Introduction. Impulses occur not only in technical work but in everyday existence. There is hammering and door banging which may cause annoyance, handclapping which denotes enthusiasm and enjoyment, motoring on rough roads which causes discomfort (especially after a good meal!), speech, electrical communication in the Morse code, and so on ad infinitum. Impulses have been treated by applied mathematicians with reference to various technical problems, e.g. Heaviside in his work on electromagnetic theory. Moreover, the subject is one which merits attention, so in what follows a brief outline will be given of recent work based upon a particular case of the Mellin inversion theorem.

Teachers of elementary Mathematics are generally very glad to find some unfamiliar field into which they can turn their pupils to exercise themselves in elementary processes. The following is a suggestion of a method of approaching certain theorems in connection with the Geometry of the Triangle which, although well known to Mathematicians, are not, as a rule, studied as part of a school course, except perhaps by specialists. The Brocard Points and Circle are generally approached, via the theory of Isogonal Conjugates (see Casey’s Sequel to Euclid, Supplementary Chapter, Section I. etc.). But many of the properties connected with these points can be obtained in a more direct manner, and this suggests some interesting investigations involving nothing but the ordinary processes of Geometry and Trigonometry.

Starting with any triangle Δ ≡ ABC, let Δ1 ≡ A1B1C1 be its pedal, Δ2≡A2B2C2 the pedal of Δ1 and so on indefinitely Since the circumradius Rn of Δn is equal to 1/2Rn-1, we may expect a steady contraction towards some definite limiting point. It is proposed to inquire into the position of this point.

The main object of this article is to suggest that John Napier took the word “ logarithm ”, though not the idea, directly from the Psammites (Arenarius, Sand-Reckoner) of Archimedes. Incidentally it will contain the results of new research into Napier's life, together with an examination of the history of some of the texts of the editio princeps of Archimedes (Basel, 1544) which exist at present in this country.

Statistical method is coming to be so extensively applied, that those who use it must from time to time feel the need of assuring themselves as to the security of its foundations. For this assurance they will naturally turn to books on the subject. But do these give much help?