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shining, whether he has north or south declination, he le always 12 hours above the horizon to places which have no latitude, as Quito, Ac. Let the two poles of the globe be placed in the horizon, and we shall have a representation of a right sphere, and the inhabitants of the globe whe lire in this position of the sphere live under the equinoctial, and, the consequence iH, that the pole sur being immovable with respect to the earth, this star will be in the northern horizon, and nightly wueu the firmament is olear, it will be visible to them in the same place, and in fact, these people have much better opportunities of examining the stare, and In consequence of becoming excellent astronomers, than those in higher latitudes, for they have the advantage of being able to examine the whole canopy of the sky in the course of the year, without travelling to other countries lor this purpose. All the stars north and south of the equinootial will in due course appear to them, for as tbelr view extends 90° northward and southward, they will be able to command a view of the whole. Daily, new stars will rise in their east, rtntil the whole tour of the sky Is completed, for when tb" sun is in Aries, (not taking any account of the pre «selon of the equinoxes) the constellation Libra, will be on their meridian at midnight, Taurus Ponlatowski will be rising and Orion will have just set, whereas, when the sun is In Libra, Orion will bave just risen, and Taurus Poniatowskt will be setting. By turning round the celestial globe, from es s t to west, we shall find that the inhabitants of the equator will lose sight of half the stars for six months. Some of the constellations, those for instance in the equlnoce tlal, as Orion, will perform a larçe circuit, golog round in a vertical circle, but the Great Bear will appear near their northern horizon, performing a small circuit, and the Southern Cross towards the south, the one being nearly oppositeto theotber. The sun will be vertical to them every six months, and his meridian altitude will never be lower than би,"—that is, it will be rather higher In altitude than the meridian sun of June in our latitude. Those who live in a parallel sphere, as at the poles, (Fig. 2), will lose sight of the stars for six months, not because they go below their horizon, but because the rays of the sun will prevent them from appearing, and when they do appear they will go round them in parallel circles, the pole star being in their zenith, and even then they .will only behold half of the stars in the rast concavities of space, but as a compensation for this, they will be blessed with the sun'в rays for six months, be appearing to describe a spiral circle round them. All the other Inhabitants of the globe live in what Is called an oblique sphere, (Fig. 3), the obliquity increasii more and more ae we approach tbe poles. In: oblique ephere in our hemisphere, the polar star ... always at such an altitude above the horizon as is equal to the latitude, and tbe consequence of living la an oblique sphere is, that the length of day and night constantly varies, tbe least to those nearest the equator, and tbe greatest to these nearest the poles. Nearly all the inhabitants therefore of tbe torrid zone will have an opportunity of seeing most of the stars in the course of the year the noted constellation, the Southern Cross, being visible to all of them. By elevating the pole to tbe latitude of any place, this will be readily apparent. Thus, London will never see stars beyond 38j° S. latitude, (bat Is, a few degrees below Formelhaut in the Southern Fish, whereas in Australia, the G reat Hear will be below the horizon, and invisible Thus the whole of the globe is visited with an equal share of the sun's rays in the course of the year, and there Is nothing hid from the heat thereof the long days of summer, making up for our loss of him during the winter.

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Sin,—My attention bas recently been drawn to a •eries of letters in the English Mecuanic, on Yt »ter Analysis, signed " George E. Davis," "W. R" and ■• Urban." "V?. R." Is anxious for an impartial opinion as to the relatire merits of FranklaLd and Armstrong's method of water analysis, and Wanklyn Chapman, and Smith's method, ¿в you will perceive by the signature to this letter, I cannot be supposed to give an impartial opinion. I will, however, place before you the points at issue between Messrs. Frankland and Armstrong and ourselves, I muet premiso that the modification of Dr. Frankland's process, described by Mr. Davis in your page», will not yield any reliable result unless a multitude of precautions, not hinted at In the letter, be taken. The volume of gas to bo measured is so exceedingly small, that if these precautions be omitted, we are certain to obtain as much stray gas as will absolutely ritiate the result. My remarks apply therefore only to the process as described by its authors.

.i'w-K>" 4uoting from memory, says that / stated that the experimental ci rors of Frankland's method exceeded the quantities to be estimated. This statement was made by my colleagues and myself, and under considerable restrictions—riz., that the errors on the рМиШ experimental mu'fi of ¡Fraukland and Armstrong exceeded the quantities to be estimated.

This le a question which 'anyone 'possessed of the

Eowers of «subtraction and comparison can settle for imself. Of course, the method may bare been since greatly improved. It may be that these experimental results do not represent the average error, but there are no other published results on which wo could form an opinion. This, therefore, was not a hasty-assertion, made in the heat of argument, as " W. H." would Imply, but simply an arithmetical fact, as he may convince himself by examining the paper in which tbe assortlon is made in the Joumil of the Chemical Society for 1SÔ8, p. 152, and following. Moreover, tltie expression was tbe result of a critical examination of Frankland's method, forced upon as by tlieextraordiuary argument employed by Dr. Frankland—viz., that as his procees and our process, when applied to the same water of unknown composition, yield different results, ours Is necessarily wrong,and his right.

There are other points in dispute between Messrs. Frankland and Armstrong and ourselves :—First, are nitrates completely decomposed by the treatment recommended by Messrs. Fraukland und Armstrong? We assert that they are not, and they, on the contrary, assert that they are. Second, is ammonia completely retained by sulphureous acid when its aqueous solution is evaporated with that acid? We assert that it is not so retained, and they imply that it Is. Lastly, they operate on the residue obtained after the water has been all evaporated away. We maintain that no method of estimating organic matter in water is valid which necessitates this condition, as the organic matter is Hablo to be greatly changed, and even in some cases totally to disappear during the evaporation. On these points we have collected many experimental data, all of the simplest kind. Any one, oven though he be not much of a chomist, can repeat our experiments; and without in any way wishing to pronounce a decision in the matter myself, I think I may request any of your readers who are prepared to go through the labour of making a water analysis by the method of Messrs. Fraukland and Armstrong to devote a few hours to the study of the paper mentioned above, and to a verification, by experiment, of the results mentioned.

A word or two in conclusion on the actual measurement of organic matter contained in water. If one kind of organic matter only existed in water, it would doubtless Ъе desirable to measure it, and would bo a very easy thing to do; but the organic matter which exists in water consists of a multitude of different bodies mixed In proportions which vary probably with every source of water supply. Therefore, the actual measurement of organic matter Is without interest. But, on the contrary, wo hardly know of a virulent organic poison which does not contain nitrogen ; and we do not know of a single germ, or egg, or living creature of any kind, which does not contain nitrogen. Therefore, the amount of the nitrogen forms a kind of limiting value beyond which the defllemant of tbe water does not extend. It may not extend so far, but at this present time we are without any means of distinguishing between one variety of nitrogenous organic matter and another. As our method of analysis deals with the nitroitcnous organic matter only, and brings out its nitrogen in the form of ammonia, we have called it the "ammonia" method, and not the permanganate, or alkaline permanganate method, as some of your correspondents have done. These latter terms are apt to lead to its beiug confounded with an older and now exploded method.

Ernest T. Chapman, .1, Redland-terrace,
Durdham Down, Bristol.

TEMPERING SMALL DRILLS. Sin,—There have been several queries and answers in your columns on tempering drille, and I presume that "Burslem " (No. 2007) had not observed the several replies previously given on the eubject, which, being one of great importance to practical and working mechanics, I beg to add my brick, as it appears that none of the answers allude to a very simple and effectual method of tempering small drills which I learnt from a working watchmaker in 18-Ю, and have proved by many years' constant use. It is as follows : — Heat the point oi the drill to redness, and plunge it quickly Into a lump of ro nmun yellow bar soap, and it will be found to be of a fine "straw" temper, and will stand better than if first hardened and then lowered to the required colour in the ordinary ш inner. The degree of hardness Is regulated by the amount of heat applied, also by the nature of the steel. Cast steel requires a lower heat than shear steel or spring steel, but no attention is required to the colours, which is a very great convenience, especially in very small drills, and also at night, when it is of teu impossible to catch the proper colour In time to ensure a fine cutting edge, and hence there is often serious loss of time (and temper also) to the workman. 1 have used this method for drills up to | diam., and consider that Its value and success result from the fact that the cutting edge is left of higher temper or degree of hardness thau the inner particles of the steel, which, of course, are cooled slower than the surface, and consequently drills tempered in this manner will not be found so apt to fly as those treated in the usual way, as described by "A Morayshire Man" (page 236), which leaves tbe interior of the hardened steel of a higher temper, owing to the reducing heat being applied to the surface. I need hardly add that the temper of the shank of the drill can be regulated by the extent to which the heat is allowed to extend back from tbe point. Amateur Tinker.

aerostation than the combination of great Initial velocity with an aero inclined plane, an Idea evidently derived from tbefact of a common kite being sustained in the air, wuen held by the line, in such a manner as to float in an Inclined position. It was also suggested. that;by fixing anraero plane of oiled silk in an inclined position to a velocipede, a step forward In the right direction might be made. However that suggestion may turn out in regard to actual flying. It is a Rood ono for velocipedes, which if moving with sufficient velocity with the inclined plane attached, would tend to rise from the ground, and thus lessen the friction and fatigue of the driver. In this rase the action is somewhat the reverse of the kite, for the carriage produces the wind, while at the вате time it holds the inclined plane in the proper position, just us the bellyband holds the kite against the natural wind.

Now a bird flying against a m 'derate breeze does not move at a much less rate than twenty miles an hour, as may bo observed from a train going at that speed. But the velocipede, as now generally constructed, oannot be driven at anything like that rate, for at ten miles an hour only the legs of tbe driver must make about ninety double strokes per minute, even to attain that speed, an evident impossibility. The "velocifere," however, offers a solution of the difficulty, for it can easily be driven at the rate of twenty or thirty miles au hour, and the oiled silk inclined plane attached, would tend to relieve tbe driver in some measure from the resistance of tbe atmosphere, very great at high velocity, by taking off a considerable portion of the weight of the carriage. The suggestion of propellers to act on the air, I believe to be impracticable.

Henry W. Keveley, Reading.

ACCUMULATING AND UTILISING POWER.

Sir,—In the vast and rapidly progressing couutrles bordering on the River Plate, English settlers find one great drawback in the scarcity, often absolute want, of fuel, the cost at any considerable distance from the ports being from £10 to £15 per ton for coal, bonce steam (until the plantations now growing, can give the requisite supply of firewood) cannot be employed as motive power. From the level character of the Pampas, water power cannot be got, consequently our only available resources are wind and the countless thousands of bullocks and horses which cover tbe country. Can any of your ingenious readers suggeet a method by which the power of a windmill or horseroundabout, working, вау three days, could be accumulated or stored up in a machine, capable of giving out tbe whole of the power thus accumulated during the fourth day, for working a set of Fowler's ploughing tacxle, pumping water for irrigation, or any other operation requiring more and steadier power than can be got out of the fluctuating action of a windmill, or the equally unsatisfactory work of a horseroundabout, it being in practice imposslble'to drive the animals so as to obtain anything upproacblng what their combiucd power ought to be. I enclose my address.

River Plater.

POTATO GROWING.

Sir,—Seeing in the number for June 10 Mr. Wllklns's plan of growing potatoes, I am induced to ask for a small space to present my brother readers with a somewhat similar system, recommended by a firstclass gardener in the Nottingham Guardian, воте little time ago. My lot happens to be cast in a potato producing county, and we are on all sides trying this method, and tbe plants (despite tbe unfavourably dry weather) are looking first-rate. His system is to rake the.surface of the ground you wish to plant, then lay down (by line) tbe Beed, 1ft. Gin. apart. When the row is complete, draw the soil over the potatoes with a hoe, to the thickness of three or four Inches, the next row 8ft. from tbe first, and so on. Now you see by this plan, the tubers are on a level with tbe surface of the ground, consequently more uuder the influence of the atmosphere and sun, which I think is a point gatned over Mr. Wllklns's system. The plants, in their growth, do not require the pea sticks, and the yield is set down at 30 tons per acre on the average. Several of us have compared the two systems, and Intend trying them side by side another season, and If we are spared, the result shall be known to the readers of the English Mrciianic.

Bakting.

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MICROSCOPIC CONDENSER, Ac.

Sib,—Your correspondent "X. Y. Z." (pago 30S) seems to be using a very deep Kellner eyepiece as an achromatic condenser. I presume he has removed the cap which covers the eye lone of the eyepiece (that lens being used uppermost). If, when this has been done, the eyepiece still interferes with the movement of the substage, I should recommend him to exchange the Kellner eyepiece for one of somewhat less power and longer focus. An ordinary objective will make а convenient condenser if used with the lower lens nexv the stage. The objective may be the next lower powcy to that used in examining the object. .eir

The wedges Into which " Arthur Gearing' (page.ays. has divided the area of bis circle, have, of cconvecurvodltues for their bases, these being small p- quiet, of tbe circumference of the circle; but In the padic box grams the wedges are triaugular, the curvnuke posbeing replaced by straight lines, neoessarily j thev'are some change, however slight, in the area ofrallol "comb and consequently causing the square to bnrardcr thin very nearly the вате area of the circle, using chbrodently no solution of tbe problem. Drvins is a

jur readers may

evening, or when

THE THAMES. er«.fl»!,hlre to he

Sir,—To those of your readers voth round the Dk»cb oar or a pair of sculls, I can recome can escape. Thou nie on the Thames, starting fromm luve for about teu about Richmond, nor is any irilic bn-uing sound u'aca necessary. 1 like my ease, aud On lifting off tbe upper having и teudency ..owards agin a cluster, and tbere steering, »ud from a lameirer hive. The dr.i'en bees

stand either bard or long-continued work, yet the abuve excuraioD is not difficult for Dio. It will bo observed that my proposal is to come esotra the river. Messrs. .Salter of Oxford, aud probably the other boat builders, let boats for this voyage, and carry them back by road. The terme are not exorbitant I paid £2 10s. for theflrst week, and 10s. per week afterwards for a pig with pair oars, pair sculls, and a email lug sail, tho latter being, iu their light boats only of use whin the wind is, as a lady friend expresses it, "abaft the funnel." The boat may be left at any convenient point where there is a boat yard, or sometimes iu charge of tho look-keepers, aud from that time the hiring ceases. This ieeouvonient in caseof a promising «pell of wet weather. The crew should consist of two, throe, or four persons. In the two latter cases, one or two should bo ladies (of moderate age), but a stogie voyager, paddling his owu canoe, will find It a most enjovable trip. 1 wont to Oxford, and to Salter, a perfect stranger, and obtained a boat without difficulty, but it would be betterto write beforehand, stating what is required.

Now as to board and lodging. There are plenty of inns along the course of the river—and they are really inns—neither hotels nor public houses. They are however, often full, particularly in;autumn, and on Saturdays and Sundays at other seasons. When this is the ca>e it ш a good plan to leave the boat in charge of a lock-keeper, and walk off to some village a mile or two inland. Very primitive accommodation will thus be met with occasionally, which will give zest to tho voyage. It is, however, rather jolly to carry with you the breakfast machinery, including the moans of getting hot water, either by a spirit lamp or by a fire of stielte on the bank. Milk can gencrallybo obtained fresh from the cow, and the other materials may be laid in at any village. A railway rug will often be found convenient, particularly if you feel inclined to disregard the popular prejudice against sleeping at night in the upon air.

There is a map of the course of tho Thames from its source, to its mouth, sold by most booksellers.which is almost a necessity to anyone unacquainted with the river. It shows the position of tho locks and inn*. and supplies much other useful information—price 2e. or 3s.

If time will allow, a sketch book, a camera, or a fishing rod may be added to the other impedimenta.

K. 8.

CHEAP GAS.

Sir,—"Cheap Gas" (3819 No. 269) asks how to reduce his " Gas Hill," aud" L. M."(page 260 Vol. XII) tells him th;it nearly all the plans lor carburotting coal gas have proved failures, or at least have bceu abandoned on account of the difficulties and the absence of the economy anticipated.

Now as the question of cheap gas is a very grave and important one to us all, touching our pockets, our eyes, and our health also, I do not think your readers will wish the subject should be so quietly disposed of in the oil-hand manner "L. M." appears to think it ought to be.

Ho certainly is not well informed upon the real facts and principles involved, and it would have been better hod he given his opinions, aud then invited those of some of the talented chemists who have contributed such valuable articles iu the pages of the English Mechanic.

I have hitherto retrained from offering any reply, hoping that some one moro able to do so would have taken up this important and pressing subject, but ав a month has nearly passed, and only one correspondent has written in reply, to tell us a very simple and good plan to regulate the flow of gas to the burners, which Is very useful as far as it goes, yet tho original question of "Cheap Gas" remains unanswered.

I have given some attention, to this subject, and have no interested motive, and perhaps a lew practical remarks may prove of interest to your readers, and help to ventilate the question more fully, though of course we must be prepared for objections from parties interested in the existing gas companies, whole Interests lie in making large gas bills at the least possible outlay iu manufacture. Hence there is a constant strife between these interested parties and their customers. Ou the one hand the gas is kt-pt at the lowest possible illuminating power that the law wilt permit, and on the other hand bitter complaints come of long bills and high prices.

I do not wish to follow this part of the subject, but only refer to it in order tbat we may get at the real state of the cose, for really cheap gas is good gas, and the question therefore'is, how arc wo to obtain fcood gas?

"I». M." would wish us to believe that the attempts hitherto made to enrich poor coal gas are uot fourni to be economical, and be tell« us of two or three patents, hut the real fact is that the number oí patented apparatus for thiü object are nearer one hundred, and are probably all equally without real claims to novelty, icing all based upon two well-known facts—viz., that Ню illuminating power of hydrogen gas entirely tie thuds upou the amount or' carbon present in its name. N—The great affinity of hydrogen gas for thehydromotrn vapour, such as benzole or uaptha. *■ thauicoul gas is rich in these vapours as it passes municahe retorts, but the gas companies find itexpemust ! B.extract a greater part of these eon dem* able of link is * ml supply their customers with a very low the valve miuating gas

move whei«e was also lowered in proportion, there but this I «i Do much to complain of, perhaps, for link will vibreasonH, well known to practical chevalve splndle-e have to do with gas as it is, let us centres are in otention to the bcst.plan left us. which what angles theitoro the illuminating element to the eccentrics should quantity required to give a certain travel one distantly be reduced, and the nature of opposite directions-om the dirty yellow red to clear the centre of motloknot least) less heat and less earNow let me takbiric acid fumes discharged into vhe.: "l¿in. of lap апцЦ(1 hence into our lunge, begívee UBäitn." which ht destruction of all property tut there Ъе le wrong а^е great question therefore is more vibration to open

Dr. Letheby, the great gas analyst, says (in his lecture upon gas lighting) that it can, as follows:—

"Experiments have been made for the purpose of detcrmiuiug the value of the light for the benzole or naphtha consumed, and the results are that every grain of the vapour taken up by a foot ot common twelve-candle gas increases its light ten per cent."*

The soundness ot the theory being thus established, it only remains to carry it out in a convenient aud efficient manner, and for this hundreds of contrivances have been proposed, patented, and discarded, chiefly owing to the fact that the gas in passing over the naphtha always takes up the lighter portion in vapour¡ and thus the fluid gradually becomes less Yolatile, and heavy, till at last no more vapour is carried off by the gas at the ordinary temperature, and tho Illuminating power of the gas is lowered to its furnier strength, till tho vessel is emptied and fresh naphtha added.

But the advantage* to be obtained heve kept tbe questiou before the miudsof the scientific world, and latterly there have been plans adopted to avoid the above-stated difficulty. The price, also, of benzole and other products of coal tar is now so much reduced, that the economical carburetting of coal gas can now unquestionably be dono with great advantage and success, resulting in a saving of at least 30 percent nett.

In No. 263, for 8th April, page 64, there Isa description and drawing of a very simple aud cheap plan for carburetting gas forusc iu the magic lantern, which will bo sufficient to explain the whole process, and which can bo made up by anyone wishing to try tho experiment himself. Such a bottle apparatus is capable of properly carburetting ten or fifteen feet of gas per hour, and I have used such a rough affair for several years with repeatedly tested results, using the benzole sold at 4s. 'id. per gallon. 1 found the power of the light increased iu au astonishing manner, as given below:

8

With common coal gas (pressure —th.) No. 2 flsh

10 tail burner, consuming 3ft. of gas per hourPower of light with common gas = 24 candles. Do. do. curhurettcd gas = 7 candles.

Naphtha consumed Ifc pint per 1U0O ÍL

Increase of light, 17Ô per cent.

It is not to be expected tbat such results could be obtained in ordinary use. but I give tbe»e facts to show what can be done by judicious management, and the use of good and small sized burners. If I bad uineda largo sized burner the advantages would not have been so striking (probably uot more than 100 per cent.) во that smalt burners should be used for rich ga.s, and if more light is required, multiply the number, but do not u.«e larger sized burners iban No. 2 or 3.

Having thus given experimental results, I may mention that I believe the best (because tbe simplest) apparatus I know of is Woodward's patent, ol winch I enclose a drawing, but I do not wish to use your columns to puff anyone's invention or patent, my object being to prove to your renden* that it is practicable to reduce their gas bills, and to lay before them the advantages of carburetting or enriching poor gas.

But there are also dangers to be guarded against, аз we all know (or should know) that naphtha is highly inflammable, and requires to be handled and used with the same care as epirits of turpentine, aud such other spirits aud fluids, therefore in fitting one of these carburetters near the meter, It muse be placed so as to be filled by daylight, and a cap and padlock fixed to prevent anyone tampering with it. The fluid is not exfrioeivc, aud is of euch strong smell, that tbe least eak or escapefof gas is Instantly detected, which Is a very important consideration.

The insurance offices have of course a voice in this matter, and a proper report must be made of the titling and nature of the apparatus, but as it will requite only to be refilled twice or thrice a year in ordinary cases, and to be always done by qualified persons, there will not bo any objections made after due and official inspection has been made.

There are other plans for using heavy naphtha, which will require to be heated over each gas burner before it will give off vapour, but these are more adapted fur the workshop, factory, or open air, in which they auswer very well, but, require toba refilled every fortnight or so. In these plans, all difficulty with Insurance offices is avoided, und whore a working man only rents a room or so, und requires one or two good lights, without outlay, or altering the gas fillings of the house, &o., it would bo tho best plau to adopt.

Dr. Iiowditch, of Wakefield, is the patentee of one of these plans, and a firm in Westminster have another (Kidd's patent), wbirii ha« been fitted to all the pendant lamps of the new terminus of tho Midland Counties Kailway, at St. Faneras, but appear expensively made.

In conclusion, I may add that where the size of the burners in use with common gas is not reduced, when tbe gas is enriched in proportion as the power of light is iHcreased, it is not wonderful that no saving is found to result, nor can tho human eye be trusted to judge of the iucreased light being maintained, for habit so misleads the judgment, that nothing but actual test by photometer can be relied on for proof of the Improvement being continued.

I have used curburetted gas in my house for eeveral years, and find the annual saving in gas to be fully maintained at nearly 50 per cent, as at firat.

C. D. С

BATH FORUM KECKKATIOXS. Sir,—In your number of Juno the 17th you invite notice*, hints, suggestions, and information on excursions, tours, Ax. Knclosed 1 beg to send you a prospectus of the Bath Free Forum Summer Amusements,

which, though not exactly of tbe character you indicate in your note, may still bo interesting to some oí your readers who are desirous ot promoting ploasaDt pastimes for summer mornings and evenings. The Bath Free Forum commenced in tbe beginning of last winter with holding weekly meetings for the free discussion of any local or general questions of importance, and it proved to be such a success that the committee of management, under tho efficient presideuey of the Bev. J. Mac Naught, M. A., decided to do something to entertain the members (and any others willing to join them) during the summer months. With that object in view, they framed the rules of which the enclosed Is a copy. In order to prevent any loes that might accrue falling ou the committee, or only a few of the more earnest friends ol the movement, about one hundred were canvassed, and readily consented to pay 10s., or any portion of Ids., that might be required for that purpose. To purchase tho necessary imp lómente, seven gentlemen advanced £10 each as a loan to the society, to be repaid when the subscriptions of members enabled the society to refund it.

The society provides boating on the river, cricketing, football, quoits, croquet, &c They have three boats, of various sizes, and such other things as may be wanted, according to the number joining. The terms of membership are—is. for gentlemen, Э«. 6d. for ladies, for th« whele of the five summer months. May to ¡September (inclusive), or Is. per month gentlemen, 6d. ladies. During the first month about Ú50 joined, and as a result the boats arc lu constant use during thv hours fixed by the committee—i. «., from h alt-past frr: to ten in the morning, and five to half-past nina in the evening. On an average, there are about 40 to 50 player* at cricket daily, about 30 to 40 croquet, and tbe other sports are proportionately well patronised, and new members are added to the list daily; so that np to the preeeut time about 150 daily avail themselves of the privileges of the society, and there le every prospect ofite being self-supporting, and possibly leaving the boats aud other implements of the society a clear profit at tho end of the season. In addition to all this, it .Js iutended to arrange excursions lor pleasure, »cientifie, geological, and archaeological inquiry, to various places of local or historical interest. A t the end of the season I think the committee of management will be able to congratulate themselves in having promoted a good deal of healthful and innocent recreation and eojoymeut, cultivated a large amount of social and agreeable Intercourse amoug many who otherwise would have remained strangers, kept many away from the public-house aud other places of doubtful amusement, and encouraged and fostered a taste for pursuits of a profitable aud educational character.

If any of your readers would like further information as to the working of this society, I shall be plea&ed to give it them either direct or through the columns of your valuable magazine.

B. P. Edwards, Bath.

SIÏOBTHAND.

Si и ; —In the multitude <>f councillors, the wieeman Fail', there is wisdom, and I trust that " Hermit" aud aay other recluse anxious to obtain a knowledge of the coveted art will be led Into the right path. I fully endorse "W.'s" state aient respecting Pitman's phonography, aud would recommeud " Hermit " to obtain "The Reporter's Guide," written by Mr. Keed, one of the best shorthand writers in the world, capable ot' writing ^00 words a minute (if necessary) and read them afterwards; he can get it through a bookseller. I am sorry to say Mr G-rierson has said without proof (at least to me) that Pitman's i* the worst system. I deny it, for 1 learnt OdeIVs, or Taylor's Improved, but Pitman's is far superior tu it. I am between 40 and ftO years old. I was anxious that s son of raine, desirous of being a compositor, should learn shorthand. About three years ago I began to tea^h him Udell's, but haviug heard a great deal of Pitman's, I made inquiries about it, and from the recommendations I received in it» favour 1 was determined to master it. I practised with my son for about 12 months, and then I received a teacher's certificate. I can now followclose upon the heels of an ordinary speaker, whilst my son (lo years of age) can write 13o words a minute, and perhaps »юге at » pinch. Another young man (lif), Ut whom I gave lessons for 12 months, but who had a sliiiht knowledge of it before, is now reporter on a paper publish.M here; and I have a report of his of the re-openintr. last week, of a church by the Bishop of Bath and Wells, which occupies two-and-a-half columns of the paper {IMhj Sews size). Phonography should not be judged of by the operation« of cuose who.-e iuaptttude would condemn »ny system, but by that of those who can and do catch aud imprison the winged words as they fly. If Mr. G.'s assertion la correct, we must be foolish (1 think the noun more appropriate) to follow sush a system. But may I ask him what other system can boast of so many admirer» as Pitman's, whose devotees are to be reckoned by thousands? What system besides publishes a " Shorthand Magazine," a "Cabinet," a weekly "Phouographer," and a " Phonographic Student," in shorthand, beides the Bible, Prayer Book, and a host of others? "Ilerrait" will fiud It unnecessary to purchase different systems and to amalgamate them; it is mero waste of time. Let him got one (I recommend Pitman's), and stick to it. bearing in mind that there is no royal road to shorthand. The phonographic motto is, "Practise aud Persevere." That widen is easily gained is lightly valued. Phonography can be road at any time, If carefully written; and as it has three positions for writing it (for reporting purposes it le uuuecesary, except, now and then), to insert any vowels,;and then geuerally one .is sufficient: whilst, hall-a-dozeu words c.m be written without taking off the pen.

T. Cridland, Williton, Taunton.

♦Lecture upon the Chemistry of Gas Lighting, by Henry Lethi By, Esq., MB.. &c. Delivered at Birmingham, beioio tbe Society of Gas Engineers, 1865.

Sir,- In the Mechanic for the 24th instant there i* some correspondence on shorthand, la which Pitmuu'e system is spoken of in disparaging terms; I hope, therefore, you will permit me to say a few word л on, the other side of tbe question. I do so on the ground that "those only who can speak from expérience ought to express an opinion on the relative values of various system*;" ncd I think yAnr correspondent, Frank ~\Y. Gritrson, will adroit me ftmoiiR that class when I state that 1 have written shorthand for nearly .to years. Pitman's for 24 years, and for the Inst eight years bave taught it extensively iu public and private. Roth your correspondents object to Pitman's system because ita thin and thick strokes represent different letters. Now, this is not exactly true. Pitman's system is based upon the sounds of the English language, and not the letters of the Roman alphabet, and bis rule U, similar strokes should represent similar sounds. Thus, he represents f and b by similar strokes, because of tlieir similarity in sound; so with f and v, //* in '/tin and tA in thine. It Is also possible, nay more, it is cu.sy, to make a difference in the thickness of the strokes when writing rapidly, and so far from being "practically illegible unless the shorthand be transcribed while the subject is fresh in the memory." it is well known that reporters hare frequently turned over their note-books to the compositore, who have from them set up the type without the .matter being transcribed into longhand; and even lads between 12 and 1«» years old have many times set %p from my notes, in which I had inserted a few vowel point*. But granting, for the take of argument, that thin nml thick strokes are not possible in rapid writing, the principle npon which they are arranged tn Pitman precludes the possibility of mistake tn reading. 1 will even grant that a case may occur where the grammatical construction of the sentence wonld not be a guide to the reader when thin and thick strokes were not observed (such cases nre very rare), yet such are the .proUfle sources of phonography, as to variety of outline, that the emergency would be provided for.

I'\ W. G.'s next objection is to the vowols. Here airalo he in in error, which is not remarkable, for he say* both Mack en ale and Pitman "bave long departed from bis memory." There are not, as he asserts, six vowel positions (it would indeed be "ridiculous" if there were), but only three—namely, the beginning, middle, and end of a consonant, and the dlfflealty ■which F. G. appears to have felt abont placing the vowels Wobm occur to none but the merest tyro. The instruction book is very lucid on this point. The fact that there are thousands of persons iu this country and America who are constantly corresponding with each other in Pitman's system, and who prefer it to longhand, both for the ease with which it can be written aiM read, is feuhlcient answer to the charge of illegibility.

In conclusion, allow me to say that the daily Times employs 10 Parliamentary reporters, 16 of whom write Pitman. These, at any rate, do not find it "complex and uusatisfactory," a** your correspondent Mac!), did.

SUTCLIFT ROBISSOIf.

ROCKSAtiT MINE, NORTHWICH, CHESHIRE.

Sir,—Allow me to give to the readers of your very «uperior periodical a short account of my visit to the Northwien rock salt mine, during Whit-week. This special mine, so opened for inspection, \% in the occupation of Mr. WtuhbB, who every year hm it Illuminated by upward* of 1,000 candles at one time, w> that for the three days it was illuminated this yeario.rju candles were consumed. The number of visitors, chiefly from Manchester and towns around, this year, was 1000, This is one of the largest salt mines in the valley of the Weaver, and will well repay a visit. Outside there is nothing to distinguish this from any other salt mine. There are the usual appliances for raising the mineral, which is generally, as here, done by two shafts, serving also for the ventilation of the mine. Down by both theso shafts visitors descend in the large kibbles or buckets used for conveying the salt to the surface. These are attached to long, flat ropes wound round a windlass, and worked by a steam engine. The shafts are each about350ft. deep, 'lite tlrao occupied in the descent is about two minutes. On reaching the bottom the sight is most magnificent. The effect o( so many lights, in higher or lower positions on the crystalline walls or massive salt pillars which.are left standing to support the roof, is similar to what oue might behold in looking down upon a large city when only the thousands of gaslights are seen streaming out into the darkness. The effect is considerably heightened by the many pillars breaking the lung line of walls, so that no very great distance can be seen without an interruption, such as would occur from one street crossing another. Thus the long Urns of light are everywhere seen in part, now aiTcandJug, or else descending, as if the street climbed a hill or descended into a valley.

During the time of inspection, not only may refreshments of all sorts be obtained, but amusements also, for a good band is iu attendance, which every now and then sends forth strains of martial or dance music, to theinspirituff notes of which many feet soon begin to thread the mazy dance.

For the instruction of those ignorant of mining operation*, a few men are kept working in another part of the mine, showing how, with their drills and other implements, they bore and blast the rocksalt, tearing it (mm its native bed in great nigged masses. It approaches the terrific when their operation for blasting i» completed and the match takes bold on the charge of powder. Reverberation follows reverberation, as If the sides and roof were collapsing, or there was a complete ruin. But the visitor is soon reassured again, for perhaps his eye fails on an illuminated V. R-, or a ship, or arch over a pool of water, aud the reflection therefrom, or aline of wtreets iu candles.

The capacity of the mine is such that from 5,000 to Woo persons might easily be contained. The floor Is mostly cveu except where the men are working, or have left a hollow which the little water has filled up. But znoftly it Is dry. It is in thl-* respect a contrast to the world-renowned Wiuliczka, which has a chapel, mining stream, fresh water lake, Ac.; but on tlie whole.it Is one of the best sights ou the Weaver, if sot in all Cheshire.

B. W.

LINK MOTION, POINT MOVERS, ECCENTRICS.

Sir,—When reading over my last letter In No. 273, I perceived an error iu that part of it which contains my observations on Mr. Harrison's letter on the link

motion. In the fourth paragraph I ha^a said, that iu the link there spoken of, '*4£iu. is the minimnra mount of vibration which the middle of the iiuk should bave when working, and to obtain that the centres of the eccentrics must bo shifted round towards each other to a position ljln. in advnuce of the diameter line upon which they stand at present." lustead of ljin. It should be l£in. 1 do not know whether it is a printer's error or my own mistako, as I kept no copy of that letter, however, it is of no great consequence, as the example then given was only meant as a sort of general illustration of the necessity there exists for motion at the middle, of the link, and also of the impossibility of constructing that apparatus so that it shail have no motion at that purt.

■' l'uul Pry " asks, " Do two prime movers ever work in connection, such as a steam engine and a waterwheel, and if so, howls the coupling arranged so that one cannot over-run the other?

It in very common for steam engines and waterwheuls to work in connection, and they do so.very harmoniously, and no special coupling is necessary for connecting them, the common coupling being qntte sufficient, as under proper management they have no tendency to over-run or drag- each other.

Ascertain the least quantity of water which will drive the unloaded water-wheel at the proper speed of the mill, also ascertain the lowest pressure of steam which will work the uuloaded engine at the same spued, then all water aud all steam over and above these ascertained quantities go to do useful work in driving the mill, aud neither over-running nor dragging can take place till either the water or the steam falls below these quantities, neither is a governor to the water-wheel indispensable iu procuring harmonious action between the two, for the steam engine governor is quite sufficient for the purpose of governing both. Thus, suppose the water in the pond is slowly rising, more will pass over the sluice into the wheel, and an increase of speed will be the consequence; but the engine governor feels that, and immediately checks It by shutting off some steam. On t.ie contrary, if the level of the water is gradually falling, less wiil fiuil its way into the wheel, aud a reduction of speed will ensne, which is also felt and promptly remedied by the enine-governor admitting more steam to the cylinder.

I do uot mean to say that a special governor to the water-wheel would not be an improvement, though not indispensable, and no person need be at the expense of putting up one for that purpose, at the steam engine governor can, by proper appliances, be made to regulate the admission of water to the wheel. *' Paul Try" also asks, "What is the practical method of setting the eccentrics upon the crauk-shaft, so that they shall have the required angular advance of the cranks?" and asks me " to select as an example, eccentrics adapted for the link motion?" "l'aul is not the only person, by a good mauy, who has asked that question in your columns, for 1 have ropeatodly noticed similar enquiries from others for several years past, but I have never met with any replica worth reading, or giving a particle of information of the least use to any person desirous of acquiring knjwledge'of that most important branch of practical mechanical engineering.

It is a " big" subject to enter upon so as to treat it properly, and a great deal must bo said about it to render it of any practical utility to "Mr. Paul" and the other readers of the English Mechanic, lam willing to go into it with your permission, Mr. Kditor, but I caution you beforehand, that I will call for a good deal of your valnable space, and, not a littJoof your engraver's time for illustrations. It Is oue of those subjects which cannot be slurred over in a letter or two, but should be properly nnd Inexhaustivoly treated, or not entered upon a t all. I must further inform you, good Mr. Kditor, that I will not be satisfied with very minute Jllustratious, but will respectfully ask you for the full breadth of the page, or at least, the breadth of two columns for my drawings, such as J see you sometimes grunt to impossible projects for the impobHiblc purpose of squaring the circle, and also to showy "pictures" of wonderful velocipedes, in which the grand secret is embodied, whereby the power required to drive them diminishes as speed increases, and going.up a hill is much less difficult than going dowu one, and which throw the "seven league boots" of the nursery tale entirely In the shade. However, joking apart, please say if you will make room for a few "practical papers aud illustrations ou setting the eccentrics and valves of steam engines." J Am is Babbler Ville, Manager,

City Foundry, Limerick.

PHRENOLOGY.—"J. T." says:- I think, Sir. the foot-notes are often intended to draw information and ideas from our correspondents, and not proofs of scepticism, as many may suppose. You, Sir. have asked our correspondent it he wore blindfolded, could he tell who was a merchant, statesman, preacher, botanist, engineer, Ac.? but the difficulty being that he could not tell the temperament of each subject ho might examine, therefore he could not correctly delineate their character. The temperament is made manifest to the touch as well as to the sight by the fineness and coarseness of the hair, by the softness and hardness of the flesh, Ac. But it also may be said that few men rise to eminence but those who have a good temperament and organisation combined. 1 have no hesitation in saying that, under the manipulation of a good phrenologist, the characters nnd qualifications of those men might be made manifest, supposing any do not possess a combination of powers: but eaofi one has special qualities in his individual sphere.

REPLIES TO QUERIES.

EXTRACTS FROM CORRESPONDENCE.

TI1E LATHE.—" X. H." says :—"I am much pleased to seethe interest that some of my brother readers are taking in the lathe, and I trust that some of our talented contributors will give us working drawings of a first class amateur's lathe. Several of my friends have told me how pleased they have been with S. .Stevens' request, No, 4070, In ' Notes and Queries ' of last week, aud with which I cordially agree. I also trust iu our New York friend (page 307) will ^'ive us something to work at; I have great expectations from his communications."

EMIGRATION".—A Onnadian correspondent sayB: —"It may be information worth knowing at the present time, to know that skilled mechanical labour is far in excess of the demand in Canada at present, and members of clever and industrous artisans cannot get employment at their trades bore."

TO MrCKOSCOPISTS—W. P. says :—<4 I enclose you a reply to one of the queries In the current English Mechanic. As amfcrosenpist of some considerable experience, I may frmu time to time be able to solve some of the problems which perplex younger workers, and shall be always «,rlad to do what I can. I am glad to see my old friend, Scientific Opi-rioii, 1b about to amalgamate with yon."

CUTTING GRANITE.—T have a piece of granite out of which I wish to take a niece an inch square and polish it by hand. Gould any brother reader inform me how I can do it ?—Chkmiccs.

[37790-BOILER SAFETY VALVE—

TV =

L

whereby ^r1 area of the aperture of the valve; I distance from fulcrum to centre of valve = 31m. P = greatest pressure of steam in the boiler = 601b. per sq. in.; L ~ length of weight from fulcrum ; to ~ weight ot the lever = 71b. lk>z. Here the area of valve n-r5 = 3 1416 X 1*5J = 7'06-SG sq. in. By substituting these values iu the above formula we Bhull obtain the weight that ought to he applied nt endof lever. Should " One in Need "require to graduate his scale to obtain less pressure, I will let him know the practical rule. The above formula appears: "Baker's Steam Engine," p. 35.—A. Tolhauskn.

[3779.J-BOILER AND SAFETY VALVES.—Our correspondent, Mr. Howell, made a slight mistake in his answer at p. 309. He therein states, first the weight ot valve, spindle, and lever, and adds to it the weight of counterpoise weight. Now, I must tell Mr. Howell, that it would not he correct to add the weight of the lever to the counterpoise weight, because the counterpoise weight gives the effective pressure of the lever in a line with the centre of the valve; aud, therefore, includes the weight of the lever. Let him rend "JonatltV answer to "O.G.," |p. 310., No. 4019, wherein he gives a very beautiful and simple rule, und which will give him all the information he requires.—ThOyas J. O'CoNMoa.

[3817.]—HANDRAIUNG.—If **J. B." will consult Langley Bank's work he will find some useful information. I cannot say whether it is the best extant. I have had Newland's, but do not make much of it, owing to the number of lines which are necessary for the working out of rails as laid down iu that work. I have seen another—Jeay's, I think, is the author. A capital small work it is. I believe it is rare in England. There is also old Peter Nicholson's work. It ia, however, looked upon now as old and out of date with the times. Of course you will not tiud the square cat in Nicholson ; but he has some capital ideas. Any other information on thia. important subject 1 will gladly give.'

[39&r.1—TO CLEAN SADDLES.-!, feel sorry for "Equestrian's''inexpressibles if he has tried the beeswax and turpentine rccpic as recommended in No. 272. Let him wash his saddle with soap and Mater, then sponge all over with old milk, and polish with a soft cloth. If he caa apply a little neatsfoot oil where there is no wear it will be all the better; but by a constaut application of the milk nothing else will be required.—Banting.

[3S09.]—WEIGHT OK WATER.-"Countryman" must have forgotten that there is 00ft. of rope added to the weigh t of the water at the bottom of the well.—Joe S.

[3889]—PREPARING CANVAS.—First strain tightly upon frames, then wash with a thin glue; when dry it is painted with a coat of oil colour made of white lead, red lead, linseed oil and turpentine; and afterwards with a second coat, iu which the red le;td is omitted, und sugar of lead with a little colouring matter substituted.—(Extract from Francis' Dictionary of Recipes.)— Jok S.

[3'J13]—BEES.—ML. W." may safely hive his swarm in the straw hive if the comb is not more than three yean old; if above that age he had better cut out the two middle combs, as the cells in those combs arc most used for breeding purposes; therefore the cells are much smaller through their having so many cocoon? or linings in them. Each year adds from lour to six to their number. I cannot quite understand why he has a box under his straw hive. What motive has an "Oxfordshire Farmer " for spriukliug the oinbs with sugar, fcc—quite an unnecessary operation, both for the bees as well as their owner? Bees have a great dislike to having their wings clogged with sticky liquid. When uecs swarm they always leave the hive with a full supply of honey in their honey-hags—enough for them to subsist oa for three days. If " L. W." would hive his in a common straw hive for convenience, and then towards evening when they are all quiet, knock them out on a board or cloth and gently place the box or hive full of comb over them, they will ascend and take possession, when they may be moved to the position they "are intended tooccupy. A swarm hived into a hive full ot comb will he a fortnight or three weeks earlier or forwarder thaa one placed in un empty hive. I do not think using chloroform as a means of taking hives a good plan. Drving is a much easier method. Thinking some of our readers niny benefit by it, 1 will describe it. Towards evening, or when the bees are in, get an empty pail and invert the hive to be driven in it. Then place aoove it an empty hive of the same diameter as the lower one, then tie a cloth round the nlace where the two hives meet, so that none can escape- Then with two stout sticks beat tho bottom hive for about teu minutes. The operatorwill hear by the buzzing souud when most of the bees have ascended. Ou lifting off the upper hive the bees will be found hanging in a ctnster, and there will scarce!* be a bee left iu the lower hive. The driven bees

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cxn be added to any of his weak stocks, whicli will derive great benefit from the addition. Should "S. W." wish to know how to unite the bees to another stock, 1 will tell lnni in nr neit—Recheps.

PWO.J-THREE WHEELED VELOCE. -" T. T. M." asks for somethinir thu I am afraid Andrew Johnson docs not supply. Some time a(t° I w" in ■*■' of a three-wheeled machine to carry two. and knowing that it would he next to impossible to tnrn with the two hind wheels fast, hit upon a plan which works admirably. It is altogether different in the back action to anything that has appeared in our Mechanic these last two years; and if our Editor will allow space 1 mean to present in a week or two the readers ot the Mechak ic with a photograph and description. I will just say for the present that the back wheels are made with a groove inside the nare, against the nave Uoop; aud then I have a thumb screw-pin to go through the hoops of the nave, then «n the axle is rivetted a small piece ot flat iron, which is made to work inside the groove of wheel. When the thumb-screw is in the axle cannot pass it, so drives the wheel round when it is required. For one rider take out the pin. and all the wheels are loose. By this method the second man has great power, and still you may cut a figure of 8 with ease, as the pin on the inside wheel falls back from its work and takes it up when going straight. If " T. T. M." is in a hurry, I will furnish him with all particulars if he will give his whereabouts in your Sixpenny Wanted Column. If not, he and others will find a really good and serviceable machine when it is illustrated. The men sit back to back, and the two actions are independent—the first driving, as in the ordinary bicycle, the second by 5in. crank axle— Banting.

[4025.]—HORSE POWER.—The ordinary rules for nominal horse power may be expressed as follows:—V mean velocity of piston, in feet per minute.

D = Diameter of cylinder in inches .
S = Stroke of engine, in feet
H Horse power of engine

D» V~s

H = for high pressure.

15 0

[table][merged small]

no slipping, and those teeth are formed by increasing the diameter beyond the primary or pitch line for the points of the teeth, to correspond with which, the spues must he deepened to a circle below or within tlfe pitch line. Now the great art nf wheel malting" mainly consists in forming and proportioning the teeth properly. Several systems with those objects in view are in use, the details of which would encroach too much on your space. A simple and good rule is to divide the pitch into 15 equal parts, of which the thickness of the tooth wou!d be 7, the space 8, the length of the tooth 12, of which 5$ parts are above the pitch line, and 61 helow the pitch line. The depth of the tooth may be from 24; to 3 times the pitch; thickness of rim and arms equal thickness of tooth ; thickness of eye equal to pitch. Those references to arms and eye, of course, are only applicable to wheels of a large class. Supposing " R. T.'s" wheel of 120 teeth to be 3in. diameter at pitch hue. 12 > : 3 . \ 30: 76, or fin. at pitch line for his pinion of 30 teeth ; the pitch of those wheels would be about -078, and the diameter of both would he iu

1 creased by the increment '057, or about —in., so that the

16 1 IS

diameters would be 8 —in- and —in. respectively. It is Tery

16 16

inconvenient to express in figures the pitch of wheels less than \in. or fin,, and hence they are usually rated so many teeth to each inch in diameter. Tims we have our wheel patterns (invariably engine eut), of &, fl. 7.8, 9,10, 12,14,18, teeth to each inch in diameter—a wheel of 8 per in. corresponding nearly to fin. pitch. And trust those remarks may be useful to "R. T." and others — Matrix.

[4037.J-RULE FOR FINDING SIZES OF WHEEL*.— *' R. T." may obtain the relative sizes of wheels by the following rule :—The sum of the number of teeth in the two wheels is to the distance between their centres as the number of teeths in either wheel is to its radius.—Stakm.

[4039.J-UAROMF.TER TUBES.-In answer to this, I think if he were to fill his tube, and should there be any large air bubbles bring them out by what the French call Laeem*nt (that is, pass a large bubble up and down until the rest have been collected by it), then heat the mercurv and whilst it is boiling seal the tube close to the end.—J. W. Liars*.

[4040.]—WHEEL-GEARING.—Properly, bevel wheels are made in pairs, and if the teeth were diminished a', infinitum they become simplv a pair of cones, the two apeces meeting at a point where the axis would intersect, as at A, Fig. 1, the wheels B and C being properly adapted to each other. If it were desired to adapt a larger wheel D to B with tbe view of changing the velocity, the former innt be mide <jf the same

33000

Stat.m. 401b. per

[4026.}—BOILER PRESSURE.—From about square inch, upwards.—StAkh.

[4028.}—FLOORING.—The flooringof chambers in Nottinghamshire and Derbyshire were of plaster till boards became so cheap. It is prepared in the following manner for floors.— The atone or gypsum, or plaster, is got in a clay hill extending from Derby to Newark on the south side of the Trent, and only a few miles from the river, and parallel to it The Btone is burnt until red-hot, and then left to cool, it is then thrashed with a flail, the same as corn, until it will pass through a fin. sieve; then mix with water until quite soft, as to carry in a bucket. Laid on reed or lath, sets in 12 hours, rubbed off with a stone or trowel next day. The stone is red, yellow, green, and white; tbe white is ground same as flour, and boiled in open bath and used for covering over plaster images, and by plasterers for setting ceilings and cornices.—A. Doubled Ay.

[4033.]—SLIDE BEST.—In reply to "J. D. L," who inquires of me how this is done, the wheel to be cut is bored out, turned upon the edge and placed upon a stud or spindle which Is attached to the slide-rest, so that the wheel face may be horizontal, and the middle of the wheel's edge level with the lathe centres. The cutting tool is a grooved steel screw a duplicate of the tangent screw to be used with the wheel. Frequently an ordinary hole or master-trap is used. This is rotated between the lathe centres, and the wheel edge forced against it by the slide screw.—W. II. N.

[4037.1—RULE FOR FINDING THE SIZES OF WHEELS.—"R. T." may proceed thns and find the diameter of his small wheel—30 x 3 = 90 x 4 = 360 quarter inches, which divided by 120 + fin., the diameter. "R. T." may see at a glance that 30 is J of 120, therefore the diameter of the small wheel must be f the diameter of the

31416 x 3

large one. Then to find the pitch of the wheels

120 31416 x 75 = -07854

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= *07$54in. pitch of large wheel, and •

the pitch of ihe piuion teeth. When the pitch and No. of

07854 x Vff}

teeth are given to find the diameter =r3in.

tbe diameter. 3 1416

W. Proudlock. P. S-—" R. T." will find some useful information on wheel

gearing in back numbers of the English Mechanic.

[4037.]-RULE FOR FINDING SIZE OF WHEELS.— "B. T."— In all wheels of uniform pitch the diameters arc directly proportional to the number of teeth, but the diameter understood is that of the pitch circle, and not the external circle of the wheel. "K. T." will beat comprehend the nature of the pitch circie by supposing two cylinders rolling in contact with each other—say of 3in. and 9m. diameter respectively, it is clear that the smaller one would make exactly three revolutions, whilst the other makes one. Now those cylinders are simply wheels in which the teeth are infinitely small, and the lines of contact are the pitch lines of the wheels. But wheels of this class are not calculated to transmit a great amount of power, nor yet would they transmit motion with the precision necessary in tbe majority of cases, as in clocks. It is, therefore, neeessary to form notches or teeth, which may lay hold of each other so that there may be

engine at the East London Waterworks, at Old Ford. Ths valve itself is like a flat hat, with a hole in tbe top, and has two seatmgs, or "beats" as they arefcalled, one round «%t brim and tbe other round the inside of the hole in the top. It is prevented rising too high by the plate at top of the zu.l' piece in the middle, which is held on by screw bolts, and d a likewise guided by being bored inside and fitted to the *« tical edges of the 8 webs, of which 4 are shown. The top a cast open like a wheel with a large hole in the nare, so tax when the valve goes up the water comes out, not only under the lower edge, but also out through the holes in the t^p These valves are very good where the lift is high, as the prwsure on thtm acts downwards only on the area of the difference between the outside diameter of the lower beat and the inside of the upper one, and as they are very .t

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angle as the original, this is shown in Fig. 2, where it will be seen the apex of D would reach beyond the intersection of the two axes. Practically, in connection with wheels of small pitch, and where it is often desirable to make considerable changes conveniently, it is quite usual ta have what may be called a master bevel and a considerable number of change pinions, and to show what can be done in such a case by a careful manipulation, I will just instance one set in my possession, which answer admirably—viz., a wheel of 60 teeth (7 teeth per inch), for which I have pinions of 20, 22,24, fee, up to 44 teeth. I may state that the angle of the master wheel was originallv made to match the pinion of 32 teeth, which renders the divergence as small as possible. Since those were made I have also made a second master wheel of 50 teeth to match the same set of change pinions, so that nearly 30 different combinations can be got by means of those two wheels. To obtain so large a scope in this way, requires the teeth to be formed with great care, and the principle could not be applied beyond certain narrow limits in connection with wheels of a wide pitch.—Matrix. [4040.}-WHEEL GEARING.—If " Kirb>" will inspect the enclosed sketch he will he able to satisfy himself that he cannot gear a larger pinion with his bevel wheel. To construct tbe wheel a and pinion b first produce the axis of wheel a, and on a line at right angles to it, set off the diameter, which is 30in.; next set off the radius of the pinion whose diameter is lOin., then from this point produce the axis of the pinion, which will cut the axis of the wheel at o; now this point must be the common apex of both cones, so that the outer and inner pitch circles shall be proportionate to each other, but to increase the pinion from £ to \ tbe size of the wheel we would have the inner diameter of the new pinion about 1 Jin. too large.—W. Proudlock.

[4041.]— BICYCLE QUERY.—1 think that " Lark's" henzoline lantern will n->t be of auy service without he could with some contrivance suspend on springs, for it is the vibration that causes it to die out; nothing beats the proper composition candle lamp, with spiral spring and rocket. "Lerk" wishes to know which part of tbe foot is best to use on the treadle. It is ,t question I have long wished to have proved. I have been a hicycle rider now twelve months (with never such plensure experienced before), and have tried both with the heel close to the treadle, and with the tread of the foot upon. For my part I ride and prefer the tread up»n the treadle ; and find less vibration, more use for Mi- calves and ankles, and also reach a larger throw mnch easier. I am acquainted with a very fanciful rider who always rides with the tread; hut he is the only one thnt ever I saw. I should much like another opinion (if proved) upon the matter.—Velocb.

[4043,]— CORNISH DOUBLE BEAT VALVE.-In answer to "F, P.," I send drawing of a 43in. valve from a Cornish

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thev siokdown the moment the action of the engine stopa, which it always does for a longer or shorter time at ihe end of the stroke, and from their peculiar form they can sink without driving a quantity of water out of their way, as moat other valves must, and hence the silence of their action. They do not do so well for short lffts, as then the valves axe out of proportion, heavy, compare! with the whole wort done.-J. K\ P.

P.S.— Inreadiug "F. P.V qoery over again, I see he aakj for an equilibrium valve, and as there is a steam valve of that name in a Cornish engine, 1 will describe tbst alto. A Cornish engine is single acting only, and in those with beams the steam comes on the top of the piston only, when the piston gets say \ of the distance down the cylinder, the steam is cut off and acts expansively for the remainder of the distance. That is called the ■ indoor stroke," because the half of tbe beam next the steam u indoors, while the other end, at least in Cornwall, goes through a hole in the wall, and is consequently out-of-doors. New the top and bottom of the cylinder are connected by a pipe closea at top by the equilibrium valve, and as soon as the ind«*or stroke it completed, the equilibrium .aire is opened and a free passage given to the steam from the ten to underneath the piston, and the outdoor stroke is made by the descent of a grent load attached to the top of the plunger of the pump in waterworks engines, or in deep mines by tbe weight of the pump rods, which usually we'gh several tons, and are sometimes partly balanced at intervals down the pit by grent beams like steam engine .beams, which wrjrk in an excavation made in the side of the pit, and having a great box filled with old metal at the reverse end, Boh that pulls the piston up again. Direct action or '* Bull " engines stand partly over the pit mouth, and the piston rod is attached direct on to the pump rods. Of course in them the steam acts under the piston. The construction of the equilibrium valve is just the same as the pump valve, only has a rod to lift it. I have drawing of cataracts at " F. P.'s" service.—J. K. P.

r4046.]—SPECTACLES.- In answer to "J. R. W.." allow me to say that he has not got his concave spectacles coneave enough, or else there is some other defect in his eyes, lor if his spectacles were properly chosen he ought to be able to recognise a person 30 yards off, and not 3 yards only. "Let him ouy a more concave pair of spectacles. As to things looking Bmaller through concave or shortsighted spectacles, this he he must expect, for the fault of shortsighted people's eyca is that they make things look too large, or bring the rays of light to a focus before they reach the retina or buck part of tbe eye. Concave spectacles diminish the apparent size of things, or in other words throw back the focus of the eye to the retina. This apparent smallness of objects seen through concave spectacles will wear off in time, and he will get to take no notice of it. As to his spectacles not being wide enough, he had better see to getting a pair that are wide enough, as he will have to get another pair more concave to suit his short sight \ further let him have some bits of wire silver soldered on to the ends of the sides of the new apeetaclee so that he can bend them to fit the backs of his e»ra. this is much better than jointed sides to turn behind the eara as the joints wear loose and soon become of no use; I have had mine so made, and they answer better than any other plan I have tried, especially for "J. R. W."who is so short•iyrhted as to have to wear spectacles constantly. He then can jump and run, and lay down without the spectacles falling off his nose, and, lastly, there would be Tory little advantage tn having plauo-concave instead of double-concave glasses, »n small us not to counteract other disadvantages.—H. W.

[40«.]—SPECTACLES.—The object of spectacles is to restore the eye aa nearly as possible to its original power. '• 3. R W.'s " eyes magnify too much; he requires a concave spectacle to coun teract this defect. He says the Bpectacles he ■i&s make objects appear* seven-eighths their real size . it is evident they are too concave. Spectacles a little less powerful would remedy this and make his eyes ache.—Optics.

[4063-]— DRYING GLUE.—"J. S." must understand that the mere putting of the air in motion will not dry his gl e. It is a fact that air of any given temperature, although saturated with moisture (and in th.it condition, us a matter of course, useless for drying purposes), becomes capable of absorbing additional moisture in proportion as its tamper atari is raised, so that " J. S." if he wishes to go scientifically to work must have some"means of securing ■ constant mflux of tur from a comparatively cool medium, healing it on its passage inwards, as much as practicable, then exhaust it, or allow it to escape as near as possible at the opposite extremity of his room. This can either be done by means of a small /an, or by means of an ordinary fire with a good high opening at the chimney—even two or three windows open at the lop—or, still better, ventilators, might answer the purpose, assuming that the temperature has beeu raised considerably before passing into the room. No good will be done without an in and out current of air.— Matrix.

[40310— MICROSCOPIC INVESTIGATION WITH PO LYRISED LIGHT.—I do not think that polarised light wiI itc of any service to " John Barleycorn " in his investigation into the development of the Tor Ma cerettiiae or yeast fungus All that he will require for that purpose will be a good | or fcin. and A or B eyepieces with or withouta "condenser.'1 Examination of acetic acid is more the work of the chemist than the microacopist, but it is convenient to call the aid of the microscope into requisition sometimes thiU reactions in minute quantities may be observed. For general polsriscopic investigation no apparatus can better answer the purpose than m " Nichol" prism below the object as a polariser, and a second prism used above the objective as aa analyser. This latter prism may be conveniently made so as to be capable of use tn this position or above the eyepiece. But in work I Sad the former position the preferable one. Want of time prevents my going into detail, but if " John Barleycorn" wishes and the Editor will allow, I will give a few general hints in a week or two.— H. P.

[4061.]— ASSOCIATE OF ARTS DEGREEE. — Every

candidate for the title of A. A. must be under IB years of age on tba day of examination. He must pass a preliminary examination in (1) grammar and analysis; (2) English composition; (3) arithmetic, including fractions; (4j geography i (5) the outlines of English history. Failure in any one of these five subjects is absolutely fatal, however high a candidate may stand in the examination 1 now describe. The other part of the examination is divided into four sections: — A English, B languages, C mathematics, and D science. Every candidate, in addition to the preliminary, must pass in two of the divisions. A, B, C, and D. Each of these divisions is divided into sections, and superior answering in one of these sections, will pass a candidate in the division. Division A is divided into four sections: —(1) Euglish history—a certain period given beforehand. (2) Political Economy j (3) English Literature—certain authors; (4) Geography. Division B: (IJ Latin; (9) Greek; (3) French ; (4)German. The minimum fordivision C is four books of Euclid and algebra to quadratic equation inclusive; D(l) Natural Philosophy; (2j Chemistry; (8J Botany; (4) Geology and Mineralogy. Nearly all candidates take division A English, as they are obliged to take history and geography in the preliminary. So that in additiou to this, one language, or chemistry; or the minimum of mathematics will nass a candidate. I passed in honours in two divisions. The examination is conducted by the University of Oxford, at various local centres in the country, such aa Leeds. Manchester, 8tc. The fees which I paid amounted to £2.—J. Harrison, A A., Bradford.

[40640-TURBINE.—- PATTERN MAKER."—A turbine wheel giving out 1 h.p., will require some 35 cubic feet per minute under a head of 20ft. To determine size of pipe, it will be requisite to know the pressure acting upon such column, after which a large percentage must be allowed for friction. A turbine will be more economical and efficient than a steam engine and boiler. Try the North Moor Foundry Company. Oldham, they supply smalt machines to utilise n town's water. I have just put in Messrs. Spon's ahe publishers) hands a thoroughly practical work upon turbines, for the use of all who wish information respecting them. - J. Gillairi>,

[4008.}— BREWERY.—"Brewer's" temperature is not too low. I pitch my mild ales at 66 ?, and, as a rule, succeed in getting them qnite bright. It is very difficult for oue who knows nothing about the position or arrangement of his brewery to give a proper explanation, as there are so many different systems iu use, and therefore a great many points at which a wort could be afTected. I will not presume to point out to "Brewer" the cause of his ales not clearing (unless I was intimately acquainted with all details concerning his place, and the system he works on). But the mode of procedure I follow, wheu troubled in any way as he is, may a**ist him in getting to the bottom of his difficulty, and perhsps discover to him where the evil lies. I examine the water and see if there is anything in it deleterious, then the malt, as to its being thoroughly dry and free from mould, *lso see that it is properly crushed, not too fine. I am also very careful in washing, uBing the liquor of a proper heat, say liO* to 168", taking care nlways to have the goods fa 1 ng into the mash tun abou 150°; this gives me a tap heat or .to 1*,v*» »ecording to the age of the malt (I like ft two months old at least). I watch the cupper well, and am careful in not raising it to the boil too quick, then a steady and regular boil of 11, to 2$ hwori, according to the hardness of the brewing water and the gravity of the worts, then blow off the Bteam on the coolers till about 180* or 190*, and do not use ton much water in refrigerating, but run regular and not too strong; see to veast, its freshness, quality, and freedom from all taint or smell; use lib. or ljlb. per barrel for mild; ase the tuns or gyles clean and sweet, and free from all mixtures of metal or anything likely to cause the least gaJvuwc action or electric curreut, then great care is requisite re the working off of the gyle tun, which a long practice can only bring to perfection; taking care not to check loo quick or yet raise by any artificial means the heat of gyle, and above all watch the proper attenuating of the

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worts, bringing them down far enough to prevent secondary action or fermentation. Is the whole- brewery thoroughly clean and sweet, if not, wash out and lime at once. These are a few very imperfect jottings and thrown together in a very hurried manner; yet "Brewer" may get some good from them, and I shall be glad to assist him or any other; only to do so with anything like a prospect n f success, 1 must have more particulars. Every breteer will understand this.—Izoks, Edinburgh.

[4007.]-MUSICAL BOX.—The cause of the musical box making the jarring noise he complains of)s probably that some of the tine springs underneath the notes are broktn off. I have had one or two lately brought me to repair with the same eomplamt and shall be happy to undertake "Salopian's" if he thinks proper.—E. Baenahd.

[4088,]— PRESERVING FLOWERS. —If "G. O. IV* wishes to dry Sowers so an to make them resemble everlasting, as in theheautifurhouquets irnt <>ver from our German friends, the process is somewhat us follows: l'rocure an apparatus winch may be made of zinc, and cylindrical in shape, open at both ends, mid with a perforated diaphragm (as shown in sketch in section).a cover or lid isalso provided for each end. Suppose the box to measure lOin. in length by4in. diameter. Sufficient very fine silver sand, thoroughly •leaned from dust by frequent washings in water, dried, and well shaken up, whilst in a heated condition with a small quantity of spermaceti, i'tni is held in readiness. The cut :ts Sowers are now dropped gently into the box by the end B so to rest upon the diaphragm C. the box being inverted. When filled the lid is replaced at B, and the apparatus turned up, as represented in sketch. After removing the cover A, the I ool Baud is caused to percolate through the perforations until the whole insterstices between the [lowers, and also the space above the diaphragm are completely filled. After replacing the lid the apparatus may be placed in an exhausted oven overnight, being careful to have the lid B placed loosely on 'he top. The sand supports the Mowers and preserves the integrity of t he petals during the process of dessidtion, and the spermaceti is evideutly intended to prevent the sand from adhering to them through the influence of the heat and moisture. When the dessicatiou is completed the lid A is removed and the sand allowed to escape which is of course available for future ope rations.— Matrix.

[40710-DRAUGHT IN BOILER.— "Jouath" savs the Sue of the chimney has been repeatedly swept, but 1 feel quite sure it does not get thoroughly cleaned. Let "Jonath '' mind and see the sweep's machine through the chimney top; in fact he must be sure to see thnt die Sues throughout, from the fire to the chimney top, be thoroughly cleaned with a really good stiff whalebone brush ; the inside of tubes or Sues makes nothing but what a stiff brush will scrub out; the incrustation inside tne boiler has nothing whatever to do with the draught of the flues. 1-believe some partof thechimnev or flues are almost blocked up with soot; let the bottom of the old flue or chimney be bricked up.—Andrew Johkson. [4078.1— RAILWAY GUARDS' WATCH.—From long practical experience 1 do not hesitate in stating my belief that pocket chronometers are a mistake. "Railway Guard " would find, if he had one, were it ever so good, that if he ran the 'J i stance of the length of a train with a chronometer in his pocket that the shaking would cause it to vary seconds, and that it would be some time before it would recover and get back to its rate again. My opinion is that a thoroughly good English lever with about ten holes jewelled and a chronometer balance costing in silver cases £3 to £10 is as good a pocket timekeeper as could be desired. If necessary, l could give "Railway Guard" names and addresses of rai'lway station-masters, clerfls and others .who carrv these identical watches and from long use have proved them to be thoroughly reliable.—Ciiro.no.

[408a.]—FLUTE.—If Mr. O'Brien will take my advice, he will keep his flute aa it is. The difference in pitch is surely not a fault, and can only be inconvenient if he wants to play with another instrument of the present concert pitch. Nevertheless, if he persists iu having it altered, he shoutd apply at Rudail's, Charing-cross. They will tell him whether they can doit, and will give him honest advice in the matter. Further, they will not charge mere than some of those needy hou«es who are ever ready to alter ins tru'uents to order, without caring whether they improve or spoil them.—jhjn Rymka.

^4flSoT]-FITZROY STORM GLASSES.—Theseare to he

nad so cheap that they are hardly worth the trouble of making, and as weather guides they are perfectly useless. I have tried several. 1 have had one undisturbed in my summer house for two years, but its indications are so wild and contradictory that there is not the slightest dependence upon it, and I only retain it for the barometer attached.—Amateur. [4086.]—EITZ ROY STORM GLASS.-The composition is two drachma ot camphor, half a drachm of nitrate of potassium, half a drachm of chlorate of ummonium, dissolved in about two ounces of absolute alcohol mixed with two ounces of distilled water. To be placed in a glass phial ibout ten inches long and three-quarters of an inch in diameter, nearly filling the phial, which is to be herm etically sealed.—Giurl.

f_40S9,]-READINGS FROM THE GLOBES.-" Gimel" is quite right iu his correction. The fact is it ought to be 9% instead of 9|, which will bring out 43 miles nearlu.

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Richard I. for his French kingdom of Poitou. It bears on the obverse, a cross patee nnd RICARnVS REXfBichard, King). Reverse, the name PICTAVIENSIS iToitou) in three lines. This coin is common, anil worth ab< l 3s. if in fine preservation. The series, to which this b. ogs, of coins struck by English princes in France, is tern ) the AngloGallic-, and it includes pieces of Aquitaine, »iton, Bourdeaux, Calais, Paris, Caen, Tours, Limoges, An* -p, Bruges, Ghent, Ypres, Tournsv, etc., embracing also almost every partof France.—Heathy W. Hkntret, M.N S, &c, &c.

[40930—SILVER COINS.—The largest silver coin is a penny of Richard I. There are no English coins of this king, this coin was coined in Poictou, (Pictaircnsis on the reverse). They were formerly very rare, but not so now. as hordes have been found. The small coin of no interest Should he glad if" A Beginner" would correspond with ma, that I may have his address.—W. Nulson Last, Bury St. Edmunds.

[4095.]-SILVER COINS.—No. 1 is of a Doge of Venice (Leonard Loredano?); the name is just where the letters are not given: on one side the Saviour and" LAUS TIB ISO LI," "praise to Thee alone." Reverse, "S. Mark and the Doge."

"Dux. 9.M.V." Doge, 8. Mark, Venice. No.

2 I read " KaROLUS REX FR,"; rev. PICTAVIENSIS. and think it is of Charles II. King of France, and struck at Poictiers.—Brrevardin

[40970-A VELOCIPEDE FORSPORTSMEN.—See reply amongst the letters.

[4100J.-SWAGING SCREWS— If "Amateur Blacksmith" does not want an Oliver to forge his set screws and bolts he could easily make some swaging tools. If he wishes to make hexagon heads to his bolts he wdl require an extra set of I tools ; but they are inexpensive if he goes the right wav about it.-J. M.

[41050-HALL MARKS.-The best book on the hall marks is " Hall Marks on Gold and Sliver Plate," bv W. Chaffers, F.S.A.. 3rd edition, price 3s. 6d , published by J. Davy and Sons, 137, Long Acre, London. It is a most useful book, and gives tables of the date, letters, and marks of every assay office in the United Kingdom, from the earliest period of their use to the present day, with fac-similiee, and a mass of valuable informarion.—Henry W. Henfhby, M.N.S.; fee.

[4106.]—GOLD COIN OF EDWARD Ill—In asking the value of a quarter-noble of Edward III, I presume that '•Casteye Diamond " means one of his fourth issue, in the 21st and following years of his reign, which bears, obrerte, a tressure (or border) of eight arches pointed with trefoils, containing the royal arms in a beaded shield. EDWARD. DEI. GRV REX ANGL. (more or less abbreviated). Reverse, a. tessure of eight nrehes with fleur-de-lis and lions alternately in the angles, containing a cross rleuree. Sometimes E in the centre. EXAL TAB1TUR IN GLORIA. Full weight, 30 grains troy. This coin is common; worth 12s. to 15s. Other quarter-nob les of preceding issues are rare, and weigh several grains more. If "CD's" coin weighs more than 80 grs. I should be much obliged if he would kindly send me u sealing-wax impression by post.— Hk.nri W. H*ifFR*Kr, Markham House, Brighton.

[41080—COIN OR TOKEN.—Is a halfcrown of what is termed "Gun Money," and was coined on account of the exigencies of James the 2nd when in Ireland; crownB, shillings, and sixpences were also struck in the same metal, and bear dates 16S9 and 1690. They were coined from old brass guns. For particulars, see "Simon's Essay on Irish Coins.' They form a very interesting collection, as they were struck with the name of the month on them, this was struck in August, 1089.—D. T. Batty, 9, Fennell-street, Manchester.

[41080-WHAT COIN IS THIS?-It is a gun money half crown of James II. The following extract is from my''Guide to English Coins." part li, p. 112;—" When James landed iu Ireland in March, 1699, to attempt the recovery of bis <iominions, he resorted to several expedients to remedy the scarcity of money in that kingdom. First of all, the value of the guinea, as being of easier carriage than the silver money, was raised one-Afth, or 20 per cent., whilst the silver coins were raised no more than one-twelfth, or 8} per cent., and other foreign gold and silver in proportion, that what money he could obtain might go a greater way. However, as all these expedients failed to procure a sufficient supply of money, he ceined brass and copper sixpences, which were made current by a proclamation dated June 18th, 1689. Half-crowns and shillings were soon after added; made current by proclamation, 27th June. Crown pieces of white metal were ordered to be' curreut on the 21st April, 1690. The half-crowns of copper and brass previousy issued, were called in in June,4C90, restamped with the die of the crown, and issued at the value of five shillings. The battle of the Boyne, on July 1st, put a stop to these base coinages, which derived their name of "gunmoney " from heing made of brass cannon, brass and copper kitchen utensils, &c." XXX. signifies thirty pence, the valuc, and " Aag.' the month when it was coined. The shUling and sixpenee are exactly like your correspondent's half-crown, except that they have " XII." or " VT.,r f.ir the value. Value of all three, tid. to la. eaoh.— Hbnjkt W. Hgnfkey. '[4118.]—PROBLEM—TUE FOLLY OF ALGEBRA—The tHestion of our friend "Algebra " is just one of those which in iv ■■'. t..-;i prove how unnecessary is his science itself. His problem is, "A gentleman having mortgaged an estate for £2000 at S percent compound interest, he is now desirous of knowing in what time he shall discharge the Baid debt and interest by paying the mortgagee of £187 yearly." Here is "Algebra's" usual flaw. There need not be any compound interest! Compound interest pertains only to such a case as when perhaps a reversion is purchased in advance; or ugain when nothing is to be paid till a reversion or life-policv becomes available. In such a transaction, no money is'paid year by year; there is a lump sum, either at the beginning or at the end. But here the mortgagee gets £ 187 yearly. The 5 per cent, on £2000 would be only £100. Therefore, anv bookkeeper, any solicitor, any accountant, any actuary, would ■imply take £100 outof the £187, as (regularlv) paying the 5 per cent, annual interest. I am well twai that our Iriend "Algebra" wants the " £2000 at 5 per cent, compound interest 'to go on accumulating, in ordsr that there may he u more tortuously big total to be met by the £I»7. But, there need not be any luch accumulation. There never tojulJ he iu plain fact, in the very case supposed. The intended complication is only a riddle for riddle sake; it is mere x, mere algebra, mere gratuitous muddle, mere needless self-mystification. So. to one half of his query, "in what time shall he discharge the said interest P" My reply is. the interest shall be discharged annually, out of the £147. Then, as to the aecoud question, we see there would remiin £87 per annum-, this would be a sinking fund paid to the mortgagee, and this accordingly ought to fructify at coniuouud interest, lay 5 per ceut. Thus the awful problem of "Algebra," when popped

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