Many members of the Association know the Gazette only in its hampered and restricted war-time form. The time is therefore opportune for some remarks on the pre-war Gazette and on what may reasonably be expected from the post-war Gazette. The history of the Gazette, however, cannot be fully understood without some reference to the history of the Association; such reference need be only brief, since a full account is available in the admirable Presidential Address by Mr. A. W Siddons (XX, No. 237, February, 1936).

Most of us have asked this question at some time or another; generally we have received some such answer as: “It’s a gyroscopic effect, of course” Further details are not easy to obtain, and the majority of books on Mechanics do not mention the subject.

Plane Analytical Geometry, and elementary Trigonometry, are the beginnings of the systematic application of mathematical analysis to Geometry, i.e. of systematic expression in terms of “number”—which is essentially “real” number.

Complete application of the generality of the algebra (within the restriction to real number) is, of course, the power of the method; and, in particular, sign of the (real) numbers is significant throughout.

Figure 1 is described in detail in my article in the Mathematical Gazette, XIX, No. 236. it is based on a tetrahedron ABCD and an arbitrary point D2. These five points determine all the other points of the figure, and if the tetrahedron ABCD is taken as the tetrahedron of reference and the coordinates of D2 are (α0, β0, γ0, δ0), the coordinates of A1, B1, C1, D1 are (- α0, β0, γ0, δ0), (α0,β0,-γ0, δ0), and so on. in what follows the tetrahedron A1B1C1D1 is called the associated tetrahedron.

Dans son “Mémoire sur le tétraèdre (Bulletin de l’Académie royale de Belgique, 1884), J Neuberg a donné des propriétés du point L dont les coordonnées normales sont proportionnelles aux rayons des cercles circonscrits aux triangles des faces d’un tétraèdre isodynamique. Nous avons étendu ces propriétés au point L défini de la même façon dans un tétraèdre quelconque T≡ABCD (Annales de la Société Scientifique de Bruxelles, 1922, pp. 173-177). P Delens lui a consacré aussi des développements mais par des méthodes assez difficiles à lire (Mathesis, 1937 et 1938).