"This is the fourth Quarterly Report on Task II dealing with Methods Development for Radio-Tracing of Coal Product Hydrocarbons With Tritium. The problem of radio-chemical purity of traces is resolved by developing a new method of labeling with tritium that generates essentially no highly tagged side products or impurities."

"The present work describes some computer-oriented techniques for the application of the laws of quantum mechanics to the problems of determining basic structure of diatomic molecules. At times, calculations of the type described here yield results which can be compared directly with experiment to check the validity of the hypotheses and technique used they may predict the results of unobserved experimental phenomena; and, in many instances, they provide quantities which are necessary for the interpretation of experimental data but which cannot be directly measured."

The methods of successive displacements or relaxation methods are investigated for a class of nonlinear problems. In particular it is shown that these methods are applicable to a large class of nonlinear problems arising from variational problems which yield elliptic equations. Constructive existence and uniqueness theorems are presented for the discrete problem and criteria are given for a practical method of obtaining solutions. The example of a discrete Plateau problem is used to illustrate the feasibility of the results. The processes are also shown to apply to uniformly elliptic problems.

"The laboratory experiments and field testing which were carried out in the development of a homogeneous gas labeling device are described. Detailed drawings of the injector and its most critical components are included. Recommendations are made for a production model of the device along with estimated costs of construction."