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THE EDUCATIONAL TIMES.

will be remembered that in the course of an The former date was supposed to be determinable calculations concerning Aerolites, or stones fall. extensive series of experiments on the diffusibility from two observations of the length of the shadowing from the cosmical regions of our globe. Ad[April, '62. of various substances in liquids, Professor Graham cast by a gnomon at the summer and winter sol-mitting that the weight of these bodies falling found that certain general laws could be traced.stices in the time of Tcheon Kong, at a place called annually upon the earth is 450,000 lbs., or A great distinction was found to exist between the Tchery-tcheon, the latitude of which place had 450,000,000 lbs. in 1000 years, Baron Reichenbach diffusive power of certain crystalline bodies, such been determined by the missionaries in 1712. has started the question whether, in the course of as salt, nitre, sugar, Epsom salts, &c., and that of Now, as the length of a shadow cast at noon during centuries, our globe might not undergo such modisuch uncrystallisable substances as gum, albumen, the solstices is a measure of the obliquity of the fication in weight as materially to affect its constarch, gelatine, and other similar bodies which ecliptic, and as this obliquity undergoes a change in nexion with the solar system. Now, as our earth unite readily with water but do not crystallise. a cycle of years, and, therefore, the length of a weighs about 13 quadrillions of pounds, the As soon as these facts had been ascertained and shadow, taken under such circumstances, changes formation of a meteoric agglomeration equal to announced, their practical application became by a corresponding calculable amount, it is evident our planet would require about 3000 trillions of speedily evident. Dialysers, having the appear- that a historical account of the length of a shadow years; hence any change like that contemplated ance of tambourines, formed of rings of gutta- in any known latitude, observed in any particular by Baron Reichenbach would occur within a space percha, over which is stretched "parchment-paper" year, may be tested by astronomical methods. of time far beyond our imagination to conceive. (formed by the action of strong sulphuric acid on This test Laplace applied in the present instance, But M. Haidinger turns his attention to another ordinary paper), have been constructed and applied and showed that the length of shadow said to have question, asking whether, if our globe, in the to various practical purposes. When required for been measured in 1100 B.C., accorded with the course of one solar revolution, receives an increase use, these dialysers are floated upon the surface of calculated length the shadow would have had in of matter equal to 450,000 lb., this increase might pure water, and the mixture to be dialysed poured 1358 B.C.,-an approximation so near that he conwithin these, when dialysis immediately com- sidered it as confirming the traditional date. Arch- orbit of equal length? Mr. Greg has proved that mences, the crystalloid substances passing through deacon Pratt, however, shows in the "Philosophical meteoric falls are less frequent at the time of perinot have been similar in weight, in describing any into the water, and the non-crystallised, or "colloid," Magazine" for January 1862, that between the helion than at the time of aphelion; but it must remaining in the dialyser. This singular action limits of error in the observations recorded, there also be recollected that the sun itself moves with may at once he rendered visible by pouring into is scope for an error of thirty-seven and a half considerable velocity through the stellar space. the dialyser a mixture of Magenta dye and burnt centuries in the calculation of the date! sugar, when the former being crystallised, passes astronomical observation, therefore," he observes, culates that the weight of meteoric matter exist. through, tinging the water of its own beautiful hue,"really gives no independent information whatever ing and moving about in every direction within "This Taking these data into account, M. Haidinger calwhilst the burnt sugar, having had its crystalloid regarding its date." As to the earlier date, that of the space limited by the earth's and sun's motions character destroyed by the heat, remains behind. 2357 B.C., which the astronomers attempted to during one year is equal to 450,000lb. multiplied The dialyser is now used to obtain solutions in confirm "by reconstructing the celestial sphere. by one billion 218,460 millions, or about half a pure water of many substances formerly thought to and reasoning from the change in the equinoxes,' have been insoluble, among which may be men- Archdeacon Pratt considers that one of the stars 450,000 lb. of meteorites as 24 millions are to tioned silica, Prussian blue, peroxide or rust of selected by M. Biot as a basis for his calculation unity; but a far greater proportion of solid matter trillion of pounds. The weight of the earth is to iron, alumina, or the basis of clay, and stannic acid, of the epoch, was wrongly chosen, and concludes distributed into small bodies would be obtained or peroxide of tin. In this way it has solved that that astronomy cannot in this instance, any more hitherto insoluble geological puzzle, the formation than in the former, fix the date assigned by tradi- balls taken into account, which appear in our atof flint, and it has aided the medical jurist in his tion, owing to the want of precision in the ancient mosphere, and many of which do not apparently were the great number of shooting-stars and fireendeavours to separate arsenic and other crystalloid observations. poisons from the heterogeneous contents of the human stomach. Much light has been thrown by ten millions of meteors of this description enter H. Newton, of Yale College, U.S., not less than deposit solid matter. it on many hitherto obscure points of physiology, According to Professor T. and in the arts of dyeing and those requiring the 3650 millions of shooting-stars and fire-balls per ready separation of different substances, it is not annum! our atmosphere every day. This would make easy to see the end of the advantages offered by the discovery.

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News," "has suggested a new method of detecting
Professor Schulze," we read in the "Chemical
small quantities of nitric acid. It is founded on
the fact that nitric acid, in a strongly alkaline
solution, is, by the action of finely-divided zinc, or
sodium, or aluminium amalgam, transformed into
nitrogen is evolved as ammonia, but with sodium
ammonia. When zinc is used, only about half the
amalgam the change is complete. When manures,
&c., are examined, the original ammonia, and that
formed by the action of the alkali, is first got rid
of by long boiling, and then the zinc, or amalgam,
is dropped into the residual liquid, and the mixture
again heated. This process will detect very minute
quantities of nitric acid."

The

tion in elementary drawing for the district schools
Kensington has opened the annual public examina-
The Department of Science and Art at South
of London, at the district school in Queen-square
("Female School of Art"). It is now decided to
purchase the house in Queen-square for 2000l., and
make it suitable by laying out 15007. more, which
is the sum still required to place the school on a
permanent footing.

FOREIGN AND COLONIAL NOTES.

RUSSIA.

Professor W. Thomson, in a remarkable paper read before the British Association in September last, and again in a recent number of "Macinillan's Magazine," endeavours to show, from purely physical data, that the sun cannot have illuminated the earth for a longer period than 500,000,000 years (probably for less than 100,000,000 years), and that it cannot continue to supply sufficient light and heat for the maintenance of life on the earth for many millions of years to come, "unless new made some progress in the publication of an acThe Swedish Government has commenced and sources, now unknown to us, are prepared in the count of the scientific exploring expedition sent great storehouse of creation." based upon a calculation of the rate of cooling work, entitled "Kongliga Svenska Fregatten be reopened. The Emperor has authorized the This estimate is out by it during the years 1851-1853. which the sun is supposed to undergo from the Eugenies, Resa omkring Jorden," that is, "Voyage continued radiation of its heat, which cooling is round the Globe of the Royal Swedish Frigate nine, to reinstate (replacer dans leurs anciennes THE University of St. Petersburgh is about to taken at 14 per cent. over a period of not less than Eugenie," under command of Capt. C. A. Virgin, functions) all the professors, masters, and officials 100 years, nor more than 100,000 years. The data appears in a royal quarto form, handsomely illus of the University, and to reopen the faculty of new Minister of Public Instruction, M. Goloofor the calculation of this progressive cooling are the trated. known temperature of the sun's surface, which is sections, of which the Zoologi is now in its fifth oriental languages, by admitting to the course all The scientific results are published in equal to that produceable by the combustion of a part, Botanik in its second, Fysik in its second; pound of coal in two seconds of time over a square and under these heads the naturalist or natural foot of surface, or about forty times as fast a rate philosopher will find all the information he may the former students of the University. — Le of burning as that of the coal burnt in the furnaces desire. The lithography of the botanical and zooTemps. of our locomotive engines; and the specific heat of logical plates is admirable, minute characteristics comprise the University, the Victor Emmanuel the sun's mass, calculated as being between the and details being brought out with all the clearness Lyceum, and the Municipality Schools, which are The educational establishments of Naples wide limits "of from ten times to ten thousand and delicacy of copper-plate. As Swedish is to rapidly increasing in number. times greater than that of water." There is too many persons an unknown tongue, physicists will Italian correspondence of a morning journal, large a proportion of the conjectural element in be glad to learn that the section Fysik is published that "a Commission of Public Instruction has these calculations to permit of very great confidence with a translation in French, so that those who proposed the establishment of 82 elementary We read in the being placed in the actual results arrived at, but are interested in the great questions of tempera- schools they are the "conjectures" of one of the pro- ture, currents, winds, and physical phenomena hamlets, 12 infant schools, and foundest of our living mathematicians, and as such generally, will find their researches facilitated by schools; but the project have excited much interest among scientific men. for Naples and the French Philosophers, at the commencement of unacquainted. The work is published at the rate however, are already in operation, and 47 eleneighbouring this publication in a language with which few are adopted. Four infant and two evening schools, 12 evening the present century, devoted much attention to of three or four parts in the year, under the super-mentary schools belonging has not Chinese chronology, and endeavoured to place the intendence of the Royal Academy of Sciences of dation. For the support of the infant schools antiquity of the Chinese Empire on a scientific Stockholm, by command of his Majesty the King about 29,000 ducats have been collected by private basis. The astronomers, including Laplace, sought of Sweden. to the old founespecially to confirm two eras-one that of the Emperor Tcheon-Kong, who, according to tradition, director-general of the Geological Survey of Aus- are conducted strictly on the Government plan, In a curious paper published by M. Haidinger, already expended. Besides these schools which lived 1100 B.C.; the other that of the Emperor tria, an analysis of which is given in a recent there are others maintained by private enterprise; subscription, of which 5000 ducats have been Yao, who is said to have flourished about 2357 B.c. number of the Critic, we find the following curious particularly one or two Evangelical schools, the

NAPLES.

yet been

57.

58.

59.

P. K. L. Beaver, Cheltenham College
A. A. Newman, Walsall: Vilvorde, Bel-
gium; and privately

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3398

3387

J. Campbell, Rev. W. Pritchett's, Old

Charlton

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3378

Mr. George Valentine

Yool, A.M., Cantab., was elected auditor. The
following are the Members of Council as now con-
Lord Brougham, President; Lord
stituted:

Arnold-On Translating Homer, Last Words. A Lecture
given at Oxford. By Matthew Arnold, M.A. Post
Svo, cl., 3s. 6d. Longman and Co.
Barrett-The Propositions in Mechanics and Hydrostatics
which are required of Questionists, &c. By A. C.
Barrett, M.A. 3rd edit., with additions, cr. Svo, cloth,
6s. Bell and Daldy.

Blake-The Historical, Biographical, and Poetical Reader;
or, Scholar's Companion. By the Rev. J. L. Blake,
D.D. Feap 8vo, cloth, 2s. T. J. Allman.

comprising a Summary of the Principal Events in
all Ages, from the earliest records to the present
time. Arranged Chronologically and Alphabetically.
New edit., cr. 8vo, cloth, 78. 6d. Griffin and Co.
Notes on the Greek and Latin
Text of the New Testament, extracted from the Bent-
ley MSS, in Trinity College Library. With the Abbé
Rulotta's Collation of the Vatican Codex B. A Spe-
cimen of Bentley's intended Edition, and an account
of his Collations. Edited, with the permission of the
Master and Seniors, by Arthur Ayres Ellis, M.A.
With an Appendix containing Six Letters of Bentley.
Svo, cloth. Bell and Daldy.

leading feature of which is that the Bible is introduced in the course of instruction, and is read and explained several times in the course of the week. It is needless to say that such schools owe their existence to the exertions of Protestants. Besides these efforts, which are strictly Neapolitan, the UNIVERSITY COLLEGE, LONDON.- The annual Philanthropic Association of Italian Ladies residing in Turin, is laudably attempting to elevate General Meeting of the Members of the College, the character of the Southern population, a great for the election of officers, and other business, was Book (The) of Dates; a Treasury of Universal Reference, proportion of its funds being derived from contri-held in the College on the 26th of February. Lord Belper was elected vice-president, in the place of butions made in England. Their first grant was made in order to meet the great necessity of the the late Earl Fortescue. The new Members of present day, that good teachers-with a missionary Council elected were:- Mr. Justice Crompton, Bentleii Critica Sacra. spirit-should be employed to visit and reside Mr. William Fowler, LL.B., Lond., Fellow of the in the small communes for longer or shorter College; and Mr. Alfred Wills, LL.B., Lond., intervals, to instruct the teachers and to organize Fellow of the College. the schools. It is supposed by many that the normal schools supply this want, and it is true that lists of certificated teachers are sent round to the communes for selection; but it is Belper, Vice-President; Mr. George Grote, D.C.L., Bullock-The Progressive English Reading Book, for Use like spreading out a feast for a man who is unable F.R.S., Treasurer; Mr. William Lloyd Birkbeck, Mr. James Booth, Mr. Francis Booth, M.D., to pay for it. Such teachers expect as a minimum the Hon. Mr. Justice Crompton, the Hon. Richard Bradley Elements of Geometrical Drawing; or, Practical salary 201. or 30l. a year, whilst there are many communes which do not offer more than from 51. Denman, Mr. Edward Enfield, Mr. Thomas Wilto 10. a year. For the present, therefore, and liam Evans, M.P., *Mr. Robert Nicholas Fowler, until the communes have become sufficiently aliver. William Fowler, *Mr. Thomas Field Gibson, to the value of education, so as to make a greater Sir Francis H. Goldsmid, M.P., Mr. Frederick D. effort, certificated masters from the normal schools Goldsmid, Mr. Arthur W. Jaffray, Mr. Frederick are out of the question, and the rising generation William Mackenzie, M.D., Mr. Richard Marmust depend on the wretched class of teachers tineau, Mr. Henry Crabb Robinson, the Right now actually in office, and many of them can scarcely Hon. Sir John Romilly, Mr. Edward Romilly. read; or teachers must be created on the spot by the Right Hon. Sir Edward Ryan, F.R.S., Mr. peripatetic or missionary instructors. The plan Alfred Wills, and Mr. Frederic John Wood. (The is now on trial, and so far has succeeded well. asterisks denote the members of the Committee of Management.) The four auditors are Mr. Henry Another object of the Ladies' Association is to form a school for 100 girls in Torre del Greco. William Busk, Mr. David Mocatta, Mr. Henry Browne, and Mr. George Valentine Yool. At a They are to be educated, fed, and to receive some articles of clothing, and the principle of the Asso- Meeting of the Council on the 1st ult., the Viceciation is to reject, no one on the ground of reli. President in the chair, the Committee of Manage- Hewitt-Elements of Geography. New edition, corrected

gious opinion."

UNITED STATES.

ment and other Committees were appointed. Dr.
Thomas Hillier was appointed Medical Officer to
the Hospital for the Department of Diseases of
the Skin.

THE annual report of the Board of Regents of the Smithsonian Institution at Washington CHARTERHOUSE SCHOOL.-Mr. Jebb, the Senior has been published, showing the operations, ex- Classic at Cambridge of the present year, was penditure, and condition of the institution for the educated first at St. Columbus College, Ireland, year 1860. The whole amount of Smithson's and then at Charterhouse School, where he obbequests deposited in the treasury of the United tained one of the open foundation scholarships. States is 515,169 dollars, from which an annual At the age of 17, when he went to Trinity Col. income, at six per cent., is derived of 30,910 14 lege, he gained the Porson University Scholardollars. The expenditure has been kept below ship and the Porson Prize. In the following the receipts, and a surplus fund of 141,100 dollars year he obtained the Craven University Scholarhas been accumulated. This is invested princi-ship, and a scholarship at Trinity College, and has pally in Indiana, Virginia and Tennesse Stocks, now carried off the highest classical honour of the and has yielded an annual income of 7716 dollars. University. The principal portion of this is expended for publications, researches, lectures, library, museum, and gallery of art.-Massachusetts Teacher.

WOOLWICH ACADEMY.

COLLEGE OF PRECEPTORS.

or

THE Midsummer Examination of the Pupils of Schools, in union with the College, will commence on Monday, May 19th. The names of all can diTHE following is a supplementary list of candidates must be forwarded to the Secretary on before the 21st instant. dates at the recent Competitive Examination for admission to the Royal Military Academy, Woolwich, who have been admitted in consequence of additional vacancies having occurred in the junior class at that Institution :

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BENEVOLENT FUND.

Rev. W. T. Jones, M.A.. has forwarded a donation of £16. 13s. 4d. to this fund, of which he is one of the Trustees. We believe that it is Mr. Jones's intention to give a similar donation every four months (making £50 a-year), for some time

to come.

Alphabetical List of the Principal College and
School Books, and New Editions, published
during the Month ending February 28.
Ahn-A Concise Grammar of the Dutch Language, with
Selections from the best Authors in Prose and Verse.
By Dr. Ahn. Translated from the 10th original Ger-
man edit. by Henri Van Laun. 12mo, cl., 3s. 6d. Trüb-
ner and Co.

Ahn's (Dr. F.) First Class Book; or, First French Course.
4th edit. improved, 12mo, cl., 1s. 6d. Thimm.
Albités-French Pronunciation, or Theory and Practice,
with Helps for Self-Tuition. By Achille Albités,
LL.B. 12mo, cl. limp, 1s. Longman and Co.
Ammianus Marcellinus. History of Rome during the
Reigns of Constantius, Julian, Jovianus, Valentinian,
and Valens. Translated from the Latin by C. D.
Yonge, B.A. With a General Index. Double volume
(650 pages.) Post 8vo, cl., 7s. 6d. (Bohn's Classical
Library.) Henry G. Bohn.

in Schools. By Thomas and Francis Bullock. Book I., 18mo, swd., id. Book II., 18mo, el., Ed. (John Heywood, Manchester.) Simpkin, Marshall, and Co.

Geometry, Plane and Solid, including both Orthographic and Perspective Projection. Illustrated by Engraved Plates. By Thos. Bradley. Part II. Oblong royal fol., hf.-bd., 16s. Chapman and Hall.

Cambridge (The) Year-Book and University Almanack

for 1862. Edited by William White.
cloth, limp, 2s. 6d. Macmillan and Co.

Crown Svo,

Child's (The)' Story Books. Nos. 1, 2, 3, and 4. Illust.

(Gordon's School and Home Series) 18mo, swd., 2d. each. (James Gordon, Edinburgh). Hamilton and Co.

Drew-A Geometrical Treatise on Conic Sections. With

a copious collection of Examples, &c. For the use of
Schools and Students in the Universities. By the
Rev. W. H. Drew, M.A. 2nd edit., cr. 8vo, cl, 4s. 6d.
Macmillan and Co.
Edwards-Mathematical Questions proposed to Candidates
at the half-yearly Examinations for admission to the
Royal Military Academy, Woolwich, from June '57 to
July '61 inclusive. Collected and arranged by the Rev.
L. C. Edwards, M.A. 8vo, swd., 3s. 6d. Harrison.

to 1862. By Jas. Hewitt. (Darton's School Library.)
18mo, cl., swd., 1s. Darton and Co.

Hunter-Examination Questions on Milton's Paradise Lost. Books I, and II., and on Shakespeare's Merchant of Venice with Introductory Remarks and selected Criticisms on Milton. Designed to facilitate generally the study of both these Poets, and especially to aid Candidates for the First B.A. Examination of the University of London in 1862. By the Rev. John Hunter, M.A., formerly Vice-Principal of the National Society's Training College, Battersea. 12mo, swd., 18. Longman and Co.

Kalisch-A Hebrew Grammar, with Exercises. By M. M.

Kalisch, Ph. D., M.A. In two Parts. Part I. The Outlines of the Language, with Exercises; being a Practical Introduction to the Study of Hebrew. Post 8vo, cl., 12s. 6d. Longman and Co.

Lessons in Spanish, containing a complete view of the Idioms of the Language, &c. Revised by the Editor of the "Popular Educator." 12mo, cl., 3s. 6d. Cassel and Co.

Ludlow

A Sketch of the History of the United States
from Independence to Secession. By J. M. Ludlow.
To which is added the Struggle for Kansas, by Thomas
Hughes. Crown Svo, cl., 8s. 6d. Macmillan and Co.
Marsh-The Student's Manual of the English Language;
Lectures on the English Language. By George P.
Marsh. Edited, with Additions and Notes, by Wil-
liam Smith, D.D. Post 8vo, cl., 7s. 6d. J. Murray.
Maurice-Modern Philosophy; or, a Treatise on Moral and
Metaphysical Philosophy, from the Fourteenth Cen-
tury to the French Revolution, with a Glimpse into
the Nineteenth Century. By the Rev. Fred. Denison
Maurice, M.A. Cr. 8vo, cl., 10s. 6d. Griffin and Co.
Nepos-Lives of Eminent Men. By Cornelius Nepos.
Construed literally and word for word, by the Rev. Dr.
Giles (Keys to the Classics). 18mo, cl., swd., 3s. Jas
Cornish.
Newman-History Epitomised and Contemporised; or,
Historia Sententiæ. By E. M. Newman. 3rd edit.,
er. 8vo, cl., 3s. Gd. Simpkin, Marshall, and Co.
Papers for the Schoolmaster. Vol. II. 1861. 12mo, cl., 3s.
Simpkin, Marshall, and Co.
Pryde-Biographical Outlines of English Literature. By

David Pryde, M.A. For the use of Schools. Post 8vo,
cl., 2s. (Bell and Bradfute, Edinburgh). Simpkin,
Marshall, and Co.
Spruner-Pütz-School Atlas of History and Geography.
By Dr. Karl Von Spruner, L.L.D., and Professor W.
Pütz. Imp. Svo, half-bound, 12s. 6d. Relfe Brothers.
Stewart-Elements of the Philosophy of the Human Mind,
in Two Parts. By Dugald Stewart, New edit., with
References, &c. By the Rev. G. N. Wright, M.A. 8vo,
cl., 7s. W. Tegg.

Tales Illustrating Church History: England. Vol. I.
Early Period. Fcp. 8vo, cl., 5s. J. H. and J. Parker.
Thomson-School Chemistry; or, Practical Rudiments of
the Science. By Robt. D. Thomson, M.D. 2nd edit.,
fep. 8vo, cl., 6s. 6d. Longman and Co.
Twells-Poetry for Repetition. Edited by the Rev. H.
Twells, M.A. 4th edit., royal 18mo, cl., 2s. 6d. Long-
man and Co.

Unwin-Training School Reader. By W. J. Unwin

First Book. First Division. Fep. 8vo, cl., 9d. Second
Division, post 8vo, cl., 1s. Longman and Co.

Unwin-Training School Reader. Edited by W. J. Unwin.
Second book. Divisions one and two. Post 8vo, cl.,

1s. each. Longman and Co. Willie's Home Exercises. Part I. Teacher's copy. Fep.

Svo, cl., swd., 4d. (Jno. Heywood, Manchester.) Simp

kin, Marshall, and Co. Woodford-Elements of the Latin Language. In two parts. Part I. Rudiments and Exercises. By Edward Woodford, L.L.D. 3rd edit., 12mo, bds., 1s. 8d. (Maclachlan and Stewart, Edinburgh.) Simpkin, Marshall,

and Co. Woodward-First Lessons in Evidences of Christianity. By B. B. Woodward, B.A. 18mo, cl., lp, 1s. Ward and Co.

Young-On the History of Greek Literature in England from the earliest times to the end of the Reign of James I. By Sir George Young, B.A. Cr. Svo, bds., 2s. Macmillan and Co.

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1261 (Proposed by J. M'Dowell, Esq.. B.A., Draw any Pembroke College, Cambridge.) straight line BC cutting the less of a given angle BAC in B and C, and divide BC in L, so that BL: LC:: m. AB: n. AC; show, by the fundamental property of the Anharmonic pencil, that the locus of L is a straight line.

·(1)

(2)

BL

...

..(3).

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1268 (Proposed by Mr. S. Watson, Haydon bridge.)-Two points A, B are taken at random Assume (ny +7) for the formula in equation (7) upon the surface of a given circle, centre O.

and we get

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(9)

What is the chance that the circle through O, A, B shall be less than of the given circle? 1269 (Proposed by Mathematicus.)-ABC is a right angled triangle, right angled at C; from AB draw AE, BF, perpendicular to AC, BC respectively, and join AF, BE; also draw CD perpendicular to AB; then if AE, BF, be made equal to AC, BC, the three lines AF, BE, CD will meet in one point.

1270 (Proposed by J. M'Dowell, B.A., F.R.A.S., Fembroke College, Cambridge.) (10). Prove, by harmonic pencils, that the centres of similitude of three small circles on the surface of a sphere lie three by three on four great circle-arcs (11). (the axes of similitude).

=64n-294n+336;

(1073-8n)2 =

from this is had n =

1073

-8n;

112

0

612691 353024

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Our Correspondent" Cantab." draws attention to Mr. W. Hopps's solution of part of Question 1246, marked 1st, in which it ought to have been shown between which pair of parallel bases the required locus will lie. Besides, the given sum of areas might be so large that the locus would consist of two parallel straight lines each outside the given parallel bases." The same remarks, of course, apply to his solution of Question 1253.

To the Editor of the Educational Times. SIR,-In reply to Mr. Miller's remarks on my solution of Question 1165, I purpose, in this communication,

I. To point out the defect in Mr. Miller's "normal" method.

II. To show his erroneous reasoning on the "pin-and-table" method; and

III. To give a satisfactory solution of the question in dispute.

I. Let Q be the point where the normal cuts the sphere. Then Mr. Miller's "several ways" of attempting to prove that the number of positions of the coin is proportional to sin, are all one in principle, being all based upon his normal method, and the defect in this method lies in passing from the number of positions of Q (which I grant him is equal to those of the coin) to the area passed over by Q. For, in order to prove that this area is proportional to the number of positions of the coin, it must be shown that, while the coin changes from any one position to its consecutive one, in any direction, the points Q are equally close to each other, for all such changes which the coin can take. Mr. Miller has not done this, and thus his "normal" method is defective.

II. In both Mr. Miller's attempts to prove that in the "pin-and-table" method, the number of positions is proportional to sin 20, he has adopted the very erroneous supposition that the points of contact "are proportional to the area over which they extend." For, suppose the pin to increase in length point by point, then the points of contact for those several lengths of the pin will be a series of circles, each contiguous pair of which will be less and less close to each other, the nearer the length of the pin approaches to the radius of the coin; hence the points of contact are not equally distributed over the table, and are therefore not proportional to the area over which they extend.

From the preceding it clearly appears that Mr. Miller has completely failed to establish anything against either my solution or "pin-and-table" method, (which are the same in principle,) and the reason of this is simply that neither method is wrong in the way he has asserted. Nevertheless those methods are incorrect. How they are so will be seen from the following solution, which I now give instead of my former one, and which I believe will bear the strictest scrutiny.

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III. Let P be the highest c point, and OE a horizontal radius, of the coin, when its centre O arrives at the plane AOBC of the grating; BC one of the A wires, and OA parallel to BC; PD a perpendicular to the plane AOBC; and produce OD to G, making OG = OP. Put OP=1, OB=z, 4GOA=0, / POG= 4. Then GOE=90°, and therefore the changes in the positions of E and G are always uniform. Also the condition that the projection of the coin on the plane AOBC shall not cut BC, is z > (1—sin2 + sin20) and taking the case when the distance between the wires is equal to the diameter of the coin, must lie between 1 and 0, and therefore the limits of 0 are 0 and sin = cosec, or e

the smallest value of coseco is 1.

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where A, B, &c. stand for the preceding terms respectively, the law of the series being obvious; hence we find

P1576 nearly. Should any objection be taken to this solution, it is obvious that, in order to prove it incorrect, it must be shown that the coin does not take a

can take, and not merely of the area passed over
by a normal intersecting a "sphere" or the
"heavens," which method I have before shown
to be defective.-I remain, &c.,
STEPHEN WATSON.

serjeant nor an old soldier is to be met with, let
the schoolmasters themselves become drill-serjeants.
Nothing could be better either for them or their
scholars than to spend a few hours a week together
on a meadow or hill-side in drilling, marching, and

[Having now given Mr. Watson's reply, we counter-marching.-Museum.
shall be under the necessity of closing the length-
ened correspondence on this subject.-ED.]

ANSWERS TO CORRESPONDENTS.

H. B.—We should advise you to put the matter
into the hands of a respectable Solicitor.
MR. HALCOMBE.-The most complete and ac-
cessible library of school books in this country
is probably that in the Educational Department
of the South Kensington Museum.
F.S.--No.

AN ASSISTANT. The Agency of the College of
Preceptors is open to all respectable Teachers.
The Secretary will insert a description of your
qualifications in the list in the usual way, but
we cannot insert it directly from yourself,
except as an advertisement.

MILITARY DRILL IN PUBLIC SCHOOLS. A

meeting was lately held in Edinburgh, under the
auspices of Lord Elcho, with a view to the esta-
blishment of a system of military drill in all the
schools throughout Scotland. The main object of
the proposal is to render more systematic the phy-
sical training of the young, by introducing drill
into every school in the kingdom, making it, as
Lord Elcho expressed it, "a necessary part of the
civil life of the country." The system is already
land, as Eton, Rugby, Harrow, &c., as well as in
many private schools; and from the warm interest
taken in the movement, at the meeting in question,

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SIXTH EDITION, 12mo, price 1s..

different position for each position of its radius in operation in most of the public schools in Eng- EXAMPLES IN ALGEBRA FOR

OE, since when is constant, the number of positions of OE is undoubtedly 2π.

I consider it of little importance what Mr.

Miller may say about my change of solution, since to arrive at mathematical accuracy out weighs, with me, all other considerations; and I can assure him that if he can prove clearly that the number of positions of the coin is proportional to sin o, I will at once acknowledge his solution to be the correct one; but this must be proved of the ACTUAL POSITIONS which the coin

by Lord Elcho, the Lord Advocate, and others,
there is every likelihood of a somewhat similar
scheme being ere long established in Scotland. In
Edinburgh little remains to be done, as military
drill has, for some time past, been taught in all the
leading schools there in connexion with the classes
for fencing and gymnastics. As for country schools,
or schools in places where neither a regular drill-

JUNIOR CLASSES.

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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. 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 for 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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SITUATIONS VACANT.
Qualifications Required.

706. Junior Classics and Mathematics. Salary 507. In Worcestershire. 783. Junior English Master. Salary 201. Near Town.

751. French, German, Drawing, and Mathematics. Salary 501. Near Manchester.

16. Junior Mathematics and French. In the N. district.

738. To superintend pupils, and to teach Drill and Gymnastics, with good Drawing. In Warwickshire.

* Assistant Music Master, good Organist, with a knowledge of Church Music. Salary from 80l. to 1007., with board. In Lancashire.

32. Moderate Mathematics, English, and clementary Classics. Salary 201 In Gloucestershire.

$3. German, Singing, Music, Drilling, and elementary Latin. In Notts. $25. French, German, Drawing, and Fencing, if possible. Salary from 407. to 507.

86. Mathematics. Salary 1507. non-resident. A Graduate preferred. In Lancashire.

907. Second Master in a Grammar School, to teach Arithmetic, Mensuration, Land-surveying, and Writing, with Junior Classics. Salary, non-resident, 81, with a good house. In Lincolnshire.

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811. Junior Assistant: a knowledge of Latin and French desirable. Salary from 207. to 301. In Berkshire.

812. Junior Classics and Mathematics, with English and Junior French. Salary 407. In Northamptonshire.

813. A Frenchman to teach French, the elements of Music (Piano) and of Natural Sciences. Salary from 40l. to 507. In Kent.

816. Junior Latin, English, and thorough Arithmetic. Age about 23. Salary 401. to 50%. In the S.W. District.

817. Junior English, Latin, and Music Master. Salary from 201. to 407. In the S.W. District.

818. Latin, French, and thorough English. Salary 601. Age about 25. In Norfolk.

819. Classics, Mathematics, and English Subjects. Salary about 607. In the N.E. District.

820. Junior Latin and French, with English subjects, and Writing. Salary about 307. In the S. District.

821. Latin and English Subjects. Salary 601. In the S. District. 823. English Master. Salary about 301. In Kent.

824. Latin (good), with either English, Chemistry, or Mathematics. In Kent. 825. Latin, with Elementary Greek, and English subjects. Salary from 201. In Devonshire.

No. in Register.

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826. Classical Master, in a Grammar School, for 8 weeks from the 1st of
May. Salary at the rate of 150l. per annum.
827. Visiting Master, for Natural Philosophy, Statics and Dynamics, and the
In Kent.
higher parts of Algebra.

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769. German, French, Spanish, Latin, and Drawing. As Visiting Master. 785. Classics, Prose and Verse Composition, Mathematics, Mechanics, Hydrostatics, English, French, and Italian. As Visiting Master.

812. French and German. A Lady. As Visiting Governess.

942. French, German, and Elements of Italian and Latin. As Visiting Master. 944. Natural and Experimental Sciences, Mathematics, German, and Drawing. A German Graduate. Age 33. As Visiting Master.

M.A. of St.

1000. Classics, Mathematics, French, and English Subjects. Andrews, and LL.B. of London. As Visiting Master. 1003. English Subjects, Junior Mathematics, Classics, and French. Age 41. Salary 401. to 457. resident, 657. to 70l. non-resident.

1004. English, with Junior Music and Drawing. A Lady. Age 17. No Salary required, but residence, and instruction in Music, French, and Drawing. 1007. German, Drawing, and Music, in all their branches. Age 33. Salary 1007. resident, from 1507. to 2007. non-resident.

1018. Drawing, Fortification, and Painting. Visiting Master.

1042. French, German, English Subjects, Elements of Italian and Latin, with Drawing. A Lady. Age 40. As non-resident governess, or for private pupils.

1058. Music, Drawing, and English subjects. A Lady. Age 18. Salary 201. 1060. Classics, English Literature, Rhetoric, Logic and Mental Philosophy. M.A. of Aberdeen. Visiting Master.

1061. Drill Master. Age 25.

1067. English, French, Italian, German, Music, and Drawing. A Lady. Age 24. Salary from 401.

1071. Classics, Mathematics, and general English. Pupils.

Visiting, or Private

1074. Latin, French, Drawing, English, and Algebra. Age 31. Salary 427. 1096. French. Visiting Master, or private pupils.

1104. Classics, Mathematics, and English thoroughly. M.A. Aberdeen. Age 23. Salary 501.

1111. The highest Mathematics, with Classics and English subjects. Age 38. Salary 1007.

1118. German, French, Dutch, English, Drawing in all styles, and Fortifi cation. Age 40. As Visiting Master.

1130. German. A Lady. As Visiting Teacher.

1133. Classics, French, Mathematics, and English. As non-resident or Visiting Master.

1143. Mathematics.

1007. resident.

B.A. Camb. Age 32. Salary 1507. non-resident,

1153. Junior Classics and Mathematics, Mensuration, and English subjects. Age 24. Salary 351. to 401.

1173. French and German, Classics and Mathematics. LL.D. of the Univ. of Paris. Age 37. Visiting, or private pupils.

1187. Mathematics, Latin, French, English, and Practical Science. Age 28. Non-resident Mastership. London preferred.

1190. English subjects, French, and German. Age 40. Salary 301. to 401. 1194. French, Spanish, Drawing, and Writing. Age 19. Salary not an object.

1196. English subjects, and Junior Mathematics.

non-resident.

No. in Register.

Qualifications.

[April, '62.

1217. German, French, and Drawing. Age 30. Salary 30l. to 407.
1218. French, German, and Drawing in all styles. Age 30. Salary from
50l. to 807.

1219. English, Mathematics, Mensuration, Music, and elementary Drilling.
Age 24. Salary 507.

1220. English, French, German, Junior Classics, and Mathematics, Vocal
Music, and Violin. Age 29. Salary 607. to 65l.

1221. Classics, Mathematics, Surveying, Fortification, and French. As
Visiting Master.

1222. Classics, Mathematics, and English. Age 23. Salary 501.

1223. Junior Latin, French, English subjects, with Plain and Ornamental Writing. Age 32. Salary 407.

1224. English, Drawing, Junior Mathematics, Vocal Music, and Elementary Chemistry. Age 22. Salary 501.

1226. Mathematics, Junior Classics, and English subjects. Age 24. Salary 707. resident, 907. non-resident.

1227. French. A Lady. Salary from 301. to 401.

1229. Mathematics, Statics and Dynamics, Mechanical Drawing, German, and French. A Swiss. Age 24. Salary 607.

1230. French, Latin, Mathematics, and Natural Sciences. B.A. Univ. of
France. Age 35. Salary 501.

1231. German, French, and Geometry. A German. Age 25.
1233. Junior Classics and Mathematics, with English. Age 37. Salary
70l. to 1007. non-resident

1234. English thoroughly, Mathematics, Mechanics, Music, and Drawing.
Age 25. Salary 801. resident; 1007. non-resident.

1235. Junior Classics, Mathematics, English, Land-surveying. Salary 1007. non-resident.

1236. Latin, French, Arithmetic, English, and Junior Greek. Age 27. Salary 357.

1237. Classics, Mathematics, including Conic Sections and elementary Calculus, Statics, Dynamics, Hydrostatics. B.A. Lond. Age 31. Salary about 1007.; or 1507. non-resident.

1238. Classics, and elementary Mathematics. Undergrad. Ch. Ch. Oxford. Age 24. Salary 801.

1239. Piano and Singing. A Lady, formerly a student of R.A.M. Non

resident.

1241. French, German, and Italian. Age 32. Salary 407.; or non-resi dent, 707.

1242. Mathematics and Junior Classics. M.A. Camb. Salary 607.

1243. Mathematics, Classics, French, with Junior German.
Salary from 60l. to 80l.

1244. English subjects, with Junior Latin and French. Age 33. Salary 351.
Age 28.
1245. English, French, Music, and the rudiments of Latin.
22. Salary 301. As Morning Governess.

A Lady. Age

Salary

1246. Piano, Singing, Violin, Harmonium, and Organ. Age 26.
about 80%.

1247. Drawing Master. Age 34. Salary 807., non-resident.

1248. English, French, Music, Singing, and the rudiments of German. A
Lady. Age 18. Salary not an object.

1249. Mathematics. Age 23. Salary 807. For Midsummer.
1250. German, French, and Pianoforte. Age 30. Salary 50l. to 80l.
1250 a. German, French, Hebrew, Drawing (elementary), English subjects,
Book-keeping, and Junior Latin. Age 25. Salary not an object.
1251. Classics, Mathematics, Writing, and French.
an object.

Age 49.

Salary not

1252. Classics, Junior Mathematics, and English subjects. Age 20. Salary 601.
1253. Mathematics, Classics, and English.
Pupils.
B.A. Cambridge.

Private

1254. Junior Classics and Mathematics, with French, and English. Age34 Salary from 30l. to 50l.

Age 24. Salary 801.

1202. French, German, Music, Drawing, and Mathematics. Salary 401.

Age 27.

1203. Classics, French, Music, Junior Italian, Drawing, and Drilling. Age 23.

1256. English, with Junior Classics, Mathematics, and French.
Salary 357. to 40?.

1255. French Language and Literature, with Elementary German. Age 34. Salary 607.

Age 21.

1210. Drill Master.

1205. Mathematics, French, and German. Age 23. Salary 50%. 1206. German and French, with Classics and Mathematics. Age 26. 1207. English, French, Elementary Latin, and Mathematics. Salary 401. to 50%.

Age 21.

1211. French, German, Painting, Drawing, and Elementary Music. Lady. Salary not an object.

A

1212. French, German, Classics, and Moral Philosophy. Visiting Master. 1213. Mathematics, Classics, French, Natural Science, and elementary German. B.A. Lond. Salary 1007.

1214. French, Fortification, Drawing, and Military Preparation. As Visiting Master.

1216. Classics, Mathematics, Drawing, and Junior French. Age 26. Salary 60l. to 80l., in a family.

2258. French, German, Italian, Classics, Mathematics, Natural Sciences,
Music, Drawing, Drilling, and Gymnastics. Age 32.
as Visiting Master.

1260. Classics, Mathematics, English, Hebrew, and Junior French. Age 32.
Non-resident, or Private Pupils.

1261. Classics, Junior Mathematics, English, Book-keeping, with Elements
of French, German, and Spanish. Age 29. Salary 801. to 1007.
1262. Mathematics. A Wrangler. Scholar of Christ's College, Cambridge.
Age 24. Non-resident.

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Salary 601.

1257. Classics, and Junior Mathematics, with English subjects.

Age 21,

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