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SECTION V.-1. Describe some of the most prevalent currents of the air and the ocean.

2. Account for the formation of dew and for its deposition in different qnantities on different substances. Why does ice form itself on the surface and not at the bottom of the sea ?

3. The Ferroe islands, St. Petersburgh, and Takoutsk in Siberia, have nearly equal latitudes; the mean winter temperature of the first is 38°, that of the second 16°, and that of the third 38°; account for this difference.

Section VI.-1. Show that the earth cannot be an infinitely extended surface. Give one reason only.

2. Why do the northern stars appear to descend as we travel southward ? Why do they appear to descend exactly as many degrees as we change our latitude ?

3. Why are some eclipses of the sun partial and some annular? Why are not the same eclipses visible in all parts of the world? Why do they not return every month? How often do similar eclipses return, and why?

ANSWERS TO THE MATHEMATICAL QUESTIONS.

Ques. 96.—Proposed by J. H. Find the weight of a circular silver shield 1 foot 10 inches in diameter and .075 of an inch thick, the specific gravity of silver being 10474 Find also its value at 6s. 9d. per ounce Troy.

Answered by Mr. Sothern, Mr. Davison, Mr. Reed, and A. M.

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Ques. 97.-Proposed by Mr. Whitham, Battersea. Given the two adjacent sides of a parallelogram and the included angle, to find an expression for the tangent of the angle of intersection of diagonals.

Answered by Mr. Righton, Mr. Morris, and Mr. Rutter. Let the diagonals of the parallelogram A B C D, intersect in the point 0. From D let fall D E perpendicular to the diagonal A C. Put a = A D, b = DC, B = LA D C, and o LAOD; then we have

az - 12 = 2 AC ~ E O,

a2 72 .. EOS

2 AC

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now from the two independent expressions for the area of the parallelogram, we have

A CX DE = a b sin B,

a b sin B .:. DE

AC hence we have by division

DE 2 a b sin B tan 0 =

EO aa which is the expression required.

Ques. 98.–Proposed by Tom Tomkins. A body of w lb. acquired a velocity of v feet per second in descending an inclined plane, whose coefficient of friction is f, and perpendicular height h feet; required the inclination of the plane.

Answered by the Proposer. = the inclination of the plane to the horizon. Perpendicular pressure on the plane

= w cos B,

... Friction on the plane = f w cos B,
... Work due to friction f w cos B x length plane,

h
= f w cos B x

Let B

sin B ,

= f wh cot B. Work due to gravity

= w h. Work accumulated in the body wh f wh cot B; but the accumulated work is also expressed by

и 2

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... cot B

2 9 h It will be observed, that the angle of inclination, in this problem, is not supposed to be very small.

LIST OF MATHEMATICAL ANSWERS. W. Davison, Sunderland, ans. 96, 97; A. M. Gillingham, ans. 96, 97; T. Sothern, Burtonwood, ans. 96, 97 ; E. Rutter, Sunderland, ans. 96, 97; G. Morris, Gosport, ans. 96, 97; W. Righton, ans. 96, 97,98; J. Bolton, o. Malton, ans. 96, 97; Sam. Dyer, Wanstead, ans. 97 ; G. Barnacle, Empingham, ans. 96, 97; J. Royds, Hollingworth Free School, 97 ; W. H. Yoel, ans. 96, 97 ; W. Righton, jun. ans. 96; J. Herbert, Woolton, ans. 96, 97, 98; J. Salter, Durham, ans. 96, 97,98; F. R. Crampton, ans. 96, 97, 98; Sam. Dyer, ans. 98,

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NEW QUESTIONS,
To be answered IN OUR NUMBER FOR JULY, 1851.

Ques. 99.- Proposed by J. H.
A spherical balloon, 30 feet in diameter, constructed of silk weighing

2 ounces 9 drams per square yard, is filled with liydrogen gas, the specific gravity of which is to that of atmospheric air as :069 to 1, a cubic foot of atmospheric air weighing 14 ounce : what weight will just balance the balloon to prevent it from rising in the atmosphere !

Ques. 100.- Proposed by Mr. E. Whittle. The expense of paving a court-yard with Dutch clinkers, at 5s. per hundred, was 401. ; required the dimensions of the court-yard, allowing 144 clinkers to a square yard, and that length of the court-yard exceeds its breadth by 15 feet.

Ques. 10).- Proposed by Nemo. Given the base (6) of an isosceles triangle, to find its perpendicular height, when the area of the inscribed circle has a given ratio (p) to the area of the whole triangle.

STATE OF PRIMARY INSTRUCTION IN THE DEPARTMENT OF TARN DURING THE SCHOOL YEAR 1849-50.

(Continued from p. 147.) Children attending the Schools.-Out of 1000 inhabitants, 68 children, on an average, attend the primary schools. In 1839, there were only 55 out of 1000 : the progress, then, is real. We are, however, below the average which, for the whole of France, is about 92 in 1000: while some of the departments, such as that of Doubs, count 176 pupils out of every 1000 inhabitants. The number of children between 6 and 14 years of age, who do not actually attend the primary schools, may be reckoned at 20,000. Many of these have already left school, carrying with them

notions the most imperfect, which they will very soon completely forget. The great majority are condemned to absolute ignorance.

School Houses.— The law of 28th June, 1833, compels communes to provide suitable buildings which shall serve both as school-rooms for the children, and dwelling-houses for the masters. The law of 15th March, 1850, has preserved this obligation. Communes are also advised to become the owners of school-houses; and in 1848 they possessed 86 school-houses, while at the present day they have, 99. About 15 new school-houses may be reckoned which shall be completed during the next year. Everywhere, in the course of my inspection, I have ascertained that the places rented by the communes to serve as schools and teachers' residences are unhealthy, badly ventilated, insufficiently lighted, inconvenient, and inadequate ; whilst some are in a completely dilapidated condition.

Purchase of Books for the Poor.--Rural schools are entirely without good books. Poverty prevents many parents from purchasing such books as are necessary for their children, or it makes them select, not those which the teacher indicates to them, but those which itinerant booksellers sell them at a very small cost. Serious inconveniences result from this state of things. I believe that it is necessary to provide in the budget a grant of 500 francs for the purchase of books for poor scholars.

Assistance to Old and Infirm Teachers. The aged instructors have spent their strength in the career of primary instruction-an office, up to the present time, so badly remunerated. They are now worn out, and will suffer all the horrors of poverty, unless the department render them assistance. I solicit for them an allowance of 500 francs. This sum will annually diminish, and, finally, will disappear from the departmental budget ; since the new law in reference to education assures to instructors a retiring pension in proportion to the duration of their services.

Infant Schools.-The department contains 9 infant schools for boys and girls, containing a total of 1001 children. There are 2 schools more than there were in 1848 : the increase in the number of children amounts to 270. All these schools, with the exception of two, are defective. There is neither a proper locality, nor sufficient apparatus, nor even an intelligent direction. These establishments require a complete reform.

Normal School.--One of the most important duties entrusted to me is, undoubtedly, the inspection of the Normal School. This duty is rendered exceedingly easy on account of the excellent condition of this establishment, which continues to deserve the praises which have been bestowed on it by the general council of the department, the academic authorities, and the general Inspectors of the University.

The satisfactory results which it is permitted me to state are owing to the unbounded devotion and the untiring zeal of the director of the school: to the strict discipline which he maintains with vigour—to his constant presence at all the exercises of the house-to the religious punctuality which is everywhere manifest, and which is the best precept on order and regularity which it is possible to give to our future instructors.

The Normal School has rendered immense service to the country: it has giren us our best instructors; it has raised, to a considerable extent, the level of popular instruction ; thanks to it, above all, should M. Charles Dupin trace out again the intellectual map of France, we shall behold the black spot * disappear by which the illustrious statistician had stigmatized the department of Tarn.

Since 1833, the Normal School has produced 174 instructors : of these 120 are communal teachers, and 9 are about to become so; 1 is assistant master in the Normal School; 3 are private instructors; 27 have left the profession ; 14 have died in the exercise of their duties; total 174 who have obtained their brevet f on leaving the school. Of this number, only 10 bave been breveted to the superior degree; this is a small number when we con. sider that the course of instruction in the Normal School comprehends all that is contained in the programme for the superior brevet.

The teachers who have come from the Normal School are infinitely superior to their colleagues. They are superior by their capacity-by the condition of their schools—by their faithful observance of rules-and, almost always, by their zeal, and by their conduct towards the local authorities and the heads of families. In the course of my inspections, I have been constantly stặuck with the marked difference which exists between the teachers who have been educated at a Normal School and those who have not been in any special way prepared for the duties of instruction. People partake of my convictions, in this respect; and Normal students are always chosen, n preference to other candidates, by local committees and municipal councils.

Since the establishment of the Normal School, only 2 of the teachers educated within its walls have been dismissed, -one for iinmorality, the other for habitual negligence in the performance of his duties. If, on the other hand, the honorary list of rewards granted by the Minister of Public Instruction to the Teachers of Tarn be consulted, we shall find that from 1842 to the year 1848, the pupils of the Normal School have obtained i silver medal, 8 bronze medals, and 19 honourable records.

Normal School for Females. The opinion which I have formerly expressed of the importance which I attach to the good education of girls, will, I trust, be sufficient to make you appreciate the strong desire which I have for the continuance of exhibitions for female candidates. The Normal School is in excellent condition, and the results obtained are satisfactory. At the last examination, out of 13 who presented themselves, 3 were breveted with the numbers 2, 4, and 6.

* See maps on this plan in the Minutes of the Committee of Council on Education for 1849-50, vol. ii.

of This corresponds to our Government Certificates.

Such is a faithful and impartial account of the state of primary instruction in the department of I'arn. I have endeavoured to give, by figures obtained from authentic sources, the results due to the law of 28th June, 1833, and at the same time, to establish the starting-point of the law of 15th March, 1850 ; so that it may be easy, at a later period, to estimate the benefits which the department may have derived from it.

A. DOMERGUE, Inspector.

TRAINING SCHOOL FOR REGIMENTAL SCHOOLMASTERS,

ROYAL MILITARY ASYLUM, CHELSEA, As many persons desirous of becoming Teachers are unaware of the existence of a School for the training of Schoolmasters for the Army, the following, we understand, are the conditions under which students are admitted into the Normal School, and the advantages which are offered them when their period of training is completed.

1. Candidates for admission must be unmarried; not under the age of 19, nor above 25; and not below 5 feet 6 inches in height.

2. They are required to pass a certain examination at the Military Asylum, in order to test their qualifications previous to admission; and to produce a certificate of character and conduct, signed either by the Clergyman of the parish in which they reside, or by the Minister of the congregation of which they are members.

3. Whilst under instruction in the Normal School-a period of about two years, they are maintained and clothed at the public expense.

When certified fit for appointment as Schoolmasters in the Army, they are required to enlist

for ten years in the Infantry, and for twelve years in the Cavalry. 4. The Pay of Schoolmasters, when appointed, is 2s. 7d. a day, with clothing and quarters, and a further allowance of 6d. a day after such period of service as the Secretary at War may decide. They are also entitled to a portion of the fees received from soldiers for their instruction.

5. They rank next to the Sergeant-Major of the regiment to which they may be appointed.

6. They are also entitled to a Pension, under the regulations for pensioning non-commissioned officers and soldiers.

Applications for admission into this Institution should be addressed to the Secretary at War, War Office, London.

May, 1851.

To Correspondents.

NATIONAL SCHOOLMASTER will find Kitto's Cyclopædia of Biblical Literature a very useful book; the other book he inquires about we cannot recommend. His suggestion we will bear in mind.

A SUBSCRIBER..We know of no book on Method, or the Art of Teaching, that we can recommend.

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