Pressure-time curves, continuous from initial shock wave incidence through the second bubble pulse, are examined in the light of acoustic theory. Calculations of impulse and reversible and irreversible energy flux are made for the various phases of the phenomenon. An estimate has been made of the amount of energy dissipation associated with the propagation of the shock front. A tabulation of the energy partition is included, and it is shown that substantial quantities of energy are radiated or dissipated by mechanisms other than these taken into account in this discussion.

Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way. The probability that a particle will be found to have a path $x\left(t\right)\mathrm{}$ lying somewhere within a region of space time is the square of a sum of contributions, one from each path in the region. The contribution from a single path is postulated to be an exponential whose (imaginary) phase is the classical action (in units of $\hslash$) for the path in question. The total contribution from all paths reaching $x$, $t$ from the past is the wave function $\psi (x, t)$. This is shown to satisfy Schroedinger's equation. The relation to matrix and operator algebra is discussed. Applications are indicated, in particular to eliminate the coordinates of the field oscillators from the equations of quantum electrodynamics.

This paper gives a brief discussion of Weber's theory of diamagnetism and of the relations between it and the more recent theory of Langevin, as well as a composite theory involving ideas from both and sometimes confused with that of Langevin.

The importance of irreversible entropy production is emphasized. The first and second laws of thermodynamics are both expressed by equalities by giving due recognition to the irreversible production of entropy. By specialization and combination of these equations, an "efficiency equation" is derived, applicable to cyclical and steady-state processes, and useful in studying the efficiency of practical processes. The thermodynamic theory involved in determining amounts of entropy produced by irreversible processes is investigated, and six cases of irreversible entropy production are treated in detail. The "efficiency equation" is applied to four practical processes to illustrate its usefulness in analyzing the causes of inefficiency in practical situations. The first and second law equations are directly applied to two theoretical problems so selected as to illustrate differences in the theoretical importance of being able to express the second law in the form of an equality. The concept of temperature is discussed, and the extent of its validity under non-equilibrium situations is analyzed.

This paper presents a review of five papers in which a generalized electrodynamics has been developed. The purpose of the review is to present the results obtained so far, leaving out duplications, false starts, and detailed calculations. The emphasis is on the sequence of ideas, the difficulties encountered, and the methods of procedure.

With an improved Geiger counter telescope, having an angular aperture of about ±15° from its axis, a series of balloon flights was made in August and September, 1947, at seven stations extending from San Antonio, Texas, to Saskatoon, Canada. The axis of the telescope in all cases was oriented in a vertical direction. All sets of equipment were compared with a standard to reduce all results to a common basis. The standard sets, in turn, were compared with an accurately constructed telescope which had been used to make an absolute determination of cosmic-ray intensity at the vertical in Pasadena.

Two flights were made from each of the seven stations. The agreement between flights made within a few hours of each other at a given station is very good. Results from two flights made at a given station several days apart are not in general as consistent. Likewise, no monotonic increase of the radiation with increase of latitude was observed. Evidence is presented for rather large fluctuations at high altitudes of the lower energy components of cosmic rays. Some of the reasons for these fluctuations are discussed.

A cosmic-ray telescope is described having an angular resolution of approximately ±15°. The distance between the two outermost trays, each containing 8 Geiger counters, is 1 meter. The area of each tray is approximately 24×24 ${\mathrm{cm}}^2$. Triple coincidences modulate a transmitter and the signals, including those giving the air pressure and temperature of the instrument, are recorded on the ground. The counting rate is such that at the peak of the curve the relative probable error during a 4 minute interval is about 1.5 percent.

Accidental counts are found to be nearly negligible at all altitudes and latitudes, but some correction needs to be made for loss in efficiency because of the inherent dead time of the counters. An absolute determination of cosmic-ray intensity at the vertical at Pasadena was made in order to express the results as nearly as possible independently of the apparatus used.

Cosmic-ray data taken during the period of a solar flare and the magnetic storm that followed 26.5 hours later during July, 1946, are reported. The results following the flare agree with those of other investigators and, in addition, serve to establish the fact that the start of the cosmicray effect and the visual part of the solar flare were simultaneous. It is pointed out that increases of cosmic rays during solar flares suggest a mode of origin of the rays. The lack of effect of most solar flares on cosmic-ray intensity is noted and differences in intensity of the flares given as a possible reason. A high altitude balloon flight with an electroscope during the magnetic storm gave results in agreement with the current-sheet hypothesis of such storms but a serious objection to this hypothesis is given.

A discussion is given of the data obtained in a recent series of flights of a B-29 airplane at altitudes up to 40,000 ft., in which a cloud chamber, actuated by Geiger counters, was operated in a magnetic field of 7500 gauss. The frequency of occurrence of single particles and electron showers at elevations of 800 ft., 14,100 ft., and 30,000 ft. is compared. Examples of heavily ionizing particles and of nuclear disintegrations are discussed. Direct measurements of the energies of cosmic-ray particles at 30,000 ft. are compared with similar measurements made at sea level. These measurements indicate that up to one-third of the particles which occur singly in the chamber, in the momentum range up to ${10}^7$ gauss-cm, may consist of protons and the remainder of mesotrons, in contrast to sea level observations which show that protons are there present in only negligible numbers.