(1) The institution of Local Education Authorities in 1902. These Authorities have been able to survey over a wide range of Secondary Schools the working of the examination system and to estimate to some extent its effects on Secondary Education as a whole. Consequent on this, but not wholly the result of it, came some general reforms, e.g. the formation of the Secondary Schools Examination Council. But L.E.A.’s are also involved in the examination system as examiners, since they test candidates for scholarships and free places in Secondary Schools. Their examination view-point is therefore a wide one, embracing that of both teacher and examiner. The full effect of this dual point of view has not yet matured, but some innovations or improvements in junior scholarship examinations have already resulted from it; for instance, the development of the oral examination and the use of the teacher’s assessment of a pupil. In some areas, too, teachers participate in marking scripts. Examinations of School Certificate standard are so far little affected, but it would be in accord with the trend of events if the wide powers of University Examining Authorities were further modified and the school record of the candidate made to play a more important part in the examination than at present.

“General Intelligence” is a will-o’-the-wisp, and Psychologists have been chasing it with Tests for a considerable time. Whether it has yet been brought to heel and can be exactly measured is still open to question, but the modern Intelligence Tests certainly discover some kind of innate ability. Is this ability purely “general,” or do some types of ability show up better than others in the Tests?

Interest in the trick that we all know was not discovered by Cardan is greatly enhanced if we think less of a cubic equation and more of a three-one relation between complex variables. It is convenient to take the relation in the form

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