New tables of coulomb functions are presented along with an introduction to their use. The ranges of parameters covered by the tabulations are those required for the calculation of reactions of protons, deuterons, and alpha-particles with the lighter nuclei, from hydrogen to oxygen, in the energy range of a few Mev. For alpha-particles the tables suffice for treatment of reactions up to about 10 Mev for $Z=9\mathrm{}$ (F) and 5 Mev for $Z=2\mathrm{}$ (He), while for protons the energy range covered is about 4 times that for alpha-particles. An indication of the principal applications of coulomb functions is given.

The factorization method is an operational procedure which enables us to answer, in a direct manner, questions about eigenvalue problems which are of importance to physicists. The underlying idea is to consider a pair of first-order differential-difference equations which are equivalent to a given second-order differential equation with boundary conditions. For a large class of such differential equations the method enables us to find immediately the eigenvalues and a manufacturing process for the normalized eigenfunctions. These results are obtained merely by consulting a table of the six possible factorization types.

The manufacturing process is also used for the calculation of transition probabilities.

The method is generalized so that it will handle perturbation problems.

A summarizing account is given of the research on barium titanate in progress at the Laboratory for Insulation Research at M. I. T. since 1943. The investigations have led to an understanding of the mechanism of ferroelectricity in the titanates and to discoveries such as the piezoelectric effect in the ceramics and the domain structure of the single crystals of BaTi${\mathrm{O}}_3$. The high dielectric constant, field strength and temperature sensitivity, and piezo-response of the barium titanate dielectrics make them useful for numerous technical applications.