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OF THE MONTH.

"Si fructus illabitur orbis.

Impavidunt ferient ruinæ ;"

nor are either Virgil or Mr. Gladstone to be congra-
tulated upon the following reading of the well-known
hexameter in the speech on the Budget,

EDUCATIONAL AND LITERARY SUMMARY quires enforcement, as we have seen frequenters of invented by him, with the view of producing a fuller the Museum reading their penny papers as composedly and purer light, with less consumption of gas. The as ever, in the immediate vicinity of these prohibitory invention consists in an arrangement of two chimneys THE most important educational event of the month notices, to the exclusion of bonâ fide literary workers. instead of one, thereby excluding the cold air from has been the publication of the Report of the Royal-In France, as in England, the translation of Horace coming in contact with the flame, but using hot air Commissioners on Education. Any one who, while is a favourite amusement. Jules Janin's heavy prose instead. For instance, take the ordinary chimney of feeling interested in the subject, does not nevertheless translation in French is to be superseded by a metrical a lamp, which, by the way, must be four inches care to wade through the ponderous blue books in version in the same language; and we learn that M. larger than it usually is; surround this by a conical which these gentlemen have stored up the result of Emile Boulard, a retired magistrate at Tours, spent outer chimney, the wide end of which should only rise their inquiries, will find very useful the abstract of the last weeks of his life in correcting the proofs of a to the level of the flame, and the point descend to a the Report just published by Messrs. Bradbury and metrical French Horace, which is said to be gracefully couple of inches below the burner, which must stand Evans. We may add, that people are now beginning and tersely translated. Talking of Horace leads us on a plate of glass screwed on to the gas-pipe. A space to ask, why six out of the seven Commissioners should to hope that some of our daily cotemporaries will, of about a quarter of an inch is left between the two have been members of the University of Oxford? now that their resources are about to be enlarged by chimneys; and owing to the access of air being cut The Secretary for Foreign Affairs has offered to allow the remission of the paper duty, try and deal a little off at the bottom of the burner, the supply can only three students of Oxford, Cambridge, and other more tenderly with the manes of the departed poet. pass down between the two chimneys or cylinders. Universities respectively, to offer themselves as It is neither fair to Horace nor to Lord Palmerston Thus the air and the gas being both heated before candidates before the Civil Service Commissioners, that the latter should be made to say, they come in contact, the heat of the flame is consifor the appointment of student interpreters in China derably greater than ordinary: and the result is, that and Japan. The age of the candidates was originally the light is much increased, and the consumption of limited to between sixteen and twenty years complete. gas greatly diminished. A common argand burner, It now appears that certain students of King's Colwhich consumed three-and-a-half feet per hour, and lege, have been for some time past qualifying themgave a light equal to thirteen candles, when fitted selves for these appointments; and to admit these with the outer cylinders, gave a light nearly equal to gentlemen (who will have an enormous advantage over twenty-two candles; while an amount of light equal all the other examinees) the limit of the prescribed to thirteen candles could be produced from little more age has been extended to twenty-five. We may add, than two feet of gas, instead of three-and-a-half. that the following book, which has just been published contributes an interesting paper to the April Number Mr. Crookes, the editor of the "Chemical News," at Paris, will be found most serviceable to such of the "Philosophical Magazine," on the discovery of students as wish to master the Japanese tongue :"Essai de Grammaire Japonaise," by M. J. H. new metaloid, which has not yet been named, was a new element, probably of the sulphur series. The Donken Curtius, Dutch Consul in Japan, enlarged discovered by the method of spectrum analysis of by Dr. Hoffmann, Professor of Japanese and Chinese, Kirchhoff and Bunsen, in some seleniferous deposits and published at Leyden in 1857; translated from the from the sulphuric acid manufactory at Tilkeroide in Dutch, with new notes extracted from the Grammar the Hartz Mountains. It gives rise to a well-defined of Father Rodriguez and Father Collard, by Leon green line, almost rivalling the Sodium line in brilPagès. ing article to the March number of the same Magazine, liancy. Kirchhoff himself communicates an intereston the Chemical Analysis of the Solar Atmosphere. As all metals are, by the exquisite method of analysis devised by him and Bunsen, clearly indicated by the bright bands in the spectrum of a flame in which they are present; and as the total nucleus of the sun is surrounded by an incandescent gaseous atmosphere, it occurred to Kirchhoff, that if we could see the in it the bright bands characteristic of the metals con spectrum of this luminous atmosphere, we should see tained in the solar atmosphere, if there are any.

The article from the pen of Mr. Henry Fawcett, Fellow of Trinity Hall College, Cambridge, on the justice of admitting dissenters to College Fellowships in the University of Cambridge, which appeared a short time ago in Macmillan's Magazine, appears to be only the prelude to a regular movement for effecting that object. A petition is now being circulated in the University just named, and has received many signatures, praying the House of Commons to do away with all the provisions in the Act of Uniformity which have hitherto prevented dissenters from holding College Fellowships, &c.

"Ego vescula alte occulis et rite repertum
Carpe manu-"

A weekly cotemporary writes :-"The private library
of the late King of Prussia, Frederic Wilhelm the
Fourth, is valuable and extensive.
about 56,000 volumes, and contains, for the greater
It comprises
part, works of History, Archæology, and Christian
Art. The library fills six large rooms of the Royal
Palace at Berlin. Humboldt's works formed a special
compartment, called the Humboldt Press,' and are
found in greater completeness, from the large work on
pamphlet, than when Humboldt himself possessed
America, which cost 3000 thalers, to the smallest
them. This library has been left by will to the pre-
sent King, with the exception of the artistic works,
which have been bequeathed to the Queen Dowager
A question arose, if all the illustrated works with
woodcuts, &c., were to be understood among the
artistic works,' which question has been decided in
favour of the Queen."

The

duced. Thus, we do not see the spectrum of the atmosphere by itself would show, dark lines are prohave fallen to the ground." we hear that a new magazine is likely to be born, if ever, serves equally well to determine with certainty Farther north, however, atmosphere, but a negative image of it. This, hownot to be long-lived. deen University Magazine."-A statement appeared a atmosphere. With the aid of a splendid apparatus It is to be called the "Aber- the presence of those metals which occur in the sun's few weeks ago, that nothing marked the grave of the from the optical and astronomical manufactory of ill-fated poetess, L. E. L. Dr. McWilliam has written to a cotemporary, stating that a monument, minute examination of the solar spectrum, and of the Steinheil, in Munich, Kirchhoff has commenced his bearing a Latin inscription, was erected by her hus-spectra of the various metals. He has already sucband over her remains. Dr. Sharpey has, we learn, ceeded in establishing the important fact, that the been appointed to succeed the late Dr. Baly as a bright lines characteristic of iron, magnesium, chromember of the General Council of Medical Educa- mium, and nickel, in the spectra of flames containing tion. these metals, correspond to dark lines in the solar spectrum. The occurrence of these metals in the sun may therefore be regarded as certain. We need not dwell on the grandeur of the discovery which has thus enabled the analytical chemist to extend his researches to the great luminary in the centre of our system at a distance of ninety-five millions of miles."

MONTHLY RECORD OF SCIENCE
AND ART.

for the undergraduates having been mooted for some The question of adopting an academical costume time past among the students of Edinburgh UniverMr. F. C. Cook, Inspector of Schools, has written to be taken to decide whether the proposed change ever, that the more intense luminosity of the sun's sity, a poll was directed by the Senatus Academicus From Kirchhoff's observations it appears, how. to the "Guardian," saying that he requires four should be made. A majority of twenty-eight decided solid body prevents the formation of a true spectrum hours, and not one hour and a half, to examine a against the adoption of any such costume. school of 150 boys in Reading, Writing, and Arith-honours of the cap and gown will therefore be reserved of its atmosphere: it reverses it, in fact, so that, inmetic. As even then Mr. Cook cannot give anything as heretofore to graduates only. —The "Great Tom" stead of the bright lines which the spectrum of the like two minutes to test the knowledge of each boy in Magazine, of which we spoke in our last, seems to the three distinct subjects, it may be doubted whether an examination conducted at this railway pace can be worth much, or indeed anything at all.-A facsimile of a portion of the Domesday Book has been taken by photography, under the direction of Sir Henry James. The experiment (which is about to be renewed on a larger scale) has been thoroughly successful; and so much of the famous book in question as relates to Cornwall may now be purchased for a very few shillings.-The "Essays and Reviews" have now reached a ninth edition; and the number of the "Quarterly" in which they were reviewed by (it is said) the Bishop of Oxford, is in its fifth. A number of critics, hostile to the "Essays and Reviews," have suddenly sprung up. Many of these writers are otherwise unknown to fame Among them figures Dr. Cumming (notorious enough, certainly, if not famous) as the champion of orthodoxy.-A London THE Evening Lectures at the Geological Museum, Book Union is about to be commenced; its design is, suspended during the Easter recess, have re-opened of course, borrowed from that of the Art Union. with a course on Geology, by Professor Warington The discovery of a new planet has become an event The prizes are to be books instead of pictures. The Smith. A Course of Lectures on Physiology, at of such frequent occurrence that it has lost much of first prize will be a library of the value of £300, and University College, by Mr. Marshall, F.R.S., is just its interest; yet it is none the less deserving of record. there will be a great number of small prizes. Further, drawing to its close. It is likely to be followed by In that region of the heavens comprised between the each subscriber is to receive a copy of some standard series of Lectures in Chemistry, Geology, Zoology, orbits of Mars and Jupiter, two new asteroids, formwork. The particulars of the Civil List pensions for and Practice with the Microscope, by other Professors ing the 64th and the 6th now known, were discovered, this year have just been published, and do not ap-of University College. the first on the 4th, and the second on the 9th, of pear to have given satisfaction in all quarters. The An interesting discourse on the recent investiga. March, by M. Tempel, an assistant in the Observatory **Critic," very reasonably, we think, protests against tions of Deville and Debray on Platinum, was delivered of Marseilles, and the discoverer of the comet of the the idea that benefactors to literature and art are to the members of the Royal Institution on Friday, 23rd of October last. It is a noticeable fact, that all being rewarded when the widows of Admirals and Feb. 23, by Professor Faraday. The method of ex- these asteroids have been discovered within the preConsuls and the teachers of the Queen are being pen-tracting platinum from the ore, employed by Deville, sent century. The first asteroids of the group were sioned."-A notice has been put up at the reading-by fusing it at high temperatures, by which the salts discovered between the years 1801 and 1807; and by room of the British Museum, that persons will not be and other impurities adhering to the platinum are dissi- the year 1845, the number discovered amounted to allowed to make use of the room for the perusal of pated by heat, is a great improvement on the old fifty, and fifteen more have been added to that number newspapers and other publications which are not sup- tedious process, by which the metal, after being ex- during the last fifteen years. An important plied from the library; as it has been found that many posed to the action of aqua regia, had to pass through series of researches in a different department of those who go there for the purpose of study are a variety of secondary processes, more or less at of science, has recently been laid before the unable to obtain desks and attendance from the num-tended with waste before it was obtained in its pure Academy of Sciences of Paris, on the composi bers of diletantti readers who frequent the Museum. state. On Friday evening, March 8, Dr. Frankland tion of cast iron and steel, by M. Fremy. We quote We consider Mr. Panizzi's ukase a most excellent gave a lecture at the same place on the Combustion the following account of these valuable researches one; but personal observation convinces us that it re- of Flame in Rarefied Air, and on the new gas-burner from the "Chemist and Druggist" of this month :

a

than pure iron; is attacked with difficulty by nitric

phuric acids; and is susceptible of permanent, but less powerful, magnetism than steel. It is a compound of great stability supports a red heat without decomposition, and only attacked by oxygen at a high temperature. Its composition appears to be Fes N, which corresponds to 9.5 per cent. of nitrogen. markable change, approaching the condition of steel, and when heated in a current of hydrogen, it does not

When heated in a charcoal crucible it undergoes a re

give off a trace of ammonia.

undertaken by Mr. Kelk, and by Messrs. Lucas, in existence for more than ten years. The edu-
Brothers.
cational papers of the non-German races treat
An Industrial exhibition has been announced to be almost exclusively of popular or elementary
held in Florence in the ensuing autumn. It is ex-
pected that it will be particularly rich in illustrations education. Only one has existed eight years,
of medieval art, for which Tuscany furnishes a pecu- and the others have been founded during the
liarly fine field.
last two years only.

PRUSSIA.

The alterations which have been going on in the National Gallery for some time past are now completed. The public will be grateful for the change which has been effected and for the greatly improved for March contains an interesting account of The "Allgemeine Deutsche Lehrerzeitung" means which have been provided for the reception of the national pictures, which can now be seen to great the public educational institutions of Berlin, advantage through the admirable arrangement which which are at present,-7 gymnasia (correshas been adopted for exhibiting them.

FOREIGN NOTES.

AUSTRIA.

ponding to our classical schools), 1 progymnasium, 5 real schools (corresponding to our commercial schools), 1 industrial school, 3 higher girls' schools, 5 higher boys' and preparatory schools for higher institutions, 23

"It had been shown by Despretz that at a red heat iron decomposes ammonia, becomes white and brittle, and increases in weight 11.5 per cent. Fremy proves that this increase in weight is due to the absorption of nitrogen, that a true nitride of iron is formed, quite free from hydrogen. Iron can only be made to combine directly with nitrogen with extreme difficulty; but a nitride is formed when nitrogen is brought into contact with the meta! at the moment of its reduction, either by hydrogen or carbon. The action of ammonia on iron is extremely slow, whole days being required to convert a few grains into nitride; but by passing ammoniacal gas through a porcelain tube containing protochloride of iron heated to redness, Fremy obtained nitride of iron in abundance. He exhibited to the Academy of Sciences, on the 26th of February, a mass weighing 200 grammes, white and brilliant; and he expressed an opinion, that as this compound can now he so easily made, it will become a valuable agent for furnishing nitrogen to mineral and organic substances. In a recent number of the "Süd-deutscher middle and elementary boys' and girls' schools, Nitride of iron is easily pulverized; is less oxidizable Volkschulbote" we have an interesting account 14 Protestant parochial and 6 Catholic paroacid, but with great energy by hydrochloric and sul- of the Educational Periodicals published in chial schools, in connexion with congregations the Austrian empire. The number of these to which they belong, 3 Jewish schools, 1 periodicals representing the various nationali- Jewish, 1 Catholic, and 4 Protestant orphan ties is in all seventeen. Of these more than asylums, 4 educational establishments under half, viz. nine, and by far the best, are the administration of societies, 2 prison schools. written in the German language. Three are of private educational establishments there written in the language of the Sclavonian part are,-1 commercial institution, 7 higher boys" of Bohemia called Tschechic; one is written schools, 27 middle and elementary boys' in the Hungarian or Magyar language; one schools, 27 higher girls' school and boarding in the Croatian; one in the Slovakish; one in establishments, 26 middle and elementary girls' "In a later communication to the Academy of Servian, and one in the Roman—a dialect of schools, 14 mixed schools for children of both Science (11th of March) Fremy describes some extremely interesting experiments: he finds that when Transylvania. The Tschechic, Croatian, Slovak, sexes, making together 102 schools. iron is submitted at a red heat to the action of coa!- and Servian belong all to the Sclavonian family these institutions there are-9 so-called schools gas it becomes regularly carbonized, forming grey, of languages, although they differ from one of industry for girls, in which they receive, graphity malleable cast iron, equal in quality to the another almost as widely as independent lan- in addition to industrial training, the usual finest charcoal iron; but under no circumstance, however carefully he regulated the dose of carbon, could guages. The Roman is a dialect derived from elementary instruction of other schools, 58 he form in this way steel, but when the compound of Roman colonists, who settled in the country evening schools, possessing more or less an iniron and nitrogen, obtained by passing ammonia over now called Moldo-Wallachia. The Hungarian dustrial character, 10 Sunday schools for those red hot iron, was submitted to the action of coal-gas, or Magyar is of Tartar origin, like the Turkish. children under 14 years, who are exempt from steel of a splendid grain was produced, a specimen of All the above languages, except the Tschechic attendance during the week, 3 so-called schools which Fremy exhibited to the Academy. He has in Bohemia, are spoken in Hungary, which is of improvement (fortbildung) for young men is generally supposed, a simple compound of iron and in miniature what Austria is in a greater de- already engaged in trade or manufactures, 36 carbon, but a nitro-carbide of iron (fer. azoto-gree. a medley of many races, with little co-infant-schools. The number of teachers, 1341; carbure). Fremy is still engaged in these researches, herence or attraction for each other. of female teachers, 469; and scholars of both which promise to yield results of great practical After the schools of the German portion of sexes, 57,213. There are thus on a average the empire, which are equal to those of any about 30 pupils to each teacher, of either sex. tions, at the Society of Arts, Adelphi, opened to the other parts of Germany, come those of the public on Easter Monday, and will continue open Bohemian Tschechs, who are a cultivated and The "Pestalozzi Societies which have for some time. The Exhibition is open gratuitously intelligent race, while the remaining national- been founded in the various countries of the by a Member's order; and it contains so many inge-ities are all represented by one periodical only. German confederation with the object of pronious inventions of a mechanical and economical cha- It is a noticeable fact, that the Hungarians or viding support for indigent teachers and their racter, that it will be found amply to repay the time Magyars possess only one educational paper, families and orphans, are progressing favourrequired to give it a careful inspection. and that this is Roman Catholic, while the Pro-ably. The "Pestalozzi Society of Saxony," testant Magyars possess none. The binding or which employs part only of its income for civilizing element of the various races of the grants in aid, and the remainder for the general Austrian empire is the German, as is clearly purposes of the society, supported last year tional periodicals published in that language. of education for two young teachers, sons of indicated by the large proportion of the educa-137 bereaved families, and provided the means The Polish or Gallician and the Austro-Italian deceased teachers.-Allgemeine Deutsche Lehare not mentioned. The names of the German rerzeitung. papers are

come therefore to the conclusion that steel is not, as

value."

The Thirteenth Annual Exhibition of New Inven

În Art, we have to notice the opening of the New Society of Painters in Water Colours, which takes place this day. The Exhibition of the British Institution, which opened as usual last March, has excited

considerable interest; the best works of which are:

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Landseer, “An Offering" (a goat bound on an altar)
Gilbert, "The Studio of Rembrandt ;" H. W. B.
Davis, "A Summer Afternoon, Pas de Calais" (a
sheep-picture, finely rendered, with a reminiscence of
the English Court" by Holman Hunt): G. Davis,
"Coaxing;" O'Neil, A Lazy Girl;" Bridell, the
"Woods of Sweet Chestnut above Varenna; " Bar-
"An Anxious Moment" (a lady questioning a
well,
physician as he quits the sick room); Lear, the
Fortress of Massada on the Dead Sea;" Houghton,
"A Conjugal Difficulty;" Erskine Nichol, “A Chi-
ropodist."

The picture in the possession of Sir Charles Eastlake, the loss of which at sea was reported, proves not to be the "Fra Angelico" purchased for the National Gellery, but one belonging to Sir Charles himself. The national picture has arrived safely at the Gallery, as well as some Majolica for the South Kensington Museum. The statue of Turner for St. Paul's, for which the painter left £1000, is progressing in Mr. M'Dowall's hands. Mr. Theed has obtained the commission for the Hallam statue for St. Paul's.

1. "Oestreichischer Schulbote," for elementary schools. Weekly.

2.

SAXONY.

FRANCE.

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Besides

According to the "Annuaire du Département de la Seine" for 1860, there are in the Zeitschrift für oestreichische Real-" Collége de France 28 chairs. Among schulen" (Real-Schools). Monthly. these are included professorships of political 3. "Zeitschrift für die oestreichischen Gym-economy; the law of nature and of nations; nasien," for Collegiate Schools. Monthly. 4. "Oestreichirches pädagogisches Wochenblatt," zur Reform der Erziehung unddes Volkschulwesens. Weekly.

6.

5. Die deutsche Volksschule." Monthly. 6. "Blätter für Erziehung und Unterricht." Quarterly.

comparative legislation (législations comparées) the history, ethics, philology, and archæology of Egypt; language and literature of Greece; Latin eloquence, Latin poetry; French language and literature in the Middle Ages; Hebrew; Chaldaic and Syriac; Arabic; Persian; Turkish; language and literature of the 6. Jahrbuch für Lehrer, Aeltern und Chinese and Tartars; Mantchoo; Sanscrit Erzieher." With Steel Engravings. Annual. language and literature; Slavonic language 8. "Mährischer Volksschulkalender. Annual. and literature; Germanic languages and litera9. Schlesischer Volksschulkalender. Annual. ture; foreign languages and literature of The greater number of these papers are modern Europe. The Commissioners for the Exhibition of 1862 have devoted to popular or elementary education, decided upon a modification of Captain Fowke's plans two only treating of higher or collegiate educa- Supérieure), intended to form teachers for the The Upper Normal School (Ecole Normale for the building, which have proved too expensive. As now modified, the total cost of the construction tion. The oldest of them has been established various departments of secondary and higher will be about £300,000. The contracts have been twenty-six years, and many of them have been education, is divided into two sections, the

Mr. Bell's monument to the Guards in the Crimea, and Mr. Behnes' statue of Havelock in Trafalgar Square, are now uncovered.

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In order to exhibit the form of the curve more clearly, let the given conic be an ellipse, O its centre, a, b its semi-axes, OF=c = (a2 — b2),AB = s = (a2 + b2)3, OS (1 PQ)=λ, OR=r, LAOR =6, 2 AOS = 4 OFP = 4; also let he the eccentric of the point D where OR meets the ellipse, the radius-vector of a point in the ellipse of which is the eccentric Z, and the semidiameter conjugate to . Then,

=3

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3 sin 0,1, or = 19° 28′. From this again we see that has four real and unequal values, two pairs of equal values, or four imaginary values, according as a>=<2b. Now, put A for the area of the locus of R; then ·.·' a2. tan 0=b2. tan p=ab. tan, .. A = ride x2d (tan 0)

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=

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62

2a2

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-f

'aob2c2 (a2 + c2)d↓ asin+b+cos↓

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0

= — (a® + a*b2 + 9a3b* + b®) — πb2c2 (a2 + c2) + xba

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rab
· (a®— a1b2 + 15 a2b1+ bo).
286

The preceding definite integrals give the entire area swept out by the radius vector (r); and when

Hence the area may be found from any one of the >2, (as in the figure) the small loops at O are included twice. But, resolving (8) into partial following expressions :fractions, we readily obtain the following indefinite integral:—

A

-

T

a2b2

(ab2-c3. sin. cos p)2 do .... (6) SA

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+s+c1s2. sin 2↓+ † (3a3b3 — abo)

log. (

a-c. u+c. siu

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(8)

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The integrals in (6), (7) may be reduced by the and from this the area of any section of the curve following properties of definite integrals:

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may be found. The double of this integral, between the limits =0, and gives the same result as that derived above from (6) and (7). Hence, putting E (Tab) for the area of the ellipse, we have

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+66 As ab approaches the limit unity, both the ellipse and the locus of R approach the circle as their limit; and when a=b, (9) gives A= Ena2. If a=26, (9) gives A: E=109: 250. The following is a more general form of the problem. A straight line moves with its ends on two given curves, and is always inclined at a given z to the line jong one of its ends with a fixed point: find the locus of a point which divides the moving line into two parts which have to one another a given ratio. Putting (xy) for the dividing point, and (h, k). (m, n) for the ends of the moving line, we can form five equations; two to express the conditions that the ends of the moving line are in the given curves, two that (x y) divides the moving line in a giving ratio, and a fifth the constant inelination. The locus of (, y) may be found by eliminating h, k, m, n from these five equations. For example, in the particular case in the Quest. we should have k-n h+c h-m

c. cos-ac. cos + b2

a-c.coso

or, λg,2=ab2—c3 . sin2 • . cos è̟.

Now, the equations of the chord PQ, and the

diameter conjugate to it, are

ay. cos 4-b2x. sin ¢=0......

and R is at the intersection of these two lines. Hence the equation of the locus of R is found by eliminating from (1), (2); and it may be put into the following forms:

T=

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The most useful of these is (5), which gives x and y as functions of p. The curve is symmetrical A = with respect to the axis of r, and it will take different forms according to the relative magnitudes of a. b. If a > 2b, the roots of the equation A-0, or c. cos-ac. cos p + b2 = 0, are real and unequal, and they give λ=x=y=r=0. The origin is then a quadruple point, through which four real branches pass, and the curve is of the form shown in the figure. If a=26, the roots of λ=0 are real and equal, the small loops at O vanish, and two ceratoid cusps are formed there.

If a<2b, the roots of λ = 0 are imaginary, and the curve does not pass through O, which is then ab a conjugate point. The 4s at which the several

(a¤— a1b2 + 15 a2ba + l®).

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h2 k2

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and the elimination of h, k, m, n would lead at once to equation (3), as that of the locus of R. Note. In my solution of Quest. 1184, ("Educational Times" for April), the 6th line should be B2-4AC>= <0,

and the 13th line

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1182 (Proposed by Mathematicus.)—What is the area of the least triangle, formed by a tangent to an ellipse, and its axes produced?

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Now, A QOS: A QOR: OS: OR:: CD: PD
:: OB: OA;
hence the ▲ QOS has a given ratio to the A QOR,
and when the one is a minimum, the other will
be a minimum also. But A QOR is a minimum,
when QR is a minimum; and this will be the case
when QP PR, or 4 QOP = POR; for the
length of any such tangent is twice the distance of
its middle point from O, and this distance is a
minimum when the middle point coincides with
the point of contact. And then ▲ QOR = OA2,
and. A QOS - OA. OB. Hence the least tri-
angle formed by a tangent to an ellipse and the
axes produced is equal to the rectangle contained
by the semi-axes.

Note.-The word "greatest" has been inadvertently put instead of "least" in the enunciation of this Question, and “maximum” for “minimum” in the 17th line of Miss Stephens's solution; moreover, her results may be obtained without the "differential calculus," as follows,

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2

as - (c

B

B

2

cos1
+ cos1
2

C

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ya = 0.

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Nicholls (Benjamin E.) Book of Proverbs Explained and
Ovidii (P. N.) Epistolæ quædam selecta, fcap. 8vo.
Illustrated from Scripture, 12mo.
Port Royal Logic (The) with Notes, &c., by T. S. Baynes,
5th edit, enlarged, 12mo.

Ragged Schools in Relation to the Government Grants
for Education.

Reading-Book (Second) New Series, Scriptural and Mis cellaneous Lessons, 18mo.

Richmond (Rev. L.) Rules to form the Ovidian Distich,
edited by J. Tate, 8vo.

Sabbath Scholar's Penny Hymn-Book (The) 32mo.
Seebohm (Frederic) Facts of the Four Gospels: an
Calculator (The); or, Short Rules for Shortening
Essay, 8vo.
Ordinary Calculations, 48mo.

1211 (Proposed by Mr. S. Watson, Hay-Short
donbridge.)-Show that the average area of all the
triangles that can be inscribed within a given tri-
angle, is of the triangle.

Skeates (Herbert S.) Popular Education in England, an

Abstract of Report, crown 8vo. Smith (Goldwin) The Study of History, Two Lectures, 8vo.

(William) Student's Manual of Ancient Geography, Maps and Illustrations, small post 8vo. Sumner (John Bird) Evidence of Christianity, new edit., revised, post 8vo.

NOTICES TO CORRESPONDENTS :We thank Mr. Bills for his information. On 1205 we may remark, that several correspon-Temple (Rev. Fred.) Sermons Preached in Rugby Chapel dents have split the original equation into factors Todd (Rev. John) Lectures to Children, First Series, new thus:

x (x2 - 1 x ) − (x + 2) = 0 ;

4x 9

.. is one root.

On 1198 we may remark, that we have received
also several solutions in this way:

2(x+y) (x2 + y2) — (x − y) (x2 — y2)=313,
or (x + y)3=73.

We are obliged to reserve many solutions for want
of space; but we must observe, that we find
unanswered forty or fifty Questions proposed
within the last fifteen months.

SOLUTIONS RECEIVED:

W. O. Phillips, M.A.-1125.
R. Wilson, M.A.-1204, 1205.
S. Bills.-1205.
Nemo.-1205, 1206, 1207.

Miss Stephens.-1198, 1201, 1204, 1205, 1207.
J. R. W.-1205, 1206.
Yks.-1204.

J. Miller.-1175.

Alphabetical List of the Principal English Pub-
lications for the Month ending April 26th.

Ahn (F.) French Method, 1st Course (Author's own Edit.)
12mo.
the given 4,
Key to Exercises in the German Grammar,
Airy (Geo. Biddell) On the Algebraical, &c., Theory of

and draw EF || AD and =ED, and join F, D; also from D apply DG- DE to meet the line passing through F, A, at G, and draw AB, BC | DG, ED; then will ABC be the ▲ required.

=

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12mo,

Errors of Observation crown 8vo

Bibliotheca Classica, edited by George Long, Hesiod, with
English Commentary, by F. A Paley, 8vo.
Cassell's Hand-Book of the Civil Service (Elementary
Hand-Books) f'cap 8vo.

Popular Natural History, V. 1 and 2 (Mammalia
complete) in 1 vol., imp. 8vo.

Circle of the Sciences (The), Vol. 3. Organic Nature.—

Vol. 3, new edition, crown 8vo.

Clark (Rev. James) Outlines of Theology, for Use of

Families and Students, Vol. 3, 8vo.

Clarke (J. E.) Children's Picture Book of Bible Miracles,

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ANSWERS TO CORRESPONDENTS.
All Communications intended for insertion, must
be authenticated by the name and address of the
writer. Rejected Communications cannot be
returned.
MR. SERJEANT.-We fear that the demands on
our space will render it impossible for us to find
room for your valuable articles.

MnTis. Your letter is unavoidably deferred.
M. TAPERNOUX.-We are happy to have an oppor-
tunity of explaining, that in noticing your
Encyclopædical Guide to the French Lan-
guage," we had no intention, in employing the
term "compilation," to indicate that it was de-
rived from other sources and not original. We
do not think that the term has generally the
meaning which you attach to it.
GEOMETRICUS.-Your letter is not accompanied
by your name and address; and your strictures
on the paper to which you refer, are simply
ridiculous. Euclid did not write in English, as
you imagine: but in Greek, and therefore did
not use either the term you complain of, or that
which you propose to substitute for it. You
have, evidently, never seen Mr. Potts' work,
otherwise you would not have ventured on the
absurd assertion "that he has taken in hand the
teaching of Euclid by symbols, and done all that
could be done in that way." The object of Mr.
Potts' work is just the reverse. He wrote
against the system-not in favour of it.
MR. LANGLEY, of Mowbray House, Academy,
Wolverhampton.-Writes that Mr. Joseph Dunn
Lester, who has just gained one of the Scholar-
ships at Jesus' College, Oxford, was for three
years a pupil of his School, whence he removed to
Shrewsbury School; before proceeding to the
University.

lean's Book-keeping, 4to.
Davidson (Rev. A. R.) Outlines of Hebrew Accentuation,
THE LATE HEAD MASTER OF ST. PAUL'S.-
Prose and Poetical, post 8vo.
Drawing Book, Black Lead Pencil Drawing Book, oblong. The head master was a fine old corpulent Greek
Edward (King) the 6th Latin Grammar, 15th Edit., 12mo. scholar of majestic presence, much respected, if not
Elements of Social Science; or, Physical and Natural Re-actually beloved, by the boys. The idea of attach-
ligion, 4th edition enlarged, fcap. 8vo.

1208 (Proposed by W. J. Miller, B.A.)- Ellis (Robert) Armenian Origin of the Etruscans, 8vo, Find x, y, z, from the equations,

x2 + 4xy+6y=28; x2+4xz+142-60; 3y2+2yz +7z2 =40.

(William) Philo-Socrates, Part I.-Among the Boys,
small post 8vo.
Galbraith (J. A.) and Haughton (S.) Manual of Plane Tri-
gonometry, Key to New Edition, fcap. 8vo.
Goodrich (S. G.) (Peter Parley) Prize Book Keepsake,
illustrated imperial 16mo.

Sense of Competition.

ment or affection from us little fellows towards so
awful a personage as Dr. Sleath was out of the
question. When he appeared, the school was
dumb. We believed in that big man; and after-
wards, when I came to years of scholastic discre-
tion, and could appreciate his merits, I knew that
he was excellent both as a schoolmaster and a man.
So
He was not a king of boys of the Arnold type.
the lads did the work well, and did not make a
noise, he was satisfied. He did not love to be di-
verted from his usual functions of educing the
classical capabilities of the seventh and eighth
Hesiod, Epics, with English Comment, by F. A. Paley, Svo. forms; and, indeed, whenever he was called in as
Lindley Gohn) Elements of Botany, Structural and Phy-a deus ex machina, it was not for a pleasant purpose.
siological, new edition, 8vo.

Hull.)-Government Appointments, Admission to; the Common
Greek and Roman Classics, Prefaces to the First Editions
of, Edited by B. Botfield, 4to.
Gregg (Tresham T.) Methodization of the Hebrew Verbs,

1209 (Proposed by Mr. W. Hopps, The bases of two triangles having a common vertex are parallel and given in length and position, whilst the difference of the areas of the triangles is constant. It is required to determine the locus of their common vertex.

1210 (Proposed by the Rev. R. H. Wright, M.A., Trinity College, Cambridge, Head Master of the Ashford Grammar School.)-Let ABC be

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COLLEGE OF
OF PRECEPTORS.-AGENCY DEPARTMENT.
ADDRESS, 42, QUEEN SQUARE, BLOOMSBURY, W.C.

REGULATIONS.

1. Applicants for vacant situations must send to the Secretary a statement of their qualifications, two copies of their testimonials, the names and addresses of their employers, if any, during the preceding three years, the salaries required, and their own addresses. The fee for insertion in the Register is one shilling. 2. The fee to be paid by any person not a Member of the College, on obtaining employment, is two-and-a-half per cent. on a year's salary. The fee payable by Members is ten shillings only. In both cases half-a-crown additional is charged for postages.

3. The requirements of Principals of Schools, Members of the College, are inserted in another Register on payment of one shilling: the fee to non. Members is half-a-crown. These fees cover all charges for correspondence, which will, if required, be undertaken by the Agency Department, and for Advertisements. 4. Every facility is afforded for interviews between Principals and Assistants at the College Offices. **All communications must be addressed to the Secretary, 42, Queen Square, W.C.

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455. French and Drawing. Age not less than 25. Salary 457. to 50l. In Kent.

457. Junior English. About 18 years of age. In Berks.
461. Classics. Salary 801. Near Town.
464. French and German.
Somerset.

Salary 601.

Required at Midsummer.

In

468. Classics, with French or Chemistry. Salary 501. In Devonshire. 470. High Mathematics. Salary 100l. to 1207. non-resident. Required at Midsummer. In Yorkshire.

474. Junior English Assistant. Age from 18 to 21. Salary 201. In Hants. 176. Junior Assistant to teach English Subjects, with Elementary Latin and French. For Midsummer. At Brighton.

483. Chemistry, Drawing, with Mathematics or Gymnastics. In Warwickshire.

486. Junior Classics, with Model Drawing. In Kent. 488. Writing Master. For Midsummer. Near Town.

490. Private Tutor to instruct in French, Mathematics, Latin, and English Subjects. Salary 501. In Hampshire.

491. (i.) Middle Mathematics, with English Subjects. Salary 607. to 80%. (i.) French and Drawing. A Parisian. Salary 407. to 50l. For Midsummer. Near Town.

492. French and, if possible, Drawing. Salary 30l. to 407. In Stafford. 493. (i.) Land-Surveying and Civil Engineering. Salary 80l. to 100%. (i.) Writing and Junior Drawing. Salary 50l. to 607. With Board, but not Lodging. In Lancashire.

ASSISTANT MASTERS REQUIRING
ENGAGEMENTS.

97. Model Drawing, Figure, and Landscape, &c. (Student of the Royal Academy.) Age 26. Non-resident.

110. Mathematics and Classics; English Grammar and Composition. As non-resident Teacher, for two or three hours a-day. Salary 701. 115. Visiting Teacher of the German Language, Literature, and History. 130. Drawing and Ornamental Writing. Age 34. Private Lessons, 2s. 6d. per hour.

136. Biblical, Classical, and Oriental Languages. M.A. of the University of Edinburgh; ten years Missionary in India. As Visiting and Private Tutor. 224. Classics and Mathematics, especially the latter. Accustomed to Teaching.

B.A. of London. Non-resident.

340. Painting and Drawing. A Member of the Institute of the Fine Arts. One guinea for each attendance within a reasonable distance of London. 376. English, French, Rudiments of German, and Music. Age 20. Salary 18 guineas. A Lady.

377. English, French, German, acquired on the Continent, and the Rudiments of Music. Age 21. Salary 201. A Lady.

402. German, French, and Piano. Age 33. Salary 507. Or as Visiting Master. 430. Drawing and Painting. Age 22. A Certificated and Prize Medallist of the Department of Science and Art. As Visiting Tutor.

443. Mathematics, Junior Classics, French, Drawing, and Writing. Age 34. As Morning Visiting Master.

451. Visiting Teacher of French, Mathematics, and Writing.
485. Drawing, Painting, Perspective, and Fortification. Age 40.
Visiting Master, at 5s. per lesson.

As

492. Classics, French, and English subjects. Age 40. Private Lessons. 497 High Classics. Age 30. A graduate of Oxford in Holy Orders. 500. High Classics, Mathematics to Trigonometry, French, and German. Age 30. As Visiting Master, or to take Private Pupils.

519. Mathematics, with Junior Classics, and French. Visiting Tutor. Age 29. 535. Mathematics to Conic Sections, Elementary Mechanics, Geometrical Drawing, and Perspective. Age 30. Salary 707. to 801.

559. English, Music, Drawing, and Painting. As Morning Governess in a School or Family. Age 21. Salary 407., non-resident.

562. German, French acquired in Paris, Pianoforte and Drawing for Juniors. Age 26. As non-resident or Visiting Master.

598. Visiting French Master.

604. French, Music, Drawing, and English. A Lady. Age 19. Salary 257. 610. Visiting French Master. Afternoons and Evenings.

615, German, French, and Drawing. Age 24. Salary 307.

625. Classics, Verse and Prose Composition, Mathematics, and the Rudiments of French. M.A. Oxford. Age 29. Private Lessons.

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637. Classics, Elementary French, and general management, or as Private Tutor. Age 32.

638. Middle Classics and Mathematics, French, Moral Philosophy, Logic, and English Subjects. Age 30. Graduate of Glasgow. Salary nonresident 1501 to 2007.

639. Classics and Mathematics, French and Italian. Age 52. As resident or non-resident Master.

640. English Subjects, French, Piano, Rudiments of German and Latin. A Lady. Age 25. Salary 507., as daily Governess, 4 days per week. 641. Moderate Classics and Mathematics, with English subjects. Age 25. A Graduate of Cambridge. Salary 100l. to 1507., non-resident. 647. German and French. As Visiting Master.

649. Classics, Mathematics, and English subjects. Private pupils. 650. French Language and Literature. As Visiting Master from 1 till 9. 653. Classics, Junior Mathematics, French, and English. Age 23. Salary 501. 655. High Mathematics, Geometrical Drawing, and Perspective, Mechanics, Classics, and History. Age 32. As Visiting Master.

656. Classics, German, French, and English, with Elementary Mathematics. Age 29. Salary 1007.

657. French and German. Age 38. Salary 50%.

663. High Classics, Prose and Verse Composition, Mathematics, Elements of Hydrostatics and Mechanics, &c. Five years' experience. Age 28. Salary 1007. resident, 1307. to 1407. non-resident.

666. Classics, Mathematics, French, English, and Book-keeping. Age 26. Salary 601. resident, 1007. non-resident. 668. Classics and Mathematics.

150%. non-resident.

B.A. Camb. Age 25. Salary 100l. to

672. Mathematics, Classics, French, and Geometrical Drawing. Graduate in Mathematical Honours of T. C. D. Age 33.

673. Modern Languages, Classics, and Mathematics. Visiting or private Tutor.

674. Classics and Mathematics, Mechanics and Hydrostatics. B.A. Camb. Age 24. Salary 1007.

675. Classics, French, Italian, Writing, and English Subjects. Age 35. Salary from 30l. to 401.

679. Junior Classics, Mathematics, English Subjects, Land-Surveying, practical and theoretical. Age 29. Salary 1007. non-resident. 680. Mathematics, Classics, Elementary French, and English Subjects. Age 19. M.A. of Aberdeen. Salary 407.

681. French, German, Junior Classics and Mathematics, Gymnastics, and Drilling. Age 33. Salary from 607.

683. Classics, Mathematics, French, and English. Age 22. Visiting or private Tutor.

684. High Mathematics, Pure and Mixed, French, German, Chemistry, and Drilling. Age 28. Educated at St. Cyr. Visiting or non-resident Master. 688. English, Junior Latin and Mathematics, with Elementary French. Age 20. Salary 251.

690. English, French, Classics, and Mathematics. Age 25. Salary from 751. to 80l. non-resident. 691. Highest Mathematics. eighteen hours per week.

A Wrangler, 1861.

To teach twelve or

692. Highest Mathematics, with Classics, &c. A Wrangler, 1861. Requires an engagement at Midsummer for about three months.

693. Classics, Prose and Verse Composition, Mathematics. B.A. Camb. in Classical Honours. Age 23. Salary 1007.

694. French, German, and Italian. Age 33. Salary 607. From Midsummer. 695. English Subjects, with Junior Latin and French. Age 16. Salary from 10l. to 201.

696. Classics and Mathematics. Graduate in Classical Honours of Aberdeen. Age 25. Salary 70%.

697. English, Music, French, German, and Drawing. A Lady. Age 30. Salary 601.

698. English Subjects, French, German, and Music. A Lady. Age 19. Salary 157. to 201.

699. Elementary Mathematics, English, French, and Latin. Salary 207. 700. German and French thoroughly, with Classics and Mathematics. A German. Age 32. Salary 507,

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