The object of the present note is to obtain a number of infinite integrals involving Struve functions and parabolic cylinder functions. 1. G. N. Watson(1) has proved that

From (1)

follows provided that the integral is convergent and term-by-term integration is permissible. A great many interesting particular cases of (2) are easily deducible: the following will be used in this paper.

The generalised Whittaker vector is Λμ which is prevented from vanishing by rejection of the constancy of ω, previously assumed by all writers. It is shown that (1) the null divergence of Λμ is equivalent to Dirac's equation, (2) the length of Λμ measures the probability of occurrence of the electron (3) components of Λμ are connected with the Dirac wave functions and.possible transformations of x5 are probably related to the Uncertainty Principle.

Through four generally placed lines in space of four dimensions there passes a doubly infinite system of quadric primals, but through five lines there pass in general no quadrics. It therefore follows that there must exist some special relationship between five lines in order that they may be generators of a quadric. This problem has been discussed by Richmond,1 who gives a condition which is in a restricted sense an extension of Pascal's Theorem. The five lines being taken in order certain points may be obtained which lie in a space. In Section I we state Richmond's criterion and show that it is sufficient as well as necessary. Section II is concerned with the twelve spaces which arise if all the different possible orders of the lines are considered. They cut by pairs in six planes whose configuration is developed. In Section III other lines connected with the configuration are introduced. It is shown that by taking crossers of the lines of our original figure in a certain manner five further generators are obtained, and that the same entire configuration of generators arises whether we begin with the five original or the five final lines. Furthermore, though the twelve spaces analogous to Pascal lines obtained from the final five are new, yet the six planes, their intersections by pairs, and the configuration dependent from them, are the same as those constructed from the original five.

In an earlier paper1 the author investigated the relation existing between the induced matrices of a group of permutation matrices and the table of group characters of the irreducible representations of the corresponding symmetric group. It was found that the traces of a particular set of induced matrices sufficed to give, by a relatively simple transformation, the complete table of characters.It was remarked also that for n > 4 the set of compound matrices of permutation matrices, on the other hand, could at most provide only part of the table; for in fact the number of compounds, n + 1. is then less than P (n), the numbe'r of partitions of n. For this reason the subject was not pursued into further detail.

In the paper by H. S. Ruse (this volume 144-152) in equation (1.5) read “Rαβ” instead of “Rαβ”; in equation (1.10) read “€αβ” and “€βα” respectively instead of “€αβ” and “€βα”.

In the paper by C. T. Rajagopal (this volume 162-167) on page 165 line 2 read “dt1” instead of “dt” on page 166 line 2 read “dt1” instead of dt” and in line 2 of the footnote on page 166 read “(16)” instead of “(15)”.