The next International Congress is to be held at Bologna in September of next year. For the first time since the Cambridge Congress of 1912, all differences of nationality are to be disregarded, and mathematicians who believe that in spite of all that has happened since 1912 international cooperation is possible, or even that because of all that has happened international cooperation is imperative, will be glad to have ample warning in order not to make plans that might inadvertently interfere with their attendance.

Considering the setting for this year’s meeting of the British Association, to doubt whether Section A will provide a subsectional programme attractive to readers of the Gazette is to overlook the notorious energy of Yorkshire mathematicians. Details are not yet available, but people who enjoy social encounters and holiday mathematics can be sure of a pleasant week at Leeds from August 31st to September 7th.

A 16-Page pamphlet which has been prepared at Burnley Grammar School and published there at the price of 6d. under the title Guide to the Eclipse of June 29th, 1927, fits into the gap between the instructions of the professional astronomer and the advice of the professional journalist. Of the five sections—the cause, what to look for, hints to photographers, the eclipse in history, an expedition which “failed”—perhaps it is the third which is the most important; the last section, a quotation from Piazzi Smyth’s account of the terrestrial effects of totality when the sun itself is clouded, is a valuable antidote when meteorological friends have operated with their usual depression and we feel that the chance of a fine morning would hardly justify us in getting up early even if we lived on the central line.

1. A Solar eclipse occurs whenever the sun, moon and earth have their centres so nearly in line that the moon hides some part, or all, of the sun from an observer on the earth’s surface. In the former case the eclipse is partial, in the latter total. The relative motions of the three bodies are extremely complicated; but as knowledge of the apparent positions of the sun and moon is of importance for safe navigation, these are regularly computed in advance and published by the Admiralty in the Nautical Almanac. Since the Nautical Almanac tables are the data for eclipse calculations, it is essential to understand the method there employed for recording the positions of the heavenly bodies, and the meanings of a few technical terms.

The following, written at the reguest of the Editor of the Gazette, gives an account of the mathematical part of the remarks made by the lecturer at the Annual Meeting of the Association last January. There are added some words dealing with geometry on a sphere, in regard to which some questions were raised at the meeting.

Mr. W. C. Fletcher opened the discussion by urging practical teachers who would appreciate the difficulties of the subject to express their views. He then asked, Did the Pappus theorem depend on parallelism? The proof which Professor Baker happened to give made it so depend.

The recent discussion in the Gazette on the subject of asymptotes to algebraic curves has tempted me to offer a short account of a method of treatment which I have found useful in my teaching, in forming clear conceptions of the nature, not only of the contact of a curve with its asymptotes, but also of such singularities at infinity as the curve possesses. Incidentally the method affords an expeditious means of determining conies of closest contact at infinity—a subject upon which most text-books are discreetly silent—including parabolic asymptotes as a particular case.

The problem of deciding whether a given number is irrational or not is frequently one of some difficulty, as in the proof that π is irrational. Several numbers which are very probably irrational have never been proved so, e.g. y, eπ. However, we have one quite simple test for deciding whether a number is irrational or not when we have the number expressed as a continued fraction, viz. if the continued fraction terminates, the number is rational; if not, irrational. In what follows we assume our irrational number given as a continued fraction :

or shortly