The earth's core may be assumed to consist of fluid metal surrounding a solid inner core which probably contains a source of heat to drive convection, but it is not possible at present to select between various possible types of convective motion in the fluid core. Types considered are characterized by some sort of radial flow streams and a tendency for the fluid to rotate on the average more rapidly near the axis to conserve angular momentum during the circulation. Though the actual flow may be quite complicated, proposed mechanisms for generating a terrestrial magnetic field are considered for some oversimplified flow patterns in an attempt to indicate what features of the flow may provide the most important possibilities for field generation. It is suggested that, without a field to absorb the energy, the flow would be accelerated indefinitely and would evolve through a succession of flow patterns, some of which would be expected to have the properties to generate a field capable of preventing further acceleration and prolonging the status quo, thus making it likely that the earth should have a field.

The generating mechanisms discussed include two induction theories, the dynamo theory of Elsasser and Bullard, which is discussed at length both in terms of velocity-current systems portrayed by elaborate models and in hydromagnetic terms, and the "twisted-kink" theory of Alvèn which is discussed only hydromagnetically. Each of these theories depends on amplifying an initial stray magnetic field up to a point where it dissipates all of the available energy, and is at least in this respect analogous to a conventional electrical generator but without a ferromagnetic core. Other mechanisms discussed depend either on the thermoelectric effect with junctions at the core-mantle interface or on a combination of thermoelectric and Hall effects in the core and mantle.

If the convective flow is rather irregular, the observed slow westward drift of the detailed pattern of the earth's field is attributed to the vanishing of the total torque on the core by the magnetic field threading through the core and mantle, as a result of an eastward drag on the outer part of the core rotating more slowly in space and a westward drag on the more rapidly rotating part of the core near the axis, with the presumption that the observed magnetic pattern is characteristic of the westward-drifting outer part. If the flow instead involves a jet stream, the flow in the jet may under some circumstances be expected to be eastward for reasons comparable to temperate-zone meteorology, so the magnetic field should exert a westward drag on it leading to the westward drift of the flow pattern.

An attempt is made within the framework of the accepted quantum physics to achieve the maximum parallelism between prediction (inference of the future observational data from the present ones) and retrodiction (inference of the past observational data from the present ones). To implement this program, it is shown that the "retrodictive state function" (extrapolation of the present data to the past) can be just as useful as the ordinary "predictive state function" (extrapolation of the present data to the future). This leads to a formalism in which time-reversal becomes a linear transformation and double time-reversal becomes a $c$-number. In spite of this formal symmetry, it can be shown that the actual success of a retrodiction depends on the satisfaction of an additional condition which is not required in prediction, and which is not always fulfilled. From the same point of view, a logical loophole is pointed out in the indiscriminate application of the $H$-theorem to the past. The so-called irreversibility of observation is interpreted in terms of the decrease of "information" in the process of inference.

For nearly thirty years the results of the Michelson-Morley experiment obtained by Dayton C. Miller on Mount Wilson have stood at variance with all other trials of this experiment. As interest in Miller's results has continued to the present time, and since the original data sheets are available to the present writers, it has seemed appropriate that the observations be subjected to a new analysis. It is now shown that the small periodic fringe displacements found by Miller are due in part to statistical fluctuations in the readings of the fringe positions in a very difficult experiment. The remaining systematic effects are ascribed to local temperature conditions. These were much more troublesome at Mount Wilson than those encountered by experimenters elsewhere, including Miller himself in his work done at Case in Cleveland. As interpreted in the present study, Miller's extensive Mount Wilson data contain no effect of the kind predicted by the aether theory and, within the limitations imposed by local disturbances, are entirely consistent with a null result at all epochs during a year.

Symmetry properties of physical laws with respect to space-inversion, time-reversal and charge-conjugation are investigated in detail in the framework of the quantized field theory. In most cases, the requirements of invariance for these transformations are automatically satisfied; in a few other cases they can impose certain conditions on the ways in which different types of interaction are to be mixed. The ideas of space-parity, charge-parity and superselection rules are coherently derived from the general formulation of field theory.

In default of the theorem of "detailed balance": $P_{\mathrm{ij}}=P_{\mathrm{ji}}$, with regard to elementary transition probabilities, several "balance" theorems are introduced and proved on the basis of symmetry of physical laws in space-time. (1) First theorem of "averaged balance" (Sec. 5): We can establish ${\overline{P}}_{\mathrm{ij}}={\overline{P}}_{\mathrm{ji}}$ by averaging over quantities of "minus class." Table V (Sec. 3) gives a list of "minus" quantities. (2) The so-called "detailed balance of collisions" in classical physics is a special case of Theorem I. (3) Heitler-Coester's theorem of "semidetailed balance" is also a special case of Theorem I. (4) Second theorem of "averaged balance" (Sec. 5): We can establish ${\overline{P}}_{\mathrm{ij}}={\overline{P}}_{\mathrm{ji}}$ by averaging over quantities with ${\rho }_R=-1\mathrm{}$. The quantities with ${\rho }_R=-1\mathrm{}$ are listed in Table II (Sec. 2). (5) Theorem of "cyclic balance" (Sec. 7): In classical physics, a chain of transitions $i\to j\to k\to \cdots \to i$ repeats itself cyclically. (6) Theorem of "long-range balance" (Sec. 7): The time average of transition probability from $i$ to $j$ is equal to the time average of transition probability from $j$ to $i$. Theorems I, II, and III, are direct consequences of inversibility (covariance for space-and-time inversion). Theorem IV is a consequence of reversibility (covariance for time reversal). Theorems V and VI are connected with ergodicity of Markoff's chains. This ergodicity is proved by the condition of bilateral normalization of transition probabilities: $\Sigma j^{}{P}_{\mathrm{ij}}=1\mathrm{}$, $\Sigma i^{}{P}_{\mathrm{ij}}=1\mathrm{}$. This bilateral normalization in turn can be derived from either reversibility or inversibility. The limits of validity of all these balance theorems in actual applications are carefully examined in the text.

The Fermi statistical theory of multiple meson production is examined, and its application to medium-energy pion-nucleon and nucleon-nucleon collisions is discussed. Various approximate calculational procedures are described and their results compared critically. It is found, by the use of a precise integration procedure, that a rigorous relativistic inclusion of the meson rest mass is necessary if one is to draw accurate conclusions from the postulates of the theory. The consequences of isotopic spin conservation are described and tables are given for the expected distribution of charged products from both pion-nucleon and nucleon-nucleon collisions. The theory is applied to the case of pion-nucleon collisions at 1.4 Bev, and is found to predict only poorly the tentative results of recent experiments. The failure of the theory to predict nucleon-nucleon collisions is also described, and possible modifications and improvements are discussed.