On Friday 12 November 1886 the Edinburgh Mathematical Society began its fifth session. If this seems rather strange for a Society which began in 1883, we must remember that the second session of the Society (as well as the first) began in 1883. At this first meeting of the fifth session an address was given looking at the progress of the Society and also looking forward to the directions it should take:

**Edinburgh Mathematical Society.**

The first meeting of the fifth session of this Society was held last night in the Edinburgh Institution - Dr R M Ferguson, president, in the chair. On the occasion of demitting his office, Dr Ferguson delivered an address in which he congratulated the Society on its vigorous growth and encouraging prospects. He contrasted the state of mathematical education at the universities now with that which prevailed thirty years ago, and expressed a hope for the further improvement of these institutions by an increased staff of extra and infra-mural lecturers. In adverting to the position of mathematical masters in secondary schools, he thought that they should more frequently be entrusted with the highest authority. After a few remarks on the methods of mathematical tuition, he pointed out the desirability of continuing to widen the work of the Society in the interests of such professions as those of the engineer and the actuary. Thereafter Mr J S Mackay read a paper on the solutions of Euclid's problems with one fixed aperture of the compasses by the Italian geometers of the 16th century; and communicated a note from Mr R Tucker giving some novel properties connected with the triangle. Mr A Y Fraser read a note by Mr W Renton on the equivocal sign. Office-bearers for the session were elected as follows:-

**President**, Mr George Thom, M.A., Dollar;

**Vice-president**, Mr W J Macdonald, M.A., F.R.S.E.;

**Secretary**, Mr A Y Fraser, M.A., F.R.S.E.;

**Treasurer**, Mr John Allison, M.A.;

**Committee**, Mr R E Allardice, M.A.; Dr Ferguson, F.R.S.E.; Mr George A Gibson, M.A.; Mr William Harvey, B.A., LL.B.; Mr J S Mackay, M.A., F.R.S.E.; and Dr Thomas Muir, F.R.S.E.