Ser. v. 89. John of Halifax.—Since every country has its Holywood, and de Sacnbosco does not distinguish Holywood from Halifax, John of Halifax has been claimed both by Ireland and Scotland, and, if I remember right, by some foreign countries. The manuscripts of his works, as well as the earlier printed editions, call him Anglus or Anglicus; and he lived in a time at which the natives of the three countries were as distinct as Frenchmen, Spaniards, and Italians. Bale, quoting Leland, calls him Halifax; as does Tanner: Pits gives his birth to Halifax. He was buried in the Maturin convent at Paris, where his epitaph existed in the sixteenth century. Pits implies that it appears from the epitaph that he died in 1256: Maestlinus expressly affirms that it can be collected from the epitaph, in the Ad Lectorem of his Epitome Astronorniae. All the authorities believe him to be English; and Leland thought he traced him as a student at Oxford. But had the manuscripts called him anything but English, the other evidence would not have weighed them down; for there are plenty of Holywoods, and there was, notoriously, a press of foreign students to Oxford in the thirteenth century. But name and residence in England may come in aid of the manuscripts.

To cut up an isosceles triangle so that the parts may be put together to form two triangles similar to the original triangle.

Let ABC be the triangle, having the angles at B and C equal, and let D be the middle point of the base. Draw a circle, passing through A, having its centre on AD, and cutting AB and AC in E and F. Join DE, cutting the circle in G.

The Dalton Plan, which has been discussed so much recently, is a change of organisation within school which affects a girl’s whole school life and her general development more than her work in individual subjects. I am obliged in describing it to devote a few minutes to speaking of general school life, and when I turn to the teaching of mathematics there seems so little to say, that could not be said as appropriately of teaching in ordinary circumstances that I do not know if it will justify the consideration of this meeting.

The process known as the differentiation of functions in the Calculus does not present the insurmountable difficulties one experiences in attacking the converse problem associated with the Integral Calculus. As is well known, there are many functions which we cannot integrate, and as the process of integration is really a summation, this means there are many areas which cannot be evaluated by exact methods. There are many cases in various branches of science in which it is required to determine the area of a closed curve obtained by plotting a series of observations. The engineer, for example, has to determine the areas of indicator and similar diagrams, the naval architect has to calculate volumes, and centres of gravity or buoyancy by approximate methods. The mathematician may be called upon to evaluate definite integrals which cannot be integrated directly, such as the elliptic integrals. The problem reduces simply to the consideration of the determination of the area between the curve y=f(x), the ordinates x=x0 and x =x0+nh, and the axis of x; and the first part of the paper will be devoted to the methods of obtaining empirical rules for approximation to the evaluation of such an area when f(x) cannot be directly integrated. In the second part, the mechanical methods of integration will be considered, including demonstrations with the different types of instruments illustrating these methods.