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EDUCATIONAL AND LITERARY SUMMARYquires enforcement, as we have seen frequenters of invented by him, with the view of producing a fuller OF THE MONTH.

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 Tåg 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 proso 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take the ordinary chimney of feeling interested in the subject, does not nevertheless translation in French is to be superseded by a metrical a lamp, which, by the way, must be four ioches care to wade through the ponderous blue books in version in the same language ; and we learn that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 bave 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 currecting 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 tbe 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 consi. for the appointment of student interpreters in China

derably greater than ordinary: and the result is, that

" Si fructus illabitur orbis. and Japan. The age of the candidates was originally

the light is much increased, and the consumption of

Impavidunt ferient ruinæ ;" limited to between sixteen and twenty years complete.

gas greatly diminished. A common argand burner, It now appears that certain students of King's Col- nor are either Virgil or Mr. Gladstone to be congra

which consumod three-and-a-half feet per hour, and lege, have been for some time past qualifying them- tulated upon the following reading of the well-known

gave a light equal to thirteen candles, when fitted selves for these appointments; and to admit these hexameter in the speech on the Budget,

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

“Ego vescula alte occulis et rite repertum | to thirteen candles could be produced from little more age has been extended to twenty-five. We may add, Carpe manu–"

than two feet of gas, instead of three-and-a-half. that the following book, which has just been published

Mr. Crookes, tho editor of the "Chemical News," A weekly cotemporary writes :- The private library at Paris, will be found most serviceable to such of the late King of Prussia, Frederic Wilhelm

y contributes an interesting paper to the April Number students as wish to master the Japanese tongue :

the of the Philosophical Magazine," on the discovery of

Fourth, is valuable and extensive. It comprises a new element, probably of the sulphur series. “Essai de Grammaire Japonaise," by M. J. H.

The about 56,000 volumes, and contains, for the greater Donken Curtius, Dutch Consul in Japan, enlarged part, works of History, Archæology, and Christian discovered by the method of spectrum analysis of

ter new metaloid, which has not yet been named, was by Dr. Hoffmann, Professor of Japanese and Chinese, and published at Leyden in 1857 ; translated from the Palace at Berlin. Humboldt's works formed a special nese; Art. The library fills six large rooins of the Royal Kira

of the Royal Kirchhoff and Bunsen, in some seleniferous deposits Dutch. with new notes extracted from the Grammar

from the sulphuric acid manufactory at Tilkeroide in compartment, called the · Humboldt Press,' and are of Father Rodriguez and Father Collard, by Leon I found in greater completeness, from the large work on

the Hartz Mountains. It gives rise to a well-defined Pagès.

green line, almost rivalling the Sodium lino in bril. America, which cost 3000 thalers, to the smallest The article from the pen of Mr. Henry Fawcett,

liancy. Kirchhoff himself communicates an interest. Fellow of Tripity Hall College, Cambridge, on the them. henry fawcett, pamphlet, than when Humboldt himself possessed

et possessed ing article to the March number of the same Magazine,

This library has been left by will to the pre-l on the Chemical Analysis of the Solar Atmosphere. justice of admitting dissenters to College Fellowships sent King, with the exception of the artistic works, I As all metals are, by the exquisite method of analysis. in the University of Cambridge, which appeared a

which have been bequeathed to the Queen Dowager.devised by him and Bunsen, clearly indicated by the short time ago in Macmillan's Magazine, appears to

A question arose, if all the illustrated works with be only the prelude to a regular movement for effect.

bright bands in the spectrum of a flame in which they woodcuts, &c., were to be understood among the ing that object. A petition is now being circulated in

are present; and as the total nucleus of the sun is 'artistic works,' which question has been decided in the University just named, and has received many

surrounded by an incandescent gaseous atmosphere, favour of the Queen." signatures, praying the House of Commons to do

it occurred to Kirchhoff, that if we could see the

The question of adopting an academical costume away with all the provisions in the Act of Uniformity for the undergraduates having been mooted for some

spectrum of this luminous atmosphere, we should see which have hitherto prevented dissenters from holding time past among the students of Edinburgh Univer.

in it the bright bands characteristic of the metals conCollege Fellowships, &c.

tained in the solar atmosphere, if there are any. sity, a poll was directed by the Senatus Academicus Mr. F. C. Cook, Inspector of Schools, has written to be taken to decide whether the proposed change lever, that the more intense luminosity of the sun's

From Kirchhoff's observations it appears, howto 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 lagainst the adoption of any such costume. school of 150 boys in Reading, Writing, and Arith-|

The

of its atmosphere : it reverses it, in fact, so that, inhonours of the cap and gown will therefore be reserved metic. As even then Mr. Cook cannot give anytbing

stead of the bright lines which the spectrum of the as heretofore to graduates only. - The “Great Tom" like two minutes to test the knowledge of each boy in

atmosphere by itself would show, dark lines are pro| Magazine, of which we spoke in our last, seems to duced. Thus, we do not see the spectrum of the the three distinct subjects, it may be doubted whether

have fallen to the ground. Farther north, however, it an examination conducted at this railway pace can be

T.; atmosphere, but a negative image of it. This, how

we hear that a new magazine is likely to be born, if worth much, or indeed anything at all.-A facsimile not to ha lone lived it is to be called the “Aber.

1,"ever, serves equally well to determine with certainty of a portion of the Domesday Book has been taken deen University Magazine."- A statement appeared a atmosphere. With the aid of a splendid apparatus

to the presence of those metals which occur in the sun's by photography, under the direction of Sir Henry for James. The experiment (which is about to be re- ill-fated poetess, L. E. L. henry few weeks ago, that nothing marked the grave of the

from the optical and astronomical manufactory of

Dr. McWilliam has Steinheil, in Munich, Kirchboff has commenced his newed on a larger scale) has been thoroughly suc- 1 written to a cotemporary, stating that a monument, cessful; and so much of the famous book in question bearing a Latin inscription, was erected by her hus.

minute examination of the solar spectrum, and of the as relates to Cornwall may now be purchased for a band over her remains.-Dr. Sharpey has, we learn,

spectra of the various metals. He has already sucvery few shillings.--The “ Essays and Reviews" have ha

ceeded in establishing the important fact, that the been appointed to succeed the late Dr. Baly as a now reached a ninth edition ; and the number of the member of the General Council of Medical Educa.

* bright linès characteristic of iron, magnesium, chro“Quarterly" in which they were reviewed by (it tion.

mium, and nickel, in the spectra of flames containing is said the Bishop of Oxford, is in its fifth. A num

these metals, correspond to dark lines in the solar specber of critics, hostile to the “ Essays and Reviews,"

trum. The occurrence of these metals in the sun may have suddenly sprung up. Many of these writers are

therefore be regarded as certain. We need not dwell otherwise unknown to fame Among them figures

MONTHLY RECORD OF SCIENCE on the grandeur of the discovery which has thus Dr. Cumming (notorious enough, certainly, if not

AND ART.

enabled the analytical chemist to extend his researches lamous) as the champion of orthodoxy.-A London THE Evening Lectures at the Geological Museum. I to the great luminary in the centre of our system at a Book Union is about to be commenced; its design is, suspended during the Easter recess, have re-opened

spended during the Easter recess. have re.opened distance of ninety-five millions of miles." 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 books instead of pictures. The Smith. A Course of Lectures on Physiology at of such frequent occurrence that it has lost much of Arst 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 a n

In that region of the heavens comprised between the

that region of the heavens com? each subscriber is to receive a copy of some standard series of Lectures in Chemistry, Geology, Zoology, or

orbits of Mars and Jupiter, two new asteroids, form. Fork.--The particulars of the Civil List pensions for and Practice with the Microscope, by other Professors ing the 64th and the Gth 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 ritic,” 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

actors to literature and art are to the members of the Royal Institution on Friday 23rd of October last. It is a noticeable fact, that al

n 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,

oploved by Deville, sent century. The first asteroids of the group were as been put up at the reading. bv fusing it at high temperatures. by which the salts I discovered between the years 1801 and 1807 ; and by room of the British Museum, that persons will not belandother 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 nity, and fitteen more have been added newspapers and other publications which are not sup. I tedious process, by which the metal, after being ex. I during the last fifteen years. Anmportant pbed from the library : as it has been found that many I posed to the action of aqua regia, had to pass through series of researches in a diferent department of those who go there for the purpose of study arel a variety of secondary processes. more or less at. of science, has recently been laid before AC 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 composie bers of diletantti readers who frequent the Museum. state. On Friday evening, March 8, Dr. Fra

he 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 I 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

lame in Rarefied Air and on the new one burner from the “Chemist and Druggist” of this month:

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• It had been shown by Despretz that at a red heat | undertaken by Mr. Kelk, and by Messrs. Lucas, (in existence for more than ten years. The eduiron decomposes ammonia, becomes white and brittle, Brothers.

cational papers of the non-German races treat and increases in weight 1105 per cent. Fremy An Industrial exhibition has been announced to be almost

e almost exclusively of popular or elementary

elusiv proves that this increase in weight is due to the held in Florence in the ensuing autumn. It is ex. absorption of nitrogen, that a true nitride of iron pected that it will be particularly rich in illustrations

education. Only one has existed eight years, is formed, quite free from hydrogen. Iron can of mediæval art, for which Tuscany furnishes a pecu. and the others have been founded during the only be made to combine directly with nitrogen liarly fine field.

last two years only. with extreme difficulty ; but a nitride is formed The alterations which have been going on in the when nitrogen is brought into contact with the meta! | National Gallery for some time past are now com

PRUSSIA. at the moment of its reduction, either by hydrogen or pleted. The public will be grateful for the change The “ Allgemeine Deutsche Lehrerzeitung" carbon. The action of ammonia on iron is extremely which has been effected and for the greatly improved for March contains an interesting account of slow, whole days being required to convert a few means which have been provided for the reception of the grains into nitride ; but by passing ammoniacal gas the national pictures, which can now be seen to great!

great the public educational institutions of Berlin, through a porcelain tube containing protochloride of advantage through the admirable arrangement which which are at present,-7 gymnasia (corresiron heated to redness, Fremy obtained nitride of iron has been adopted for exhibiting them.

ponding to our classical schools), 1 progymin abundance. He exhibited to the Academy of

nasium, 5 real schools (corresponding to our Sciences, on the 261 h of February, a mass weighing

commercial schools), l'industrial school, 3 200 grammes, white and brilliant ; and he expressed an opinion, that as this compound can now he so

FOREIGN NOTES.

higher girls' schools, 5 higher boys' and preeasily made, it will become a valuable agent for fur.

AUSTRIA.

paratory schools for higher institutions, 23 nishing 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 oxirlizable Volkschulbote" we have an interesting account 14 Protestant parochial and 6 Catholic parothan pure iron ; is attacked with difficulty by nitric acid, but with great energy by hydrochloric and sul.

and out of the Educational Periodicals published in chial schools, in connexion with congregations phuric acids; and is susceptible of permanent, but the Austrian empire. The number of these to which they belong, 3 Jewish schools, 1 less powerful, magnetism than steel. It is a com- periodicals representing the various nationali- | Jewish, 1 Catholic, and 4 Protestant orphan pound of great stability ; supports a red heat without ties is in all seventeen. Of these more than asylums, 4 educational establishments under , and only attacked

y oxygen at a half, viz. nine, and by far the best, are the administration of societies, 2 prison schools. high temperature. Its composition appears to be .. Fe, N, which corresponds to 9.5 per ceut. of nitrogen. |

written in the German language. Three are Of private educational establishments there When heated in a charcoal crucible it undergoes are written in the language of the Sclavonian part are,-l commercial institution, 7 higher boys' markable change, approaching the condition of steel, of Bohemia called Tschechic ; one is written schools, 27 middle and elementary boys' and when heatid in a current of hydrogen, it does not in the Hungarian or Magyar language ; one schools, 27 higher girls' school and boarding give off a trace of ammonia.

Tin the Croatian : one in the Slovakish; one in establishments, 26 middle and elementary girls' “In a later communication to the Academy of S. Science (11th of March) Fremy describes some exof Servian, and one in the Roman-a dialect of schools, 14 mixed schools for childreu of both

Besides tremely interesting experimenta: 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, forining grey, I of languages, although they differ from one of industry for girls, in which they receive, graphity malleable cast iron. equal in quality to the lonother almost as widely

! in quality to the another almost as widely as independent lan- in addition to industrial training, the usual finest charcoal iron; but uuder no circumstance, how

Iguages. The Roman is a dialect derived from elementary instruction of other schools, 68 ever carefully he regulated the dose of carbon, could he form in this way steel, but when the compound of noman.co.

ind 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, Jor 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 haslin Bohemia, are spoken in Hungary, which is

n'in Hungary which is of improvement (fortbildung) for young men

I improvemen come therefore to the conclusion that steel is not, aslin minia is generally supposed, a simple compound of iron and

id 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 value,"

the empire, which are equal to those of any about 30 pupils to each teacher, of either sex. The Thirteenth Annual Exhibition of New Inven-lethe tions, at ihe Society of Arts, Adelphi, opened to the other parts of Germany, come those of the

SAXONY. public on Easter Monday, and will continue open

Bohemian Tschechs, who are a cultivated and The “Pestalozzi Societieswhich 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 contaios 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 favour. required to give it a careful inspection. In Art, we have to notice the opening of the New

and that this is Roman Catholic, while the Pro-ably. The“ Pestalozzi Society of Saxony," Society of Painters in Water Colours, which takes testant Magyars possess none. The binding or which employs part only of its income for place this day. The Exhibition of the British Insti- civilizing element of the various races of the grants in aid, and the remainder for the general tution, which opened as usual last March, has excited Austrian empire is the German, as is clearly purposes of the society, supported last year considerable interest; the best works of which are :- indicated by the large proportion of the educa- 137 bereaved families, and provided the means Landseer, “An Offering'' (a goat bound on an altar) ; Gilbert, “The Studio of Rembrandt ;" H. W. B.

itional periodicals published in that language. of education for two young teachers, sons of Davis. ** A Summer Afternoon. Pas de Calais" (a The Polish or Gallician and the Austro-Itahan deceased teachers. --Allgemeine Deutsche Lehsheep-picture, finely rendered, with a reminiscence of are not mentioned. The names of the German rerzeitung. . the " Ènglish Court" by Holman Hunt): G. Davis, papers are

FRANCE. “Coaxing ;'' O'Neil, “ A Lazy Girl;' Bridell, the i. “ Oestreichischer Schulbote,” for elemen- According to the “ Annuaire du Départe“ Woods of Sweet Chestnut above Varenna ;” Barwell, “ Ao Anxious Moment" (a lady questioning a to tary schools. Weekly.

ment de la Seine " for 1860, there are in the physician as he quits the sick room) ; Lear, the

el

2.

2. “ Zeitschrift für Oestreichische Real-". Collége de France" 28 chairs. Among ** Fortress of Massada on the Dead Sea;' Houghton, schulen” (Real-Schools). Monthly.

these are included professorships of political A Conjugal Difficulty;" Erskine Nichol, “ Å Chic 3, “ Zeitschrift für die oestreichischen Gym-economy; the law of nature and of nations; ropodist."

nasien,” for Collegiate Schools. Monthly comparative legislation (législations comparées) The picture in the possession of Sir Charles East. 4. 'Oestreichirches pädagogisches Wochen- the history, ethics, philology, and archæology lake, the loss of which at sea was reported, proves not to be the “ Fra Angelico" purchased for the Na

blatt," zur Reform der Erziehung unddes Volk- of Egypt; language and literature of Greece ; tional GcHery, but one belonging to Sir Charles him. schulwesens. Weekly.

Latin eloquence, Latin poetry; French lan. self. The national picture has arrived safely at the 5. “ Die deutsche Volksschule.” Monthly. Iguage and literature in the Middle Ages; Gallery, as well as some Majolica for the South Ken. 6. “Blätter für Erziehung und Unterricht." Hebrew; Chaldaic and Syriac; Arabic; Persington Museum. The statue of Turner for St. Quarterly. Paul's, for which the painter left £1000, is progressing

bian; Turkish; language and literature of the

6. Jahrbuch für Lehrer. Aeltern und Chinese and Tartars: Mantchoo; Sanscrit in Mr. M.Dowall's ha.ds. Mr. Theed has obtained the commission for the Hallam statue for St. Paul's.

Erzieher.” With Steel Engravings. Annual. language and literature; Slavonic language Mr. Bell's monumont to the Guards in the Crimea, 8. “ Mährischer Volksschulkalender. Annual. and literature; Germanic languages and literaand Mr. Behnes' statue of Havelock in Trafalgar 9. Schlesischer Volksschulkalender. Annual. ture; foreign languages and literature of Square, are now uncovered.

The greater number of these papers are modern Europe. The Commissioners for the Exhibition of 1862 hare de decided upon a modification of Captain Fowke's plaas

re devoted to popular or elementary education, The Upper Normal School (Ecole Normale for the building, which have proved too expensive..

two only treating of higher or collegiate educa- Supérieure), intended to form teachers for the 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 thein have been education, is divided into two sections, the

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section of Litei ature, and the section of sciences. branches of the curve cut OA may be found bv It employs 20 masters.

putting y = x tan o in (3), and then ascertainings The Faculties are in number five-viz., the values of 0when x = 0; or by putting " = 0

.88.cos? +a*%* +5a2b4) dt theology, law, medicine, science, and litera-in (4). We thus obtain ture; and in these there are in all 82 chairs; I 2a3.8ec20. =c? [3a + (a?–462))],

aloc?(q2 +c)dy. 20668.dk 7 for Catholic theology, 19 for law, 26 for wbich, when a=26, gives medicine, 18 for sciences, 12 for literature.

- b*cus***) (at.sinab+b'.cus4)2

3 sin 8.=1, or 0. = 190 28'. In the Upper School of Pharmacy there are from this again we see that 0. has four real and 8 chairs. unequal values, two pairs of equal values, or four

+a+62 +9a2b4 +66) — 76%co (ao +c?) + b* imaginary values, according as a> = < 26. Now, put A for the area of the locus of R; then

(a* +64); MATHEMATICAL QUESTIONS AND

:: a. tan 0=b2 . tan grab . tany, SOLUTIONS.

a*b*+15a264 +69). 1175 (Proposed by Mathematicus.- From the focus F of a conic, draw any radius vector

The preceding definite integrals give the entire FP, make PQ perpendicular to it meeting the

area swept out by the radius vector (r); and when conic again in Q: then if R be the middle point of Hence the area may be found from any one of the

Sohela > 26, (as in the figure) the sinall loops at O are PQ, determine the equation and area of the curve following expressions :

included twice. But. resolving (8) into partial which is the locus of R, and exhibit its for m.

fractions, we readily obtain the following inde

finite integral:SOLUTION BY W. J. MILLER, B.A., ELTHAM.

63. sin. o . cos 0)do .... (6)

SASA = (3a*b*~a*be) {1x + tan- (
w w [b(a= sinab + b2 cos 4)* - ac3 sinalcosseto + 1394+ fc*so. sin 24++ (3a313ab)
- (a* sino + 6* cos***)

log. (470:sin ) + zal_cs* . sia .

z f (72az +12) dm In order to exhibit the form of the curve more A=şa*63) ia-2)2 (32+62): do ............. (8)

(a +c.cos ); .. clearly, let the given conic be an ellipse, o its where z=C. cos p.

and from this the area of any section of the curve centre, a, b its semi-axes, OF=-=(a?627,AB The integrals in (6), (7) may be reduced by the

may be found. The double of this integral, be=&= (a* + 32)2, OS (1 PQ)=1, OR=r, LAOR following properties of definite integrals:

tween the limits o=y=0, and o==gives the =. AOS = LOFP = 0; also let the the

same result as that derived above from (6) and (7). eccentric L of the point D where OR meets the

F (sin? ) cos o . =0, and

Hence, puiting E (=mab) for the area of the ellipse, ellipse, e the radius-vector of a point in the ellipse

we have of which o is the eccentric L, and f, the semi.

A 06 - 7482 + 15a 21,+ + 66 diameter conjugate to g. Then,

Ē 246 +1a 6% + 6u261700"

...... ....(9). p=a. cosa 0+ 62 • sino o=(a +c. sin o) (a-c. sin o),

As a:6 approaches the limit unity, both the | F (sin? ®) do=2 / F (sin” o) do = fi=a”. sino @ +22. cos?o=(a+c.cos )

ellipse and the locus of R approach the circle as (a-c.cos);

their limit ; and when a=6, (9) gives A= E=maa.

Ifa=21, (9) gives A: E=109 : 250. The follow72

ing is a more general form of the problem. A a -c.cos -c.cos Q =

straight line muves with its ends on two given ca.cosa p-ac. cos 0 + 62

curves, and is always inclined at a given Z to the 2 f F (cos:o) do.

line joomg one of its ends with a fixed point: a-c.cos o

find the locus of a point which divides the moving or, ap;=abo-63. sinop.cos $. Thus, from (6) we have

line into two parts which have to one another a Now, the equations of the chord PQ, and the

given rativ. Putting (x y) for the dividing point, diameter conjugate to it, are

and (h, k). (m, nb) for the ends of the moving line,

we can forin five equations; two to express the X.cos $ + y sin ø=1 ..............(1)

2a28

condicions that the ends of the moving line are in

(a*b? +c. sin d. cos?o) do ay.cos 6-box. sin $=0 ............ (2)

the given curves, two that (x y) divides the moving and R is at the intersection of these two lines.

line in a giving ratio, and a fifth the constant inHence the equation of the locus of R is found

clination. The focus of (1, y) may be found by by eliminating o from (1), (2); and it may be put

eliminating h, k, m, n from these five equations. into the following forms :

For example, in the particular case in the Quest.

(a 24 +co.cost o.sino) de we should have aʼl?c?y* (a=y2 + ?ra) aty + b?) ? a*b*-a-yo-67 a+cx )

1

m ke all -allac.sinie.cos 0 + ab? (a* sin:0 + 64cos?) i

h2 , kmon2 = , (g' Su-a + b . tos-0) (d. sin' + to.cos^6) 1 = f (2a2l+ + c. sin 4. cos? ) d+;

hem km = 2; i. putting m*=25*—c*=a* + baRb2 +6, we have

..........(5). az.cos o 63.sino pa

and i he elimination of h, k, m,n would lead at The most useful of these is (5), which gives x

r 8aboc. do 64 a464 (3362-a) do

once tu equation (3), as that of the locus of R. and y as funcions of o. The curve is symmetrical | A =

Note.- Tu my solution of Quest. 1184, ("Eduwith respect to tlie axis of x, and it will take dif

cational Times” for April), the 6th line should be ferent forins according to the relative magnitudes

B2-4AC>=<0, of a, b. fa > 2b, the roots of the equation 1=0, or ca.cos o-ac.coso + b* = 0, are real and un

and the 13th line equal, and they give 2 = x=y=j=0. The origin

Hill, is then a quadruple point, through which four

a+b2 + 15 a+64 +69).

absina. w . . real branches pass, and the curve is of the form shown in the figure. If a=2b, the roots of 1=0 | Again, from (7) we bave are real and equal, the small loops at vanish, and two ceratoid cusps are formed there.

Il e< 26, the roots of 2 = 0 are imaginary, and 862(a2.sin2 +62.cos?4)3 +4°c sinb.cost! 1182 (Proposed by Mathematicus.)— What the curve does not pass through 0, which is then

(a'sin? + 6* cos? 1)?

Jis the area of the least triangle, forined by a a conjugate point. The Ls at wbich the several

n i. df tangent to an ellipse, and its axes produced ?

2=FP-c.cos o=a-c. cos o

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SOLUTION BY W.J. MILLER, B.A., Eltham.

any triangle whose sides are a=0; B=0, x=0, and

own and I Nicholls (Benjamin E.) Book of Proverbs Explained and

"

Illustrated from Scripture, 12mo. let the bisectors of the angles meet the opposite Ovidii (PP. N.) Epistolæ quædam selectæ, fcap. 8vo. sides in D, E, F whose equation is

Port Royal Logic (The) with Notes, &c., by T. S. Baynes, Let AOBCPI be a quadrant

5th edit, enlarged, 12mo.

Ragged Schools in Relation to the Government Grants of an ellipse and its circumscribed circle, and QPR a

21" 22 (Cos 2 + cos' 21 for Education.

Reading-Book (Second) New Series, Scriptural and Mistangent to the circle; then, if|

e

p vil

Const.

m : cellaneous Lessons, 18mo.
| aB - (cost Bucos
PCD be 1 OA, QCS will be a

Richmond (Rev. L.) Rules to form the Ovidian Distich.

edited by J. Tate, 8vo. tangent to the ellipse.

Sabbath Scholar's Penny Hymn-Book (The) 32mo. ya = 0.

Seebohm (Frederic) Facts of the Four 'Gospels: an

Essay, Svo. Now, A QOS: AQOR :: OS : OR :: CD: PD! 1211 (Proposed by Mr. S. Watson, Ilay.

by, Mr. S. Watson, Hay Short Calcnlator (The); or, Short Rules for Shortening :: OB;OA;

donbridge.)- Show that the average area of all the Ordinary Calculations, 48mo. hence the A QOS has a given ratio to the A QOR, triangles that can be inscribed within a given tri- Skeates (Herbert S.) Popular Education in England, an

Abstract of Report, crown 8vo. and .. when the one is a minimum, the other will angle, is 4 of the triangle.

Smith (Goldwin) The Study of llistory, Two Lectures, be a minimum also. But A QOR is a minimum,

8vo. when QR is a minimum; and this will be the case

(William) Student's Manual of Ancient Geography,

Maps and Illustrations, small post Svo. when QP = PR, or _ QOP = L POR; for the Notices to CORRESPONDENTS :

Sumner (John Bird) Evidence of Christianity, new edit., length of any such tangent is twice the distance of We thank Mr. Bills for his information.

revised, post 8vo. its middle point from 0, and this distance is a On 1205 we may reinark, that several correspon.

Temple (Rev. Fred.) Sermons Preached in Rugby Chapel minimum when the middle point coincides with

in 1858, 1859, and 1860, 8vo. dents have split the original equation into factors Todd (Rev. John) Lectures to Children, First Series, new the point of contact. And then A QOR = OA',! thus:

edition, 18mo, and :. A QOS =0A, OB. Hence the least tri.

Vaughan (Charles John) Memorials of Harrow Sundays: angle formed by a tangent to an ellipse and the

« (x2 – 40) -(x+) = 0;

Sermons, 3rd edition, crown Svo.

Wood (Alphonso) Class-Book of Botany, new edition, axes produced is equal to the rectangle contained

revised, 8vo. by the semi-axes,

.: x=-j is one root.

Wordsworth (Dr.) Greek Testament, Index to, by Rev.J. Note. The word greatest” has been inad-On 1199 we may remark, that we have received

Twycross, vertently put instead of " least" in the enunciation

Young (J. K.) The Mosaic Cosmogony not " Adverse to also several solutions in this way:

Modern Science." of this Question, and "marimum" for "minimum"|

2 (x + y) (32 + y2)-(x - y) (x"-32)=313, in the 17th line of Miss Stephens's solution ; moreover, her results may be obtained without

or (x + y)3=73.

ANSWERS TO CORRESPONDENTS, che "differential calculus," as follows,

We are obliged to reserve many solutions for want al Communications intended for insertion, must 23b alb of space ; but we must observe, that we find

be authenticated by the name and address of the unanswered forty or fifty Questions proposed 2x vai - 23 jut-Tai - xäji'

writer. Rejected Communications cannot be within the last fiiteen months.

returned. .: A is a minimum (x=46) when a---2xo =0,

SOLUTIONS RECEIVED:

MR. SERJEANT.-We fear that the demands on W. 0. Phillips, M.A.-1125.

our space will render it impossible for us to find or x = R. Wilson, M.A.-1204, 1205.

room for your valuable articles. S. Bills.-1205.

Mytis.-Your letter is unavoidably deferred. Nemo.-1205, 1206, 1207.

M. TAPERNOUX.-We are happy to have an opporMiss Stephens.-1198, 1201, 1204, 1205, 1207. 1199 (Proposed by Mr. Con will.)-Given in J. R. W.-1205, 1206.

tunity of explaining, that in noticing your

“ Encyclopædical Guide to the French Lana plane A, one of the base Zs, the sum of the Yks.--1204.

guage, we liad no intention, in employing the two sides containing it, and the sum of the sides J. Miller. - 1175. including the other base L; to construct the A.

term “compilation," tu indicate that it was de

rived from other sources and not original. We SOLUTION BY MR. W. HOPPs, HULL. Alphabetical List of the Principal English Pub.

do not think that the term has generally the lications for the Month ending April 26th.

meaning which you attach to it. Con. With the two

GEOMETRICUS.-Your letter is not accompanied given lines form the Ahn (F.) French Method, 1st Course (Author's own Edit)

by your name and address; and your strictures LADE = the given til 12mo.

on the paper to which you refer, are simply and draw EF | AD and

- Key to Exercises in the German Grammar, ridiculous. Euclid did not write in English, as

12mo,
- EI), and join F, D; Airy (Geo. Biddell) On the Algebraical, &c., Theory of

you imagine: but in Greek, and therefore did also from D apply DG = DE to meet the line Errors of Observation crown 8vo

not use either the term you complain of, or that passing through F, A, at G, and draw AB, BC Bibliotheca Classica, edited by George Long, Hesiod, with

which you propose to substitute for it. You

English Commentary, by F. A Paley, 8vo.
DG, ÉD ; then will ABC be the A required. Cassell's Hand-Book of the Civil Service (Elementary

have, evidently, never seen Mr. Potts' work, Dem.-Produce CB to meet FE at H. Then, Hand-Books) f'cap 8vo.

otherwise you would not have ventured on the AS FED, BCD are similar ( 11 s); but FED is Popular Natural History, V. 1 and 2 (Mammalia absurd assertion " that he has taken in hand the

complete) in 1 vol., imp. 8vo. isosceles (con.), ... BCD is isosceles also. Hence Circle of the Sciences (The), Vol. 3. Organic Nature.

teaching of Euclid by symbols, and done all that AC + BC = AC + CD = AD = the first given line Vol. 3, new edition, crown 8vo.

could be done in that way." The object of Mr. (con.) Again, by sim. AS, GD (= ED): ABClark (Rev. James) Outlines of Theology, for Use of Potts' work is just the reverse. He wrote

Families and Students, Vol. 3, 8vo. =FD : FB=ED:HB.

against the system-not in favour of it. Clarke (J. E.) Children's Picture Book of Bible Miracles, MR. LANGLEY, of Mowbray House, Academy, .. AB=HB.

square 12mo, Consequently AB + BC = HB + BC=HC=(s)

Scripture Parables and Bible Miracles, in

Wolverhampton. Writes that Mr. Joseph Dunn ED=The second given line (con.) Lastly, LÀCB 1 vol., square 12mo.

Lester, who has just gained one of the Scholar. =ADE (|| S)=the given L..

- Sunday School Reader or Reciter, new edit., ships at Jesus' College, Oxford, was for three

18mo. Note. - By the aid of Question 1126, “ Educa. Constable's Educational Series: Lessons, Sheets from

years a pupil of his School, whence he removed to tional Times," this Question, as well as many First Reading Book, folio.

Shrewsbury School; before proceeding to the others similar, may be solved by propositions

--- Ruled Books to Mac University

lean's Book-keeping, 4to. contained in Euclid's Ist Book.

Davidson (Rev. A. Ř.) Outlines of Hebrew Accentuation, THE LATE HEAD MASTER OF St. Paul's.

Prose and Poetical, post svo

Drawing Book, Black Lead Pencil Drawing Book, oblong. / The head master was a fine old corpulent Greek
NEW QUESTIONS.

Edward (King) the 6th Latin Gramınar, 15th Edit., 12mo. scholar of majestic presence, much respected, if not
Elements of Social Science; or, Physical and Natural Re-

ligion, 4th edition enlarged, fcap. 8vo.
1208 (Proposed by W. J. Miller, B.A.) - Ellis (Robert) Armenian Origin of the Etruscang, 8vo,

ment or affection from us little fellows towards so Find x, y, z, from the equations,

- (William) Philo-Socrates, Part 1.-Among the Boys, awful a personage as Dr. Sleath was out of the

small post 8vo. x2 + 4xy + 6ya = 28;

| question. When he appeared, the school was Galbraith (J. A.) and Hanghton (S.) Manual of Plane Trix2 + 4x2 + 14z* - 60;

ane Triel dumb. We believed in that big man; and after

gonometry, Key to New Edition, fcap. 8vo. 3y2 + 2yz + 7z* = 40.

Goodrich (8. G.) (Peter Parley) Prize Book Keepsake, wards, when I came to years of scholastic discreillustrated imperial 16mo.

tion, and could appreciate his merits, I knew that a by Mr. W. Hopps, Hull.) - Government Appointments, Admission to; the Common he was excellent both as a schoolinaster and a man. The bases of two triangles having a common

Sense of Competition. vertex are parallel and given in length and posi. 1° Greek and Roman Classics, Prefaces to the First Editions

He was not a king of boys of the Arnold type. So

of, Edited by B. Botfield, 4to. tion, whilst the difference of the areas of the tri-Gregg (Tresham T.) Methodization of the Hebrew Verbs, noise, he was satisfied. He did not love to be di

the lads did the work well, and did not make a angles is constant. It is required to determine 3rd edition, revised. the locus of their common vertex. Henslow (Rev. J.S.) Dictionary of Botanical Terms, new

verted from his usual functions of educing the edition, fcap 8vo.

classical capabilities of the seventh and eighth 12210 (Proposed by the Rey. R. H. Wright. Hesiod, Epics, with English Comment, by F. A. Paley, 8vo. | forms; and, indeed, whenever he was called in as M.A., Trinity College, Cambridge, Head Master!"

| Lindley (John) Elements of Botany, Structural and Phyola deus ex machind, it was not for a pleasant purpose.

siological, new edition, Svo, of the Asbford Grammar School.) -Let ABC be - Glossary of Botanical Terms, new edit, 8vo.

Once a Week.

actu

e

COLLEGE 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.

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*** All communications must be addressed to the Secretary, 42, Queen Square, W.C.

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No. in
SITUATIONS VACANT.

Register.

Qualifications.

630. Drawing, French, Chemistry, Natural Philosophy, Writing, MatheNo. In

Qualifications Required. Begister

matics, and Gymnastics. Age 23. Salary 407, to 501. 455. French and Drawing. Age not less than 25. Salary 451. to 50l. In 636. General English Subjects: either resident or non-resident. Salary as Kent.

resident about 201. 457, Junior English. About 18 years of age. In Berks.

637. Classics, Elementary French, and general management, or as Private 461. Classics. Salary 801. Near Town.

Tutor. Age 32. 464. French and German. Salary 601. Required at Midsummer. In | 638. Middle Classics and Mathematics, French, Moral Philosophy, Logic, Somerset.

and English Subjects, Age 30. Graduate of Glasgow. Salary non468. Classics, with French or Chemistry. Salary 501. In Devonshire.

resident 1501 to 2001, 470. High Mathematics. Salary 1001. to 1201. non-resident. Required at 639. Classics and Mathematics, French and Italian. Age 52. As resident Midsummer. In Yorkshire.

or non-resident Master. 474. Junior English Assistant. Age from 18 to 21. Salary 201. In Hants.

640. English Subjects, French, Piano, Rudiments of German and Latin. 476. Junior Assistant to teach English Subjects, with Elementary Latin A Lady. Age 25. Salary 501., as daily Governess, 4 days per week. and French. For Midsummer. At Brighton.

641. Moderate Classics and Mathematics, with English subjects. Age 25. 483. Chemistry, Drawing, with Mathematics or Gymnastics. In War A Graduate of Cambridge. Salary 1001. to 1507., non-resident. wickshire.

647. German and French. As Visiting Master. 486. Junior Classics, with Model Drawing. In Kent.

649. Classics, Mathematics, and English subjects. Private pupils. 488. Writing Master. For Midsummer. Near Town.

650. French Language and Literature. As Visiting Master from 1 till 9. 490. Private Tutor to instruct in French, Mathematics, Latin, and English | 653. Classics, Junior Mathematics, French, and English. Age 23, Salary 501. Subjects. Salary 501. In Hampshire.

655. High Mathematics, Geometrical Drawing, and Perspective, Mechanics, 491. (i.) Middle Mathematics, with English Subjects. Salary 601. to 801. Classics, and History. Age 32. As Visiting Master. (ii.) French and Drawing. A Parisian. "Salary 401. to 501. For

| 656. Classics, German, French, and English, with Elementary Mathematics. Midsummer. Near Town.

Age 29. Salary 1001. 492. French and, if possible, Drawing. Salary 301. to 401. In Stafford. | 657. French and German. Age 38. Salary 501. 483. (1.) Land.Surveying and Civil Engineering. Salary 801. to 1001. 663. High Classics, Prose and Verse Composition, Mathematics, Elements of (i.) Writing and Junior Drawing Salary 501. to 601. With Board, Hydrostatics and Mechanics, &c. Five years' experience. Age 28. but not Lodging. In Lancashire.

Salary 1001, resident, 1301. to 1401. non-resident.

666. Classics, Mathematics, French, English, and Book-keeping. Age 26. ASSISTANT MASTERS REQUIRING

Salary 601. resident, 1001. nou-resident.
ENGAGEMENTS.

668. Classics and Mathematics. B.A. Camb. Age 25. Salary 1001. to

1501. non-resident. 97. Model Drawing, Figure, and Landscape, &c. (Student of the Royal | 672. Mathematics, Classics, French, and Geometrical Drawing. Graduate Academy.) Age 26. Non-resident.

in Mathematical Honours of T. C. D. Age 33. 110. Mathematics and Classics; English Grammar and Composition. As 622 Moder

As 673. Modern Languages, Classics, and Mathematics. Visiting or private non-resident Teacher, for two or three hours a day. Salary 701.

Tutor. 115. Visiting Teacher of the German Language, Literature, and History.. 674. Classics and Mathematics, Mechanics and Hydrostatics. B.A. Camb. W. Drawing and Ornamental Writing. Age 34. Private Lessons, 28. 6d.

Age 21. Salary 1001.

675. Classics, French, Italian, Writing, and English Subjects. Age 35. 136. Biblical, Classical, and Oriental Languages. M.A. of the University of

Salary from 301. to 401. subhargh; ten years Missionary in India. As Visiting and Private Tutor. |

679. Junior Classics, Mathematics, English Subjects, Land Surveying, sics and Mathematics, especially the latter. Accustomed to Teaching. B.A. Of London. Non-resident.

practical and theoretical. Age 29. Salary 1001. non-resident. 340. Paintindoned

680. Mathematics, Classics, Elementary French, and English Subjects. rainting and Drawing. A Member of the Institute of the Fine Arts. |

Age 19. M.A. of Aberdeen. Salary 401. guinea for each attendance within a reasonable distance of London. 681. French, German, Junior Classics and Mathematics, Gymnastics, and : Bligtish, French, Rudiments of German, and Music. Age 20. Salary Drilling. Age 33. Salary from 601.

683. Classics, Mathematics, French, and English. Age 22. Visiting or ontinent and the Rudiments

private Tutor. of Music. Age 21. Salary 201. A Lady.

684. High Mathematics, Pure and Mixed, French, German, Chemistry, and Gerinan, French and Piano Ace 33. Salary 507. Or as Visiting Master: Drilling. Age 28. Educated at St. Cyr. Visiting or non-resident Master. Jrawing and Painting. Age 22. A Certificated and Prize Medallist | 688. English, Junior Latin and Mathematics, with Elementary French, e Department of Science and Art. As Visiting Tutor.

Age 20. Salary 231. Mathematics, Junior Classics, French, Drawing, and Writing. Age 34. | 690. English, French, Classics, and Mathematics. Age 25. Salary from

751. to Sol, non-resident, isting Teacher of French, Mathematics, and Writing.

691. Highest Mathematics. A Wrangler, 1861. To teach twelve or wing, Painting, Perspective, and Fortification. Age 40. As eighteen hours per week.

692. Highest Mathematics, with Classics, &c. A Wrangler, 1861. Requires French, and English subjects. Age 40. Private Lessons.

an engagement at Midsummer for about three months. Classics. Age 30. "A graduate of Oxford in Holy Orders.

603. Classics, Prose and Verse Composition, Mathematics. B.A. Camb. in lassics, Mathematics to Trigonometry, French, and German. Classical Honours Age 23. Salary 1001. d. As Visiting Master, or to take Private Pupils.

694. French, German, and Italian. Age 33. Salary 601. From Midsummer. matics, with Junior Classics, and French. Visiting Tutor. Age 29. 695. English Subjects, with Junior Latin and French. Age 16. Salary ematics to Conic Sections. Elementary Mechanics, Geometrical from 101. to 201. ig, and Perspective. Age 30. Salary 701. to 801.

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Age 25. Salary 701. or Family. Age 21. Salary 401., non-resident.

697. English, Music, French, German, and Drawing. A Lady. Age 30. an, French acquired in Paris, Pianoforte and Drawing for Salary 601. s. Age 26. As non-resident or Visiting Master.

698. English Subjects, French, German, and Music. A Lady. Age 19. Visiting French Master.

Salary 151. to 201, 4. Music, Drawing, and English. A Lady. Age 19. Salary 251. 699. Elementary Mathematics, English, French, and Latin. Salary 2013 siting French Master. Afternoons and Evenings.

700. German and French thoroughly, with Classics and Mathematics. A wan, French, and Drawing. Age 24. Salary 301.

German. Age 32. Salary 501. erre and Prose Composition, Mathematics, and the Rudiments enach. M.A. Oxford. Age 29. Private Lessons

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18 guineas. A Lady 377. English, French, German, ac

As Morning Visiting Master.

186. Drawing, Paint

Visiting Master, at 58. per lesson.

492. Classics, French, and Eng 497 High Classics. Age: 500. High Classics, Mathematic

319. Mathematics, with Junio

Mathematics to co

53. English, Music, Drawing

32German, French

of French, Music, Draw

61. Visiting French $4, German, Frenc

825. Classics, Verse and

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