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1201 (Proposed by Mr. Matthew Collins.)- | .. 322MATHEMATICAL QUESTIONS AND

= + (2x + ?),
Without the belp of Fluxions, or the differential from which quadratic in x, we obtain
SOLUTIONS.
Calculus, or any reference wbatever to or reason.

_1+ 1O .
ing about infinitely small quantities; show how to
15 (Proposed by Mathematicus.) -10 is find, by plain common Algebra alone, the value of
required to find the point at which a right angled | x, that will render x-72 or -3, or 23-25, or
triangle must be fixed; so that when its right sin x cos”x, a maximum.
angle is struck by a blow perpendicular to its

1206 (Proposed by Nemo.)— There are two plane, it may begin to revolve about an axis SOLUTION BY Miss STEPHENS, OF CAMELFORD vessels A and B, each containing a mixture of water parallel to its hypothenuse.

PROPRIETARY SCHOOL.

and wine, A in the ratio of 2 : 3, B in the ratio of

3:7; what quantity must be taken from each to SOLUTION BY MR. STEPHEN Watson.

Let x-xo=max.

form a third mixture, which shall contain 5

or x– x=-M suppose In any triangle the line from one of the angles

gallons of water and 11 gallons of wine ? 10 the middle of the opposite side passes through

x~8+=--M

SOLUTION BY J. W. R. its centre of gravity ; hence if the triangle be

x-=-M fixed at any point in this line, and then struck at

Let x = number of gallons to be taken from A the angle by a blow perpendicular to its plane, it x=} + V:-M

from B will begin to revolve about a line parallel to the and in order that x may be real, M cannot be

Now if x be divided in the ratio of 2: 3, the quan. side bisected by the line. greater but may be equal to · which is therefore

tities of water and wine to be taken from A will its greatest value, in which case x=}.

be respectively

and it, and the quantities of

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1159 (Proposed by Mr. Stephen Watson.)

| 1203 (Proposed by Penumbra.)-Given an A semi-ellipse is placed in a vertical position, and

water and wine to be taken from B will be respec. out at the base, the sum of the two sides, and the dis. a heavy particle is just set in motion at the highest at the

tance between the angular point and the point of tiv point of the curve, and descends down it by its ta

il contact of tbe escribed circle touching the base; own weight; required the point at which it will con

to construct the A. leave the curve, and its velocity at that point.

Thus, to determine x and y, we have
SOLUTION BY THE PROPOSER.
SOLUTION BY W. 0. PHILLIPS, M.A. 2x 3y. 3x7y 5.1

5to: *+ iš= 5:11) .......... (1) Let xy be the coordinates of the point where

Con.-Let L and I re. the particle leaves the curve; a, b the semi-axes

present the two given

*+ y =16 S .......... (2) of the ellipse, b being vertical ; v the velocity, and

lines, and form the From (1) 4x + 3y : 6x + 7y=5; 11, r the radius of curvature, at the point (ty); and o

EBD = given 1, making the angle which the normal at (xy) makes with the

EB = L and BD = i.

whence 7x=y; axis of x. Then v2 = 29 (6-y), and the centri.

Produce BD to F, so that

from (2) x+7x=16, fugal force at (ry) is

DF=L+l; then BD +

or 8x=16, .. x=2, 0229 (6-y) a*b*: but this force is also =g sin e DF (= BĚ)=L+21......................(1)

and y=7x=14. Also produce BE to H, so that BH=BF. Bisect

Hence 2 gallons must be taken from A and 14 BH in I, and draw IF, and from I apply IM=

from B. IH to meet FE produced ; also draw EN IMI,

and through N draw KC i BH, and CA || EN. Tobax. 69c2 " patys + b*q=' The A required is ABC.

NEW QUESTIONS. , 2 (1-4) a + ..

Dem.- ABC = given Z(con.), and BD = 1 (con.) Moreover, (sim. As) NK :IH=FN: FI

1216 (Proposed by W. J. Miller, B.A., =NE: IM=(con.) IH,

| Eltham.)- In the figure to the solution of Queswhere c is the focal distance ;

. .. NK=NE.

tion 1175, (“ Educational Times” for May) if w But CN = NK, :: BI = IH (con.) and CK is ||

be the l between the conjugate semi-diameters BH (con.) :. CN=NE.

P p, and co. cos x=s: cos ¢, prove that ca, sin 20
Consequently, as ACNE is a , we have
AC=AE:

= -2ab. cotw, and that
which determines the point (ry), and the required :. AB+ AC=AB+AE=EB=(con.)L.. .... (2).
velocity is

It now only remains to show that D is the point SA= f[26°94 —c* (362– a^) cos] dy.

of contact of the escribed circle with the base r=✓ 29[6-*(7c+a+Vc-a)].

BC.
Since FCK is an isos. A ( 11 s), we have

1217 (Proposed by W. J. Miller, B.A., CF=CK (=2CN=2AC).......... (3). Eltham.)- Find the average area of all the recto

But (1), BF=L+21; 1183 (From Todhunter's Calculus.)- A cer.

angles that can be inscribed in a given triangle, or

.: BC + CF=L+21; tain territory is bounded by two meridian circles,

in a given circle, and also of all the squares that also (3), BC + 2AC=L+21.

can be inscribed in a given square. and by two parallels of latitude, which differ in

But (2), AB+ AC=L; longitude and latitude respectively by one degree,

.. adding, AB+3AC+ BC=2 (L+1), 1218 Proposed by Matthew Collins, A.B., and is known to lie within certain limits of lati.

j.e., AB+3 AC +(BD+DC)=2 (L+1). Dublin.) - Prove that a prime number p = 2n + 1 tude ; find the probable superficial area,

But (2 and con.), (AB + AC) + BD=L+l; will divide 13" – 1 whenever p is of the form 13m SOLUTION BY MR. STEPAEN WATSON.

.. subtracting, 2AC + DC=L+l.

+ 1, 13m + 3, or 13m + 4; and when p is not of Hence, AB + AC + BD=2AC+DC.

any of these forms, prove that it will divide Let o be the latitude of a place equally distant And taking AC from each, we get from the two parallels of latitude ; then the two

AB + BD=AC+DC.

13" + 1. latitudes are 0-,0 + }, and the surface lying be- Now, it is well known that the angular point (N.B. - The author of the first correct demontween these parallels is,

opposite the base of a A, and the point of constration of this new theorem, published in the 2017[sin (0+1) - sin (0-1)=4wr2 sin 4 cos e, tact of the escribed circle with the base, bisect its “ Educational Times" before the 1st of next Sep: r being the radius of the earth, also the portion of P

cl perimeter. Therefore D is the point of contact tember, shall receive the “Educational Times"

Tof the escribed circle with tbe base BC. this surface lying between the meridian circles is,

gratis for one year from the proposer.) Note. The proposer of this Question is proo'arsin cos 9. bably not aware that it is similar to Question 1, Divide a right angle geometrically into two parts,

1219 (Proposed by Mr. W. Hopps, Hull.) — Hence if a, B be the two latitudes between in the Ladies and Gentlemen's Diary for this

such that the tangent of one part shall be equal to which the territory is known to lie, the required year.

the side of the otber.
area is
B-5
1205 (Proposed by Mr. B. Marks.)- Given

SOLUTIONS RECEIVED:-
(B--1)
9.3) - 13x-6=0, to find x by a quadratic.

Mr. S. Bills.-1191.
SOLUTION BY J. R. W.

Mr. Stephen Watson.-1165, 1169, 1177.
App? sind in

Notices TO CORRESPONDENTS :-.
90 (B-a-1)
i [sin (B-$-sin (a + *)] Multiply by x, then:

We shall give the earliest possible attention to 9.24 – 13.ro - 6x=0.

the Problems sent by Mr. Matthew Collins, B.A. apa sin cos } (a+B) sin } (B-a-1) Transposing, Ix4 – 9.ro =4x2 +6x,

We trust shortly to have less pressure on our 45 (B-a-1)

columns, and we shall then endeavour to carry out o. 934–9x: +3=429 + 6x + 2,

the suggestions of S. W.

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ON ABRIDGED NOTATION. substituting these values of (-1) and (-1') in (17) aminations. In 1860 the students contributed By the Rev. R. H. WRIGIT, M. A., Trin. Coll., Cam- and (18) they become identical, that is;

£544 odd to the funds of the institution. Its bridge: Head Master of the Grammar School, ! a cos A + B cos B+g cos Č=0.... (19) income, however, being almost entirely confined Ashford.

hence P, Q, R range in the same straight line. to the payments of the pupils, and to occa. Ma. EDITOR,--Having on several occasions con:! But (19) is identical with (9), hence,

sional donations, is so inadequate to the necessary tributed my mite towards the Mathematical part Those six enunciated points lie in the same expenditure, that the institution must either be of your valuable Journal, I have ventured once straight line

closed or re-constituted in a solvent and self-support. more to offer you a slrort paper on the applica. The above particular properties appear to being state. The first alternative is greatly depre. tion of abridged notation to certain geometrical both interesting and remarkable, for which reason cated by the noblemen and gentlemen named above, problems. It is well known to most of your readers I selected them as an introduction to the discus- and also by Mr. Gladstone, the Chancellor of the who may take an interest in this interesting sysa sion of a more general property proposed, in the Exchequer, inasmuch as the classes are acknow. tem, " That if any point be taken within a triangle, “ Mathematician,” by my late talented friend Mr. ledged on all hands to have supplied an urgent and lines be drawn through it, from the angular Weddle, page 209, Vol. II., and solved by another public want and produced excellent educational points to the opposite sides, a new triangle will be departed friend and eminent mathematician, Pro. and moral results. The object now sought to be formed by the intersection of those lines and the fessor Hearn, of Sandhurst; and similarly by my- | attained is to make them self-supporting for the sides of the triangle; and if the three sides of the self, in that same volume. The Proposition runs future, and with that view it is proposed to re-connew triangle and the sides of the primary triangle thus, « Let lines be drawn from the angles of a stitute them on a more permanent basis and in a be produced, the three corresponding pairs will meet triangle through two points and terminating in the collegiate form, the government to be vested in a respectively in three points, which three points will opposite sides, then

will opposite sides, then if the extremities of each set council, composed partly of a limited number of

the extremities of each ser conneil. composed Bart be in a straight line.” This property has been dis- of lines be joined, two inscribed co-polar triangles friends of education, with power to confer associate. cussed by myself in the “Educational Times” years will be formed. Also from the angular points of ships and small scholarships on students. The adback, and occurs in some of the elementary books

the primitive triangle let lines bc drawn parallel vantages of such an arrangement, it is suggested, on the subject.

to the corresponding sides of these triangles, and would be manifold and various; the tastes, and intersecting those of the other: it is required to minds, and feelings of the members would be edu. prove that the three points of intersection range in cated to a higher standard ; their opportunities of the same straight line."

contact with the best of their fellows for purposes Should an interested reader wish to apply the either of friendship, of study, or of business, would beautiful system of abridged notation to this pro- be much enlarged; and as they profited by their blem, he must bear in mind that if a=0, B=0, studies they would acquire titles of distinction and g=0, represent the sides of a triangle, then the prizes of honour. On the production of a list of sides of any inscribed triangle may be represented young men intending to pay for instruction in the

classes, or otherwise to contribute to the funds of by a + nB+=0, " + 3+ ly=0 , mat + the college, to an extent which may afford a reasonFor reasons hereafter obvious, I purpose to

able assurance that an annual income of not less investigate a particular case of this. For instance, ly=0 where l, m, n are constants, and lastly in than 7001. may be derived from these sources, it let the new triangle be formed by the feet of the order that the lines joining corresponding angles of is proposed to raise by donations a fund of 2,0001. perpendienlars from the angular points on the the two triangles may meet in a point we must have to give practical effect to the project. The scheme opposite sides. Let ABC be the primary triangle the condition l m n = -l. These useful proper- was earnestly recommended to the meeting last and D E F the new one. Now, in my former ties, of which I have made extensive use in a work evening by the chairman and by the Rev. Charles papers I bave shown that we have for

shortly intended for publication, have been fully Mackenzie, Mr. E. G. Clarke, the Rev. Richard ÉP-a cos A + B cos B + g cos C=0.... (1) discussed by myself in former Numbers of the Whittington, Mr. Marshall Carpenter, and other DP acos A - B cos B + cos C=0....(2 “ Educational Times."

gentlemen. Resolutions were passed to the effect DE acos A + ß cos B-ycos C=0.... (3)

that it was highly desirable that the basis of the BC «=0..........................(4)

present institution be enlarged, its constitution AC B=0..........................15)

COLLEGE OF PRECEPTORS.

remodelled in the form of a college, with the pri.

vileges of associateship, and pledging the meeting Now, if D F and AC be produced to meet, they! At the Meeting of the Council on the 15th of

to obtain members to the number of 1000 before will intersect in some line whose eonation vill be Junc; present A. Hill, Esq., Y.P., in the chair' ; the 1st of July. Four of the students at the even. represented by Mr. Andrews, Mr. Bidlake, Mr. Clennell, Mr.

1r. ing classes took part in the discussion, namely, a cos A - B cos B+ g cos C + AB=.. (7) Isbister, Dr. Jacob, Rev. Mr. Jones, Mr. Long, Mr. E, G. Clarke, Mr. Marshall Carpenter, Mr. The same may be said of D E and A B Dr. Pinches, Dr. Schaible, Dr. White, and Dr.

; Bolton, and Mr. Day. Mr. Carpenter is one of a cos A + B cos Bancos C+ =0....(8) Wilson; the following gentleinen were elected

two who have recently obtained public appoint. And if we eliminate a from (1) and (4) and sub. Members of the College:

ments, and Mr. Clarke has gained the Tancred stitute in (7) and (8) we get the values of

Mr. S. H. L. A. Bechaux, B.A., Cambridge.

Exhibition at the University of Cambridge for Mr. E. S. Clack, Hackney.

the Study of Law.-The Times. 1=2 cos B , X'=2 cos C

Mr. J. H. Clifft, Bath. : (9) and (8) are identical, and the three inter.

Mr. S. Crew, Great Berkhampstead. sections are on the same straight line whose equa.

Mr. D. Cruickshank, Southampton).

Alphabetical List of the Principal College and on is Mr. J. J. H. Harris, Evesham.

School Books and New Editions published during
a cos A + B cos B + y cos C=0
Mr.J. H. Hay, Kennington Oval.

the Month ending June 30th.
......(9)
Again, let there be a second inscribed triangle
Mr. C. Whitaker, Spalding.

Bentley (Robert) Manual of Botany, illust., fcap. 350.

Binns (Willian Elementary Treatise on Orthographie formed by joining the middle points of the sides of

Projection, 2nd edit., 8vo. the primary triangle, which we will call D'E'F'

Bourne John, Treatise on the Steam Engine, 5th edit., 4to. PROPOSED COLLEGE FOR THE CITY OF LON- Bullock (Thos. and Fred.) Illustrated History of England EF-a sin A + B sin B+ sin C=0....(11)

DON.-On the 17th of June, a public meeting, at ). with Questions, fep. 8vo.
DF a sin A - B sin B + y sin C=O.... (12)
which Mr. R. N. Fowler, the banker, acted as Caldwell (Rev. R.) Comparative Grammar of the Dravidian,

Sro.
D'E a sin A + B sin Ba sin C=O....(13)

chairman, was held in Sussex Hall, Leadenhall Campin (Francis) Practice of Hand-Turning in Wood,

Street, with the view to promote a scheme recently Ivory, Shell, &c., sm. post Svo.
AP parallel to EF B sin C+y sin B=() (14)

Carter (F. H.) Bookkeeping adapted to Commercial and propounded at a meeting convened at the residence

Judical Accounting, roy. Svo.
BQ parallel DF y sin A +ä sin C=O (15)
of the Bishop of London, by Earl Granville, Lord

Cheere (Rev. Edward) Church Catechism Esplain d. new
CR parallel DE å sin B + 8 sin A=0 (16)

Lyttelion, Mr. Henry Hoare, Mr. Harry Chester, edit., fcap. 8vo. e Mr. H. Sykes Thornton, and others, for re

For the line passing through the intersection of

Graduation under the Medical and

Scottish Universities Acts.
(19) and (15) we may write
establishing the metropolitan evening classes, held

Circle of the Sciences (The) Vol. 5, new edit., cr. 8vo.
a sin A-8 sin B + y sin C +( sin A
for many years at Crosby Hall, upon a new and Clarke (Hyde) New and Comprehensive English Diction-

I • ta sin C)=0

broader basis. The classes in question, of which ary, 2nd edit., corrected, i2mo. .............. (17)

the Prince Consort is the patron, were established. | Cumin (Patrick) Popular Education of the Bristol and the line passing through the intersection with the approval of the late Bishop of London, Curtis J.C.) Elements of the History of England, 18mo.

Plymouth Districts, 8vo.
esin A + B sin Basin C+' (a sin B
by the Rev. Charles Mackenzie and others in 1848, Dower's Popular Atlas for Schools, Families, &c., 12 Maps,

roy. 8vo.
+8 sin A)=1).............. (18)
and have since been the means of conferring in- I.

Dunce's Dessert (The); or Horatian Trifles and Homeric for eliminating wand B respectively from (11)

calculable benefits in the way of education upon

in the way u Pulication upou Cream, Part 4, to. and (14) and substituting respectively in (17) and ey wom ? | young men engaged in business in the city. From Famous Boys, and How they became Great Men, sth

enlarged edit, fcap. 8vo. 1848 to the present time the number of pupils who have received instruction is about 6000, and since Forbes (Duncan) Bmaller Hindustani and English Dic.

tionary, imp. 16mo. dz_2 sin A. sinc

11856. when the Society of Arts' examinations Jeans (H. W.) Navigation and Nautical Astronomy, Pt. sin A - Sin 213 mar and -X

began, the pupils of these classes have carried offi, nes

138 certificates, many of them of the first class, and Johnson (Thos.) Græcorum Epigrammatum et Poematum 2 sin A. sin B

Delectus, editio nova, 12mo. 18 prizes; and 10 of them have obtained clerk ,

| Lamborn (Dr. R. H.) Rudimentary Treatise on the Metal. su *A + sin B-siu C

ships in the public service after competitive ex. lurgy of Silver and Lead, 12mo.

AB

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GUY'S STANDARD SCHOOL-BOOKS. Scotch. It has much the same meaning as truis; I

London University, and Oxford and Cambridge Middle uyig' SCHOOL

CUY'S SCHOOL QUESTION-BOOK Class Examinations. By J. WIARTON, M.A. for “to kill” is to tuck up. In Gaelic, the kilt is 1G feile-beag; and the time of its separation from the Astronomy, and all Miscellaneous Subjects: to which is U

II. on Ancient and Modern History, Geography,

Just published, Parts 1.-VI., 1s. each, ancient feile-beag into a waistcoat and kilt is given a Chart of History, coloured. "A New Edition, T HE KEY: containing Complete Soluuncertain, as is also the adoption of the sporan, or thoroughly revised and much enlarged. 12mo, price

1 49. 61. roan lettered. pouch, so remarkable a feature in the Highland

tions to the Questions in the Examples in Algebra

... for Senior Classes. By J. WHARTON, J.A., M.C.P. costume.-The Ladies' Treasury.

GUY'S PARENT'S FIRST QUESTION-BOOK. With
Engravings. New Edition, price 1s. cloth.

III.
Mr. J. N. Smith, S.C.L., Oxon, Principal of GUY'S ELEMENTS of ANCIENT MODERN, and

SIXTH EDITION, 12mo, price ls., Marlborough House School, Brompton, was pre- BRITISH HISTORYwith Examining Ouestions at AXAMPLES IN ALGEBRA ron sented, at a meeting of the former pupils of that the End of each Section, New Editions, 12mo, price U JUNIOR CLASSES; adapted to all Text Books school, on the 20th April, with a handsome silver | 39. 64. each, roan.

and arranged to assist both the Tutor and the Pupil. By ten service as an expression of their esteem and London: CRADOCK & CO.; and SIMPKIN, MARSILALL. I J. WHARTOX, M ., 21.C.P. and Co., the only Publishers of Joseph Guy's School

IV. gratitude

Books; complete Lists of which may be had on application. SEVENTH EDITION, ENLARGED, 12mo, 2s., Mr. W. T. Miller, B.A., formerly of Eltham,

LT OGICAL ARITHMETIC; being a Kent, has been appointed Mathematical Master in THE REV. H. M. WILKINS'S NEW GREEK U Text-book for Class Teaching, and comprising Huddersfield College.

READING BOOK.

Elementary Arithmetic, with Rules for Mental and PracNow ready, in 12mo, price 5s, cloth,

tical Calculations; and a Course of Fractional and Propor.

tional Aritmetic, an Introduction to Logarithms, and In Crown Octavo, price 6s.,

Selections from the Civil Service, Collere of Preceptors, I LOGY, for the use of Schools. By the Rev. HI.

and Oxford Examination Papers. By J. W ARTOS, MUSGRAVE WILKINS, M.A., Fellow of Verton College.

M.A., M.C.P.
Oxford ; Author of "Notes for Latin Lyrics,” in usu in
AND GEOLOGY.
Harrow, Westininster, and Rugby Schools.

Also, Fourth Edition, Corrected,
By DAVID PAGE, F.G.S.,

WILKINS'S PROGRESSIVE GREEK DELECTUS. ANSWERS TO QUESTIONS IN THE LOGICA
Author of " Text-Books of Geology."
New Edition, price is.

ARITHMETIC. Price 6d.
WILLIAM BLACKWOOD and Sons, Edinburgh & London. London: , LONGMAN, GREEN, LONGMAN & ROBERTS. C.F. HODGSON, 1, Gough Square, Fleet Street.

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COLLEGE OF PRECEPTORS.-AGENCY DEPARTMENT.

ADDRESS, 42, QUEEN SQUARE, BLOOMSBURY, W.C.

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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 balf-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 balf-a-crom. 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.
Qualifications Required.

538. Junior Classics and English Subjects. Salary 301. to 351. In Wors

cestershire.
476. Junior Assistant to teach English Subjects, with Elementary Latin 539. French, German, and Drawing. Salary 201. In Wilts.
and French. For Midsummer. At Brighton.

540. Mathematics. Salary 801. Near Town. 488. Wʻriting Master. For Midsummer. Near Town.

541. Writing, English, French and Junior Classics. Salary 301. to 351. 491. French and Drawing. A Parisian. Salary 401. to 501. For Mid In Kent. summer. Near Town.

542. Classics and English Subjects. Salary 701. to 801., non-resident. At 492. French and, if possible, Drawing. Salary 301. to 401. In Stafford. Brighton. 493. Writing and Junior Drawing. Salary 501. to 601. With Board, but

not Lodging. In Lancashire. 495. Classical and First English Master. Salary 601. In Town.

ASSISTANT MASTERS REQUIRING 496. French, Latin, and English Subjects. Salary 401. In Yorkshire. 497. French, German, and Mathematics to Conic Sections. Salary 601. to

ENGAGEMENTS. 701. In Gloucestershire.

hegister.

Qualifications. 498. Junior Assistart; Elementary Latin, &c. Salary 301. In Suffolk. 499. English, Algebra, Book-keeping, Land-Surveying, and Penmanship; 97. Model Drawing, Figure, and Landscape, &c. (Student of the Royal some knowledge of Latin desirable. Salary 401. In Kent.

Academy.) Age 26. Non-resident. 500. Mathematics to Trigonometry, Elementary Classics, and English Sub 224. Classics and Mathematics, especially the latter. Accustomed to Teaching. jects. Salary 407. to 501. In Lincolnshire.

B.A. of London. Non-resident. 503. French thoroughly, good Penmanship and Drawing, with English 340. Painting and Drawing. A Member of the Institute of the Fine Arts. Subjects. Salary 401. Near Town.

One guinea for each attendance within a reasonable distance of London. 504. Writing and English Subjects. Salary 201. In Town.

430. Drawing and Painting. Age 22. A Certificated and Prize Medallist 505. Articled Pupil, for not less than two years, to be taught Latin, French, of the Department of Science and Art. As Visiting Tutor. Drawing, Arithmetic, &c., in return for services.

443. Mathematics, Junior Classics, French, Drawing, and Writing. Age 34. 506. English Master, age about 22. Salary 301. In Worcestershire.

As Morning Visiting Master. 508. Junior Mathematics, with English Subjects and Drawing. Salary, 201., 451. Visiting Teacher of French, Mathematics, and Writing. to 301. In Herts.

497 High Classics. Age 30. A graduate of Oxford in Holy Orders. 509. Junior Assistant. In Town.

559. English, Music, Drawing, and Painting. As Morning Governess in a 511. Janior Assistant. In Yorkshire.

School or Family. Age 21. Salary 401., non-resident. 512. Third Master in a Grammar School; to teach English Subjects, Writing, 562. German, French acquired in Paris, Pianoforte and Drawing for Book-keeping, and Arithmetic. Salary 701. In Shropshire.

Juniors. Age 26. As non-resident or Visiting Master. 513. Mathematical and Classical Master. Salary 1201., resident. Near Town. | 639. Classics and Mathematics, French and Italian. Age 52. As resident 514. Classics and the Elements of Mathematics. Salary 601. In Dorsetshire. or non-resident Master. 516. English, Writing, Arithmetic, and Junior Latin. Salary 251. Near 647. German and French. As Visiting Master. Birmingham.

649. Classics, Mathematics, and English subjects. Private pupils. 516. Mathematics, Latin, and general Subjects. Salary 601, to 701. Near 650. French Language and Literature. As Visiting Master from 1 till 9.

672. Mathematics, Classics, French, and Geometrical Drawing. Graduate 517. French, and general Subjects. Salary 601. In Kent.

in Mathematical Honours of T. C. D. Age 33. 518. French and Drawing thoroughly, with English Subjects. Salary 802., 683. Classics, Mathematics, French, and English. Age 22. Salary 701. to 801. non-resident 901. if with Singing. In Herts.

681. High Mathematics, pure and mixed, French, German, Chemistry, and 520. French, Latin, Junior Mathematics, and English Subjects. Salary 351. Drilling. Age 28. Educated at St. Cyr. Visiting or non-resident Master.

688. English, Junior Latin and Mathematics, with Elementary French. 321, (i.) Classics and Mathematics, Mechanics, Mensuration and Land. Age 20. Salary 251. Surveying. Salary 501.

690. English, French, Classics, and Mathematics. Age 25. Salary from (1.) Junior Assistant; good Penman. Salary 251. to 301. Near Bristol. 751. to 80l. non-resident. * English Master. Salary from 351. to 401. In Guernsey.

691. Highest Mathematics. A Wrangler, 1861. To teach twelve or 045, General English Master. Salary about 401. Near Town.

eighteen hours per week. JZk, Physical Science. especially Chemistry, and the usual branches of | 692. Highest Mathematics, with Classics, &c. A Wrangler, 1861. Requires Iglish, with Book-keeping. Salary 601. to 1001. Near Town.

an engagement at Midsummer for about three months. 525. English Master. Non-resident. Salary 707. to 901. In Liverpool.

696. Classics and Mathematics. Graduate in Classical Honours of Aberdeen. 521. Junior Assistant. Salary 401. In Brighton.

Age 25. Salary 701. 527. (i.) French, German, and Music. Salary: 551.

697. English, Music, French, German, and Drawing. A Lady. Age 30. (11.) English, Writing and Arithinetic. Salary 502. In Yorkshire. Salary 601. 06. Gul general English Master. Salary 351. to 401. In Hants.

698. English Subjects, French, German, and Music. A Lady. Age 19. 930. English faster. Salary from 351. to 451. In Town.

Salary 15l. to 201. 6, (L) linglish, Mapping, Land-Surveying, Writing, and Book-keeping. 699. Elementary Mathematics, English, French, and Latin. Salary 201. Salary 357.

700. German and French thoroughly, with Classics and Mathematics. A . (ii) French and Drawing. Salary 351. In Kent.

German. Age 32. Salary 501. 952. English Master. Salary 501. In Belfast.

701. French and Classics. B.A, of Univ. of Paris. Age 33. Salary 501. 53. (1.) Enzlish Master. Salary 251.

708. Highest Classics, Junior Mathematics, French and German, Age 22. (11.) Latin and Frenchi. Salary 501. In Hants.

Salary from 1507. to 2001. Non-resident. ...) English, Junior Latin, and Drawing. Salary 201.

709. Junior Latin and Mathematics. Age 22. Salary 301. ".) Article Papil, who would be prepared for the Matriculation exami 710. German, French, and Piano. Age 30. Salary 60%. to 701. won of the l'niversity of London or for the Cambridge or Oxford Middle 712. Classics, French grammatically, Pencil and Water-colour Drawing aan ination. Premiun for 3 years. 507. In Worcestershire.

and moderate Mathematics. Age 25. Salary 80%. waton and English Subjects. Salary 301, to 351. In Kent.

| 713. English Suljects, Music, and the Rudiments of Drawing. A Lady: 1:54 Vaster for the Commercial department in a Grammar School. ago 23. Salary according to duties required. Salary 301. In Lancashire.

| 711. Classics and Mathematics. Age 37. Salary 607.

Manchester.

Near Town.

Class

College of Preceptors.-Agency Department continued.

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Register.
Qualifications.

Register.

Qualifications. 715. English Subjects, Mathematics, Navigation, Land Surveying, Latin, 762. English Subjects, and the elements of Latin. Age 17. Salary 101. Elementary French, Violin, and Piano. Āge 23. Salary 601.

with time for self-improvement. 716. Classics and Mathematics, Junior French. Age 23. Salary 701. to 801. 763. English Subjects, Junior French, and Latin. Age 201. Salary 301. to 401. 717. English, Arithmetic, Writing, and Junior Latin. Age 21. Salary 251. 765. English Subjects, with Junior Latin. Salary 601. 718. German, French, and Italian. Age 50. Salary 601.

766. Junior English Master. Age 26. Salary 2012 to 25l. 719. Latin, History, English, Junior Mathematics. Age 21. Salary 401. 767. Mensuration, Land Surveying, Junior Mathematics, Writing Plain 720. English, History, Junior Mathematics. Age 21. Salary 401.

and Ornamental, Drawing, Mapping, and Junior Latin. Age 21. Salary 35l. 722. German thoroughly. Age 30. Salary 1001.

768. Classics, Mathematics, French, Italian, and English Subjects. As 724. French. B.A. of the University of Paris. Age 31. As Visiting Master. Visiting Master. 725. Mathematics, pure and mixed, French, German, Practical Chemistry, 769. German, French, Spanish, Latin, and Drawing. As Visiting Master.

Fortifications, and the Subjects of Military and Civil-Service Exami. 770. Mathematics, Mensuration, and Junior Classics. M.A. Cambridge. nations. Salary 1001, resident, 1501. non-resident.

Salary 501. 726. Drill Serjeant. Age 30. 4s. per lesson.

771. French, Latin and English. A Frenchman. Age 38. Salary 701. to 80l. 727. French, English, and Junior Mathematics. A native of Paris. Age 25. 772. Mathematics, French, Music, Junior Latin, and English. Age 26. Salary 701.

Salary 601. 728. French and Italian. A Doctor of Laws of the Univ. of Paris. As 773. Classics and Middle Mathematics, English Literature, French gramVisiting Master, or Private Tutor.

matically, Chemistry theoretically. Salary 1201. 729. Junior Assistant, English Subjects, with Junior French. Age 26. 774. Music, French and English Subjects. A Lady. Age 18. Salary 252. Salary 251.

775. Latin, German, French, English, Mathematics, and Drawing. Age 28. 730. French, Mathematics, and Natural Philosophy. A Pole. Age 32. Salary 601. Salary 501.

776. English, and Junior Mathematics. Age 21. Salary 301. to 401. 731. French. A Bachelier-es-Lettres. Age 30. Salary 401.

777. Latin, French, English, and Mathematics. Age 20. Salary 451. to 502 732, Classics and Junior Mathematics, Modern History, and Geography. 778. Classics, French, Mathematics, Mensuration, and English. Age 42. B.A. of Oxford, Age 25, Salary 1001.

Salary 601. to 701. 733. Highest Mathematics with Classics. B.A. of Lond. Age 28. Salary 779. Junior Classics, and Mathematics. Age 16. No salary required, but · 1501. to 2001. non-resident.

time for self-improvement. 734. Classics, Mathematics, and French. Age 45. Salary 601. to 701. 780. French, Elementary German, and Landscape Drawing. B.A. of the 735. Classics and Mathematics, especially the latter. B.A. and Mathematical University of Paris. Age 37. Salary 501. to 60l. resident; 801. to 1001.,

Scholar of Univ. of London. Requires an engagement during the long non-resident. vacation.

781. French, Elementary Music, Latin, and Greek. B.A. of Paris. Age 22. 737. Classics, Greek and Latin Versification, Mathematics, Elementary Salary 301.

Statics and Dynamics, French. B.A. London; first in Classical Honours. 782. Classics, English, and Junior Mathematics. M.A. of Aberdeen. Age Age 34. Salary from 1201.

22. Salary 801. 748. Music (thoroughly), Singing, English generally, in a School. A Lady. 783. Classics. M.A. of Aberdeen. Age 28. Salary 701. Age 22. Salary 301.

784. English, Junior Latin, French, and Mathematics. Age 30. Salary 101. 739. English, French, and German. Age 39. Salary 301. to 401.

785. Classics, Prose and Verse Compositions, Mathematics, Mechanics, 740. French, Drawing, Fortification, Mathematics, Surveying, Painting in

Hydrostatics, English, French, and Italian. As Visiting Master. Water Colours. Salary 1001. resident, non-resident preterred.

786. Junior Classics and Mathematics, with the Natural Sciences. 741. Mathematics, Elementary Classics, and Drawing, Vocal Music, Age 787. French, and Middle Classics. B.A. of Paris. Age 21. Salary 507. 35. As Visiting or Non-resident Master.

788. Elementary Mathematics, and Classics. Requires an engagement for 742. French, Rudiments of German, and English thoroughly. Age 31. the Long Vacation. Salary 501.

789. Middle Classics, and Mathematics, French and Drawing. B.A. of 742 A. English, Middle Classics, Junior Mathematics, Rudiments of French

Glasgow. Age 23. Salary 701. Music. Age 20. Salary 501. to 601.

790. Latin, Middle Mathematics, Mensuration, Land-Surveying, and English 743. French, German, Mathematics, Drawing, and Music. Salary 1201. Subjects. Age 22. Salary 401. 744. Writing Plain and Ornamental, Drawing, Water and Oil Colour 791. French, German, Music, and Drawing. Age 27. Salary 601. Painting. Age 26. Salary 551. to 601., non-resident.

792. Classics, Mathematics, and English Subjects. Sen. Op. 1851. Age 26. 745, Classics, French, German, and Italian, and Junior Mathematics. Age Salary 1501., non-resident. 33. B.A. Oxford. Salary, resident, 1001. ; non-resident, 1801.

795. French, English, Latin, Junior Mathematics, Elementary Drawing, 746. Latin, Elementary Greek, Algebra, French, and English. Age 21. Mapping, Writing. A Frenchman. Age 26. Salary from 601. to 701. Salary from 251. to 301.

796. English and German thoroughly; the rudiments of French and Music. 747. Classics and Mathematics. B.A. Cambridge. Age 24. Salary from A Lady. Age 21. Salary 251. to 301. 902. to 1001.

797. Classics, Mathematics, Book-keeping, French and English Subjects. 748. French. Age 30. Salary 501.

Age 40. Salary from 801. to 1001. 749. Latin, Greck, English, Euclid, Algebra, Elementary French. Age 19. 798. German, French, Drawing, and Music. Age 28. Salary from 406. Salary 35l.

to 501. 750. French, Gymnastics and Drilling. Age 36. Salary 401.

800. Classics, Alathematics, and English Subjects. Non-resident preferred. 751. French, German, Mathematics, Fortification, History, Geography. Salary 1001. Age 37. As Visiting Master.

801. High Classics, Moderate Mathematics, and English. Age 24. Salary 752. Engish, Junior Latin, and Junior Mathematics. Age 19. Salary 301. from 701, to 801.

802. French, Spanish, Drawing, and the elements of German. Age 30. 753. Middle Classics and Mathematics, Book-keeping, Mensuration, English Salary 401. In Town. and French grammatically. B.A. Queen's University, Ireland. Age 25. 803. English, Junior French and Latin, with Drawing. Age 22. Salary 30%. Salary 501.

Seidentresi.

804. High Classics and Mathematics. Salary 1201., non-resident ; resia 754. Junior Assistant. Age 20. Salary from 251.

dent, 901. 756. French, German, and Italian, Classics and Mathematics, Natural 805. General English Subjects. Salary 201. Sciences, Music, Drawing, Drilling and Gymnastics. Age 32. Salary

806. Lecturer on Physics, Chemistry, Botany, Geology, with Moderate from 801, resident; non-resident preferred.

Mathematics. 757. Landscape and Figure Drawing, Painting in Oil and Water Colours, 807. English and Music. A Lady. Age 18. Salary nominal. Fortification and descriptive Geometry. As Visiting Master.

808. Middle Classics, Mathematics as far as Conic Sections, French and 758. Lectures on Natural Philosophy and Cheinistry. Age 28. As Visiting English. Age 24. Salary 501. to 60%. Master.

811. Junior Classics, English, French, Drawing, Book-keeping, and Land759. French and Drawing, English and Arithinetic. Age 23. Salary 401. Surveying. Age 27. Salary 701. 760. Englishı, Latin, French, and Junior Mathematics. Age 22, Salary 812. French and German, A Lady, as Visiting Governess. 401. to 501.

813. French, Drawing, Junior Latin, and English Subjects. Age 35. 761. Mathematics, Mechanics, Mensuration, Book-keeping, English Subjects, Salary 501.

Elementary Drawing, and Water Colours. Age 22. Salary from 351. to 401. I

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Printed and Published, monthly, by CHARLES FRANCIS HODGSON, Gough Square, in the Parish of St. Bride, in the City of London; and sold by W. Aylott and Son,

.8 Paternoster Row; and W. Wesley, 2 Queen's Head Passage, Paternoster Row. JULY 1, 1861.

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