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By counting squares find the area A included between the x-axis and this part of the curve. Write down an expression for the area included

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cally in such a position as to enable accurate readings to be made of the deflections of the free end of the horizontal stick.

Tie a weight on a loop of string that can be slid to any part of the horizontal stick between the 25 cm. and the 100 cm. mark.

Place the weight in turn at the graduations 25, 40, 55, 70, 85, 100, and observe with the greatest possible accuracy the deflection of the end of the stick (the 100 mark) produced by the weight at each position.

Tabulate the observations and make a graph, using as abscissæ the distances of the weight from the edge of the table, and as ordinates the corresponding deflections of the end of the stick.

The graph will be of the form y = Ax2 + Bæ3. Determine A and B by substituting in this equation the co-ordinates of two points of the graph.

2.

Fix two lengths of wire horizontally between the table uprights, one about 50 cm. above the table and the other a little higher. The lower one is to be deflected by weights; the upper wire merely affords a zero from which to measure the deflections of the lower, and should be loaded slightly by a middle fixed weight.

Apply loads centrally to the lower wire so as to get deflections of between 1 and 10 cm. In all about 6 values of load should be used, and observations of the deflections should be made both while the load is being increased and while it is being decreased.

From the observations calculate the tension in the wire and the stretch of the wire at each observation. Tabulate these results, and from them obtain a mean value of Young's modulus of elasticity.

THE ORGANISATION OF THE TEACHING OF MATHEMATICS IN PUBLIC SECONDARY SCHOOLS FOR GIRLS.

INTRODUCTORY.

Rather more than half a century has elapsed since Professor Maurice, speaking on the occasion of the opening of Queen's College, London, uttered his often-quoted belief that women students were not likely to advance far in Mathematics.

Mathematics was, however, introduced into the curriculum of Queen's College, and of Bedford College, shortly afterwards founded, because, to quote from the same speech, "we believe "that if they learn really what they do learn, they will have got, "not what is dangerous, but what is safe"; or, as Professor Hudson worded it thirty years later, "because it (algebra) is a part of mathematical truth and no one ought to be wholly "alien from that important department of human knowledge.'

Mathematics was thus, in 1853, formally recognised as a subject not altogether suited to the capacity of women, but one of which the more highly educated women should not be wholly ignorant. We find, however, that in the curriculum of the schools founded in the same decade by the two famous Queen's College students, Miss Beale and Miss Buss, the only branch of Mathematics studied was arithmetic. The teaching of the subject in the schools of that time was in the hands of poorlyequipped, but keen, teachers who gave a remarkable impetus to arithmetical work in girls' schools between the years 1862 and 1865. In 1862, sixty-eight per cent. of the girls examined informally by the Cambridge Local Examiners failed in arithmetic; in 1865, three years later, three times the number of candidates were presented, this time formally, for the same examination, and seventy-one per cent. passed, the remaining twenty-nine per cent. either failing in or not entering for that subject.

66

In 1867, the report of the Schools' Inquiry Commission (Lord Taunton) was published, condemning the superficiality and want of thoroughness of the education in girls' schools. The immediate result was the foundation, four years later, of the National Union for improving the Education of Women of all Classes," and the first work of this Union was the establishment, in the following year, of the Girls' Public Day School Company. For the first time Mathematics became one of the recognised subjects of the curriculum of girls' schools, beginning with the High Schools, which were rapidly started all over the kingdom

by this Company; it was realised that this branch of science would best correct the faults condemned in the Report of the Commission of 1865-7, and its inclusion as a school subject was strongly urged by the famous inspectors of the sixties and early seventies. Sir Joshua (then Mr.) Fitch wrote in 1875: "Girls are more in danger of falling into desultory habits of reading and of thought, and . . therefore need more the bracing and the mental precision furnished by "studies of another kind. For this reason I should like to see some of the time now devoted to ancient history rescued "for the study of science in some form or other. Whether it would be better to give greater prominence to pure science' including advanced arithmetic, algebra, and geometry, or to Home branch of applied or experimental science, I should be disposed to leave for determination. But it is clear that for the formation of habits of exactness and for the purpose of bringing the intellectual character of the pupils under the best possible discipline it is of the highest importance to give greater prominence to scientific teaching.”*

Mathematics has thus been recognised as a subject for study in girls' schools for some thirty or forty years, but at first the difficulties were great owing to the fact that the supply of wellqualified teachers was wholly inadequate. The Honours

Examinations of the Universities were not open to women until 1881, when Cambridge formally admitted stulents of Newnham and Girton Colleges to the Tripos Examinations, and, in consequence, the equipment of those teaching before that time was in the main meagre: a smattering of arithmetic an 1 algebra, with little knowledge of principles, and perhaps two books of Euclid learnt more or less by rote. by the twenty years following the opening of the Triros Examination to Women, 250 students took honours in Mathematics at Cambridge alone, and it was with the entrance into the teaching profession of this band of highly qualified women that the organisation of mathematical teaching may be said to have begun.

At the present day, Mathematics is taught with remarkable uniformity of matter and method-in all publ schools for girls and in all the best private seh factor, which have mainly determined the spe organisation of mathematical teachin Band are:

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