the slimee, after being concentrated in the Brunton's machine to about 45 per cent., were further enriched to about 70 per cent., and so delivered for sale. The crushing mill in common use in England was described, and the inconvenience attached to it, as compared with the simpler form used in Germany, was pointed out. In the apparatus that had been referred to, it was probable that about 80 per cent, of the lead ore produced in England was prepared.

On the lower, or crushing mill floors, which the author had erected, some attempts had been made to secure continuity of action by the use of self-acting machinery, wherever it was possible; though from the circumstances of Spanish labourers being employed, who were totally unaccustomed to the use of machinery, it was necea sa y that the machines should be of the simplest kind. The stuff which required crushing was conveyed in waggons to the lower floors, being first broken to a size which would pass through a 5-inch ring. This was effected by manual labour, in preference to a stone-breaking machine, as the former allowed of a separation ef a small quantity of pure ore, and of a large quantity of waste, which would afford unnecessary work for the .crushing mill. The stuff, after being emptied from the waggons into the hopper of the crushing mill, was passed through the rollers, and, when crushed, was elevated by a Jacob's Ladder, and delivered into a classify ing trommel, composed of two shells, an outer one of perforated iron plate with holes 1 j millimetre in diameter, and an inner one with holes 10 millimetres in diameter. The crushed material was delivered into the inside of the trommel at one end, and passed onwards, the trommel being inclined. All the sludge and slime were got rid of through the outer shell, the inner shell retaining and delivering apart any particles over 10 millimetres in diameter. These were returned to the crushing mill, to be again passed through the rollers, and the particles, ranging in size between 1 1 millimetre and 10 millimetres, were delivered at the further end of the trommel, and passed on to a second, or sizing, trommel, composed of one shell only, and were then subdivided into four sizes, viz., 2J, 5, 7', and 10 millimetres, each size being treated in a separate hutching tub. For the operation of hitching, the convenience of having all the particles treated of one, or nearly of one, size, was obvious; und in some cases of refractory ores it Whs a necessity. 1 h - botching machines employed were entirely

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eelf-acting and continuous in action; a fast and a loose pulley being attached to each machine. Contrary to the form adopted in England, the sieve was stationary, the water being put in motion by means of a loosely-fitting piston. The stuff was delivered into a small hopper, and travelled the length of the sieve, a distance of 28 inches, by which time a perfect separation was effected. It had been found advantageous to increa* e the length of the stroke, and the number of strokes per minute, for the larger sizes. By an ingenious movement, a quick down stroke uni a slow return stroke had been given to the piston. The crushing mill was more compact than the form used in England, the rollers being kept in contact by the compression of india rubber buffers, in place of a long lever, with a heavy weight attached. The sludge, which passed through the hole» of 1J millimetre in diameter, in the first, or fbi-ilyinE trommel, was delivered into a separa tor,—an iron cylinder about 2J feet high,—where it met a stream of water of sufficient strengtli to carry the smallest and lightest particles upwards. and deliver them into a launder, whence they were conveyed, by the water, to the sludge trunks and slime pits, and were subsequently treated in round buddies and in Brunton's Cloth. The солпхт particles were prepared by manual labour, in a common trunk or tie.

Th* amount of work crushed and prepared on the lower floors was about 55 tons per day of ten hours. The actual cost in Spain was 21s. 2d., hut the equivalent of labour would be performed in Englioh mining districts for 13s., the latter »urn being at the rate of 2 83 pence per ton of raw material treated, or 2«. per ton of clean ore produced. If, however, self feeding apparatus was introduced to supply the botching machines, which could easily be done, the latter cost might be reduced to 2 07 pence, and Is. 5}d. respectively.

The cost of preparing similar work in England, with machine crusher and machine botchers, was, the author believed, about 2s. Cd. per ton of clean огр. The whole of this machinery was driven by a 10 h.p. portable engine, supplied by Messrs. Ransomes, Sims, and Head. The cost of erection of the crushing mill floors complete, including the engine, was about £1500. The same arrangement in England would have cost about £1200. Most of the machinery was supplied by Messrs. Sievers and Co., of Kalk, near Cologne. No sep irate crushing mill for the preparation at "chatts " had been erected, as wheu the " chatte" had been allowed to accumulate, the present machinery could be adapted for their treatment in an hour or two, advantage being taken of a time when new rollers had been put in.

The author ob'erved that whereas, in England, the machinery employed in dressing operations was for the most part made at the mine with the ordinary statt", in Germany there were manufactories giving employment to four hundred hands, dedicated alnaoet exclusively to the construction of dressing machinery ; and it was not surprising to find, in the machines issued from them, bettor proportions, greater elegance, and more efficiency and durability than those used in the mines of this country.

The machinery described in this paper had been iu use for two years, and, having given good results in Spain, no difficulty ueed be feared in its application elsewhere.

EXPERIMENTAL PHYSICS.—A contemporary Staus that the Imperial Academy of Science, Lille, has offered two prizes— one for the best work on some branch of experimental physics; the other on the rue of the thermometer in medicine. The prizes will consist of l'ino francs each.

FlO. 4.

COFFEE ADULTERATIONS, AND HOW TO DETECT

THEM WITH THE MICROSCOPE.

Br J. Muts», Ри. D.

(From the Food Journal.)

Having seen in our last number the properties of cofT<*r,

let us no*' take a glance at those of its chief adulterant.

Chicory, as employed for this purpose, is the dried and

roasted root of the common endive, so dear to the lovers of

winter salads, as a substitute for lettuce. This plant is to

be seen growing wild la many of our hedgerows, and belongs

to the botanical order of Composite. It is very similar to the

common dandelion, which belongs to the same order, but it is

readily distinguished by the colour of its flower, which is

blue, while that of the dandelion is yellow. The chicory

root also bears a great resemblance to that of the latter

plant, being, like it, soft, and exuding when squeezed the

milky jaice so well known to all of us who hive enjoyed, as

children, the pleasure of wandering in the fields.

Our wild Eughsb plant is not, however, so much esteemed in the market as the German and French varieties, which are specially cultivated for mixing with colfee. The following analysis will show the composition of chicory root in its dried state, and also that of its aih, to which we shall have occasion to refer hereafter :—

I.—Bried Chicory.

Moisture 17-Ю0

Gum *>-«6

Sugar 1MM

Extractive (bitter) 18000

Fat VOg

Woody fibre. &c 39 202

Mineral matter * 670

II.—Composition of the Ash.

Potash 0-C7Í

Soda M"

Lime 0-250

Mugnesia 0*184

lrorT «085

Sulphuric Acid **'%*

Vhloriae °"13'

Carbonic Acid OU,»)

Phosphoric Acid •*■

■Ä J^G7Û

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From these resulte it is evident that this plant containa no principles which would render it to any extent a useful substitute for coffee, as we look in vain for the caffeic acut, or the théine* already shown to exist in the latter article. But what shall we say if, besides containing; nothing valuable, it should be proved to he positively injurious when freely consumed? Let us hear Dr. Johnston on this subject :—" Taken in moderate quantities, the ingredients of chicory are probably not injurious to health, but, by prolonged and frequent use, they produce heartburn, cramp in the stomach, loss of appetite, acidity In the mouth, constipation with intermittent diarrhoea, weakness qf the limbs, tremblings, sleeplessness, a drunken cloudiness of the senses, &c. At the best, therefore, chicory is a substitute for coffee to which only those to whom the price is an object ought to havo recourse." Tu these remarks we would add that we prefer not being poisoned even at the must moderate cost; and in cases where "price is an object," we would advise the public to abstain from paying anything at all for such a filthy beverage as chicory-coffee undoubtedly is to persons of unvitiated taste. Wc might bring up many other charges against this nasty infusion, but we will only give one more, and that is a dictum of Dr. Bocr'a, to tho effect that the continual use of chicory causes amaurosis, and, consequently, blindness. Since giving our coffee results last month, we have been seriously remonstrated with by a grocer, who declares that he and his brother tradesmen put nothing else into their coffee but chicory. This is, however, only a repetition of the old story, told long ago by Dr. Pereira, who said that "while the grocers, on the one hand, cheat their customers by adulterating coffee with chicory, the chicory dealers in turn cheat the grocers by adulterating chicory." Whether the grocers arc, ur are not, the chief sophisticators, is comparatively immaterial, for the fact remains that the public continue to suffer. The grocers cannot, however, be held innocent, as they bay ground chicory, which article the) can purchase at a cheapcrrate than the;/could l/iedriedraot iliclf; and of what then do they, in their innocence, imagine it to be composed? Out of twenty samples ot ground chicory purchased lately in London (but of the analyses of which we have not space at present to give details) more than hair were found to be adulterated.

We now turn to the detection of the adulterations of coffee. Many simple processes have been from time to time proposed, to ascertain whether tins article be pure or not, without saying exactly what is the adulterant; and of these wc subjoin a few.

1. Take the packet of coffee as it comes from the grocer's, :n your baud; and, having given it a good squeeze, lav it gently on the table, and open it. If the contents be found adhering together in a cake, the sample is not pure.

2. Drop gently a teaspoonful of coffee on the surface of a glass uf water, and observe if auy of it sinks immediately; if so, it is bad. Let the whole be now slightly stirred, and notice the colour imparted to the water. If this be a decided brown tint, then the coffee is adulterated, most probably with chicory or burnt grain of some kind.

3. Make an infusion of the coffee in the usual way, pour ionic into a cup, and let it stuud till cold; if a skin or scum should form on the surface, there is reason tu suspect baked animal matter, such as horse's liver.

If, however, we seek method« of discovering the precise adulterants employed by means of chemistry, the subject becomes at once much more difficult, aud the results not always reliable. One method is to treat 25 grains of the sample with an ounce of ether, in a closed bottle, for an hour, with frequent agitation; and then, having poured off the sulution so obtained into a weighed watcli glass to evaporate to dryness; ascertain the weight of the residue. The undermentioned matters, treated in this way, gave the following results:—

Coffee (plantation Ceylon) 373 grains

Chicory (best English) ISO

Roasted Grain 90"

Several years ago (in 1852), when public attention was ¡nach directed to this subject, Messrs. Graham and Stenhouse published a report "On the mode of detecting vertible substances mixed with coffee." Thcv found that the most striking points of difference between chicorv and coffee consisted in the much greater quantities of grape sugar and sand winch exmtcd in the former than in the latter. A reference to the various analyses in the present article, and that of last month, will easily show these distinctions. Dut ¡t unfortunately happens that an equally great proportion of sugar exists in most succulent roots, such as dandelion beet and parsnips, and that in wheat and most kinds of grain the silica is as large as in chicorv. Taking these points into consideration, we cannot therefore place any great reliance on chemistry for the detection of such adulterations ns form l he subject or our present consideration. On hearing this inaiiv ol our readers will doubtless exclaim: "Well if chemistry cannot help you, how did vou make the iuvesti-ntious reported last month?" We answer, by means of tlu- microscope; and wc will now endeavour to show how this instrument is used, and how any person possessing one mar easilv examine coffee.

The credit of first seriously calling attention to the use of the microscope as a detector оГ adulterations belongs decidedly to Dr. Hassall, whose food examinations created so much sensation about fifteen years ago; anil it is now imperatively necessary that every analyst who turns his attention to lood should be not only a good chemist, but also a practised microscopist. In treating this branch of our subject, we will divide it into distinct heads for moro easy reteyencc.

1. Mode or Ehplotment.—The microscope is to be placed upon a steady table, so that the source of lu/ht shall lie on Ine.left of ike obserrer, and the " body" ol the instrument is to bo placed in a slightly inclined positiou. The operator, looking into the instrument, is then to move the mirror about, with its reflecting surface turned to the light until a perfect illumination of the microscope is produced!'

2. Source or Liout.—The best light is that reflected from a white cloud ou a bright day, direct sunlight being always avoided; but, if the day be dull, good lamplight is much to be preferred to bad daylight. The best source of artificial light ss that of a good moderator or paraffin lamp, which should be so arranged in height as to bring the flame about halfway between the stage and the mirror, and about a foot away from the instrument. The upper part of the chimney of the lamp should be fitted with a reading-shade, to throw the light down on the mirror, but prevent its being diffused about the room, exactly like the lights over a billiard table.

3. Mouhtino The Object.—For this purpose the operator
should be provided with some slips of good patent plate glass,
Sin. long by lin. wide; also with a box of thin glass covers,
cut either in squares or circles, though the former arc the
cheaper, and do quite as well. lie should likewise get some
stout needles anil fit them into small pieces of wood to act
as handles, leaving only about Jin. of the point end of the
needle sticking out. When about to examine the object, he
should place a slip of glass on a piece of white paper, and put
a few grains of the coffee (taken from the sample on the point
of a penknife) near one end of tho slip. This portion of coffee
is now to be moistened with a drop of water, and allowed to
soak for some time. The operator then takes a pair of needles,
and by тенпв of them thoroughly tears all the grains to

Íiieces, so thin as to be almost transparent. A few оГ these
ragments are then to be drawn to the centre of the slide,
moistened with a drop of water, and a thin glass cover to be
adroitly dropped over them, taking care, bv letting one end
of the cover down first, tu expel all air bubbles. The ubject
is now ready for use; but, until one has had some experience,
the complete avoidance of air bells is very difficult, and it is
therefore advisable for the operator to make himself familiar
with their appearance under the various powers of the micro-
scope. The same hint applies to pieces of hair, which arc
apt to fly about, and through which, along with air bubbles,
most ludicrous mistakes have been made by inexperienced
persons.

4. Examination or Tue Object.—The slip, with the
ubject mounted, is to be placed on the stage of the micro-
scope (which has been previously fitted with the i-in. power
and "C " eye piece), aud the body of the instrument is to be
brought down to within little more than half an inch from the
object. The operator now looks into the instrument, and

fently turns the body further down till the object appears,
he focussing is then to be completed by the fine adjustment,
and the whole object minutely examined by moving it about
gently in various directions. It is always advisable to
acquire the habit of keeping hnth eyes open when looking into
the instrument; and this ubility io, as it were, concentrate
all your thuughts on one eye is much more easilv learned
than wonid be imagined, and is a great saving to the sight,
which is apt to he impaired by much labour at the micro-
scope.

fi. MlCKOSCOI'IC APPEARANCES 0Г PlRE Соггее,— AH
our preparations being now complete, we look at a sample of
pure coliee, ami find it presents an appearance similar to
that shown in Fig. 1. We notice that there are two totallv
distinct forms visible. (1.) Several little flat fragment's
marked all over with irregular angular celle. These are
fragments of the body, or substances of the seed; and the
cells arc those which contained the essential oil. «lrcadv
referred to last moulu. (2.) A number of peculiar oval, or
rather lance-shaped bodies, resting on a fibrous membrane,
and haling tooth-like oblique markings between their edges.
These are fragments of the outer skin or lesta of the seed,
and arc wonderfully characteristic of pure coffee. None of
those structures appear in any of the usual adulterations of
this substance.

6. .ViicBoscono Chabactkes or Pure ClIICORÏ — Having changed our slide, and substituted pure chicory for pure colfee, we at once see a vast alteration. Here are no lance-shaped bodies, nnr angular cells, but instead we have the appearances shown in Fig. 8. We now notice a mass of round and elongated cells, evidently of a soft tissue, which form tlie^ principal portions of the substance of the chicory root. We also observe a number ol long tubes laid in bundles over the cells, having a most characteristically and beautifully marked surface. These tubes come from the centre of the root, aud, once seen, can never be mistaken, except for the similar tubes of dandelion, which we will next describe.

7. Microscopic Ciiahactehs or Dandelion,—These are shown in Fig. 4, and are so similar to chicorv as to be readily uiistakciilile for that root. On examining ihem more minutely, however, with a Jin. power, a difference is observable. The cells arc mure elongated, and the tubes arc more decidedly marked in complete rings, while here and there we hud masses uf a structure closely resembling the ribs of an animal.

In Fig. 2 we show the appearance of adulterated coffee, in which the reader will recognise all of the structures above mentioned. For the detection of roasted grain, we depend mainly on the appearance of granules of starch, which can be identified by their size and shape. The cells of turnip are much larger than those of chicorv. while particles of saw dust, especially mahogany, can be picked out from coffee by means of a needle, and readily identified. Mineral colouring matters may be discovered by burning some coffee in a small porcelain crucible.whcn, if the ash be red, it is certain that Venetian red, or other ferruginous earth, has been added to deepen the colour.

As iu this worid partisans can be found for almost any dogma, no matter how ridiculous it may be, provided that it is only asserted loudly and unblushingly enough, —so our grocer friends have, by dint of continual asseveration, got a large number of people to positively believe in clucorv-coffee and cull tilín filthy root an Improvement! The 'terrible absurdity of this idea must be manifest to anv one who glances for a moment at the subject. Chicory' is a root, while coffee is a seed. The former, buried in'the ground' deprived of the influence of sunlight or oir, only contains а few of the crudest vegetable matters, so to speak; while the latter, flourishing under a tropical sun, has all those complicated and refined organic principles, such as alkaloids, for the formation of which the action of light, &c., appears to be absolutely necessary. The advocates оГ chicory adulteration know well that it produces a sensation of oppression iu the stomach, and they take advantage of this to pretend that chicory-coffee has strength, and are believed by ignorant persons who cannot discriminate between that quality and indigestion, and whose palates have long since been thoroughly vitiated. Another cry of these apologists for adulteration is, that, thanks to chicory, coffee is brought down within the means of the poor, who" otherwise could »ot afford to drink it. This is very like bringing down champagne for the use of the poor by adding three-fourths of smuil beer,

only that in this case two good things would be spoiled, whereas chicory is too nasty to spoil at all. The simple fact i¿ that, as a rule, the poor get little or no coffee iu their shilling mixture, while the grocers get that sum per lb. for a substance which would not fetch 6d. per lb. it* it were sold ¡a ts own name. But we live in a country of "vested interests," and as the grocers have a "vested interest " in thi« adulteration, it is temporised with, and was for я time actually legalised, under a trifling restriction, which was seldom even complied with.

In conclusion, we have simply to ask that the public should somewhat bestir themselves, and apply the spur to our tardy legislators, so that it shall be made a misdemeanour to seil. under any circumstances, a mixture of chicory and coffee. This would not hurt any of the chicory epicures, as they could still buv their succulent mouthful in a separate form, while it would protect the great mass of the community froma daily-perpetrated fraud. Our authorities every now and then make a spasmodic dash at something, and lately their hobby has been " tea dust " and " re-dried leaves ; " bat afterall, even with the terrible addition of the frolicsome Chinese pigs, about which we have heard so much during the last fewweeks, the sale of such commodities is no worse than the daily winked-at traffic in chicory-coffee.

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FRICTION.—VII.
Вт С. Deapee, A.B., L CE.
{Continued from page 33.)

Tue Wedoe.—As the characteristic property of the wedge is that it owes its mechanical advantage to the existence of friction, it will be proper, iu this aeries of articles, to give at length an account of it.

As the wedge is sometimes, though rarely, urged between the resisting surfaces by pressure, we have a theory for its action founded upon statical principles, but almost invariably the wedge is driven by means of impact or a blow; we must therefore look to dynamics for the solution of the problem of the wedge iu this case.

To commence with the 'statical theory, let ABC, Fig. IS, be an isosceles wedge, P the preasnrc acting at right angle» to -A B, and let D E and D' E' be pcrpeudiculars to the sides of thc.'wedge erected at D and I)' the points of contact between the sides and the resisting surfaces, or, rather, the points through which the resultants of the mutual pressures pass, forthe wedge may be in contact1 with the resisting surfaces at several points. Since everything is supposed to be symmetrical on each side of the axis of the wedge, D and D'

will lie on the same horizontal line, but it is clearly matter о indifférence where the line D I)' is situated, since the question is one concernina; angles alone.

Now, when the wedge is on the point of moving under the influence of the pressure, P must be in equilibrium with the reactions (¿' Q' acting along D E and IV h', and the fricciona и Q, fi Q' acting along D С, ¡У C, at right angles to the reactions Q Q\ therefore the resultant of Q and p Q acting along D K, making an angle л with D E, together with the resultant of Q' and ц Q', acting along D' K/, must be in equilibrium with P; therefore, by the conditions of equili~ brium, calling these resultants R and R', we must have the components of R and hY parallel to P equal to P.

Let i be the semi-angle of cleavage of the wedge, or AC В = 2í, then since R and R' are manifestly equal, we have

2R sin. (i + ç}) = P.

And if we wish to know the pressure T exerted by the wedge

in any other direction, making an angle a with D E, we

must have the component of Riu this direction equal to T, or

R cos. (a + p, = T.

Equating the two values for R found from these two equa-
tions, we have

P cos. (a + 0)
T = — x

г sin. (i + e))

a = 0, then T becomes equal to Q, aud its value given by

P cos. d>.

Q = - x

2 sin. (i + рл

If a - i, then T becomes horizontal, and its value i* given by

P
T = — x cot. (i + j)).

Let us now suppose that tho wedge has been forced into its position, and that it is required to tied the force P' neceasarv to extract it again. In this case we have the reaction» Q Q aiding P', to that R acts on the other side of E D at the angle a> ; we have, therefore,

ÏR «in. - 0 = I"

Example 11.—An isosceles wedge, whose angle of cleavage is !>°. is forced into its position by a pressure of 1121b. If the си-efficient of friction be J, calculate the least force required to extract it,

From the above we have

P = 211

And

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