The subject about which I have to speak to you to-day is one which was bound, in the course of time, to occupy the attention of the Mathematical Association. This Association was founded, as you know, for the purpose of improving geometrical teaching, but since its foundation, some sixty years ago, its activities have widened. It no longer confines itself to Elementary Geometry, but has issued reports on the teaching of Arithmetic, Algebra, and Mechanics. None of these, however, except possibly the last, touches on anything more advanced than School Certificate work, and even the Mechanics report does not deal with anything far in advance of this standard.

Poincaré, dans sa conférence prononcée au Musée pédagogique de Paris en 1904, déclarait déjà qu'ily avait lieu de penser en dérivées non en différentielles. II me semble utile pour l'enseignement de se conformer résolument à ce principe et d'abandonner les explications assez compliquées qui sont classiquement données sur le symbole d. Pour la différentielle premiére, passe encore : Je puis comprendre l'égalité accroissements infiniment petits.

The Royal Society received its first Charter in 1662 from that “Defender of the Faith ” and “universal lover and patron of every kind of truth ”, Charles II, The movement in human thought which made its foundation inevitable had already a long history behind it. In literature the Renaissance manifested itself in a new interest in the classics of Greece and Rome and in the application of the wisdom of the ancients to modern life ; in philosophy it rejected scholasticism and declared its faith in the exercise of reason and free enquiry ; in art it delighted in the reproduction of human and natural forms ; and in science it conceived that the boundaries of man's knowledge of the universe were infinitely extendible by properly conducted experiments to the glory of God and especially to the relief of man's estate.

Through any point 0 in space a straight line POP1 can be drawn meeting the opposite edges AD, BC of a tetrahedron ABCD in the points P, P 1 respectively; another straight line QOQ1 can be drawn to meet DB, AC in Q, QI; and another straight line ROR1 to meet DC, AB in R, RI.