In a previous paper (Jack 1970, § 5) the pre-zonal polynomials were defined by the surface integral (1) below. In that paper they were evaluated using a series of differential type operators acting on the sums of powers of the roots of a matrix.

The present paper, although it is a continuation of Jack (1970), is self-contained and consists of three parts. The first part, §§ 3–7, shows how the pre-zonal polynomials may be calculated, certainly for low degree, using only the first of the differential operators. The next part, §§ 8–11, is devoted to establishing various recurrence relations between the pre-zonal polynomials and to conjecturing similar recurrence relations between the zonal polynomials (James 1964, p. 478). In the final part, §§ 12–14 the pre-zonal polynomials are evaluated directly from the integral (1) below, in terms of the augmented monomial symmetric functions.

The attempt is made to exhibit the necessary correlations between fragment excitation (or prompt neutron number), fragment kinetic energy, and a-particle energy, in α-particle-accompanied ternary fission. Treating a single mode of mass and charge division on the assumption that the ternary process develops directly out of an intermediate binary phase, and using the mutual electrostatic potential energy of the nascent binary fragments of this phase and the additional kinetic energy developed at the moment of α-particle emission as independent variables, various formal results are obtained and discussed in the light of the experimental evidence.

In terms of a classical description, it appears likely that (for a given mode of division) the nuclear configuration at a-particle release in ternary fission is subject to much smaller variations than is the nuclear configuration at scission in binary fission in the corresponding mode. Possible inadequacies of this classical description are very briefly discussed.

On treatment with t-amyl-alcoholic sodium t-amyloxide, sulphones of the type TsCHAr.C6H4.NPhCH2R lose the elements of toluenesulphinic acid giving the Schiff base ArCH2.C6H4.N = CHR, which can be hydrolysed to ArCH2.C6H4.NH2.

We consider, for a given ordered set E with minimum element O, the semigroup Q of O-preserving isotone mappings on E and examine necessary and sufficient conditions under which an element fε Q is such that the left [resp. right] annihilator of f in Q is a principal left [resp. right] ideal of Q generated by a particular type of idempotent. The results obtained lead us to introduce the concept of a Baer assembly which we use to extend to the case of a semilattice the Baer semigroup co-ordinatization theory of lattices. We also derive a co-ordinatization of particular types of semilattice.

Closed form solutions of some triple equations involving trigonometric series have been obtained, in each case, by reducing them to a single integral equation. The results have been applied to determine the distribution of stress in the interior of an infinitely long elastic strip containing a pair of Griffith cracks situated on a line perpendicular to the bounding lines of the strip.