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Summary The paper consists of a general adjustment of the data relevant to the radius and ellipticity of the Earth, the lunar parallax and the differences of the moments of inertia of the Moon. The anomalies of gravity recently found to persist over distances of 10° and 30° imply similar anomalies in the deflexion of the vertical and provide a means of estimating the additional uncertainty that they introduce. When this is taken into account it is found that the data are satisfactorily consistent. Attempts are made to find additional checks on the existence of the anomalies of gravity represented by harmonics of degrees 2 and 3 other than the main ellipticity term, but they are indecisive, and the final solution is a compromise between solutions with and without them. The chief changes from current values are a reduction of the Earth's equatorial radius from 6371.388 km. to 6371-099±0.116 km. (s. e.) and the value of g at Potsdam from 981.274 gals, to 981-2606±0-0010 gal.; owing to recent work by the Anglo-Iranian Oil Company the British stations are now strongly connected with the new determination of the absolute value of g at Teddington. The change in the equatorial radius is due to the use of free-air instead of isostatic reductions; reasons are given why the latter may have introduced a systematic error.

A comparison study is made of liquid water content measurements using conventional devices with those integrated from optically measured drop size distributions. In clouds of low to medium droplet size (

This paper deals with Lyapunov-type analysis of the dynamic stability of a linear elastic column subjected to an axial stochastic load. Within the past decade, the interest in stability of stochastic systems of differen tial equations has rapidly increased, as indicated by the large number of papers on the subject. The intent of this paper is to provide sufficient conditions on the absolute value of the excitation applied to the column problem in order to insure mean-square global stability. Although this problem has been investigated by several authors by considering the concept of almost sure stability, the bounds provided are related to only the mean value of the absolute value of the excitation, or, at best, the standard deviation of a Gaussian process with zero mean. In the present paper, we are able to relate the required bounds, for mean-square global stability, to the mean and variances of the excitation. The bounds are applicable for any general continuous random process. The sufficient bounds are obtained by using a Lyapunov type of approach, introduced by Bertram and Sarachik and extended here for stability in the mean-square sense.

To reach a better understanding of the correlation between molecular structure and intermolecular attraction, a comparison was made of swelling equilibria. With this aim we studied the absolute value of the swelling equilibrium under the influence of polar and polarizable groups, which were introduced in solvents and polymers with different molecular structures. The influence of temperature, cross-linking, external pressure, and mechanical strain on the position of the equilibrium was also studied. Any general treatment of swelling is obviously limited by our present knowledge of the properties of liquid mixtures. Experimentally, however, the study of high polymeric solutions and gels offers several advantages over that of ordinary liquids. Our experiments, designed to elucidate the structure of polymers, also reveal properties of some organic liquids which could not be observed easily by other means. Results obtained with commercial rubbers will be given in this paper, while analogous measurements on a series of copolymers with increasing numbers of nitrile groups will be dealt with in a second paper.

IN a paper by E. Bruche on “Wirkungsquerschnitt und Molekulbau”1 it is stated on p. 1105 that the curve which shows the variation of the effective cross-section of methane molecules with respect to slow electrons for different velocities of the electrons (we shall call these curves Q-V-curves, since the velocity is given in terms of volts) is of the argon type, namely, that as the velocity of the electrons decreases from 4 volts to 1 volt (that is, from 2V to 1V) the Q-V-curve passes through a maximum and then rapidly sinks to a much lower value. This result was also obtained by R. B. Brode.2 In a later paper by C. Ramsauer and R. Kollath,3 Bruche's Q-V-curve is extended to still lower electronic velocities (to about 0.39V) and is found to pass through a minimum. We have now determined the Q-V-curve for methane by Townsend's diffusion method and have also found that the absolute value of the effective cross-section Q of methane molecules is very low, like that of argon, and that the Q-V-curves of argon and methane closely resemble each other over the range of velocities investigated, which in our case was from 1.74V down, to 0.3V. The minimum Q obtained for methane by Ramsauer and Kollath was 4.7 cm.2/cm.3 at a velocity of 0.62V; our value is 4.3 cm.2/cm.3 at a velocity of 0.52V. The minimum in our curve is a little less sharp than in the curve of Ramsauer and Kollath.