Societies and Academies

Abstract

LONDON. Royal Society, June 17.—Sir William Crookes, president, in the chair.-Dr. E. J. Russell: Soil protozoa and soil bacteria. In view of the claim recently made by Goodey that soil protozoa cannot function as a factor limiting the numbers of bacteria in soils, the author has brought together the evidence on which this view is based. It has been shown in numerous experiments that the numbers of bacteria in normal soils are relatively low, but they can be raised by any treatment that kills trophic forms and not spores. Starting, in the first instance, to find the properties of the factor which keeps down the bacterial numbers, and without framing any hypothesis as to its nature, these were found to be:(a) active, and not a lack of some essential;(b) not bacterial;(c) extinguished by heat or poisons, and after extinction does not reappear;(d) can be reintroduced by adding a little untreated soil;(e) is favoured by conditions favourable to trophic life in the soil. These properties indicate that the factor is biological. Search was therefore made for organisms fulfilling these conditions and numbers of protozoa were found. Definite evidence has been obtained that trophic forms occur as normal inhabitants of the soil, and the estimates of numbers so far available show that they are considerable. There is the closest possible relationship between the extinction of the protozoa and the extinction of the limitingâ factor, and also between the re-establishment of the protozoan fauna and the settingâ up of the limiting factor after reinfection with small quantities of soil.-Prof. W. M. Hicks: The enhanced series of lines in spectra of the alkaline earths. A discussion of the enhanced series of the alkaline earths is carried out in order to determine their relation to the sun. For this purpose the results given for Mg, Ca, Sr by Fowler in his recent Bakerian Lecture are used, and, in addition, the corresponding series in Ba and Ra are considered. It is found that the quantity?', giving the doublet separations, is given with great accuracy in terms of the oun, as follows:-Mg, 568; Ca, 6; Sr, 588; Ba, 56P; Ra, 6?1?; where is four times the corresponding oun for the element. The satellite separations are also found as functions of the same quantity. Further it is shown that these series strongly support the general relations given in a former communication that the first ^-sequence depends on a multiple of the atomic volume, and that the diffuse sequence is such that the denominators of the first lines, when the wave number is expressed in the form A-?/(den)2, are themselves multiples of A' or of the oun.-Prof. H. F. Baker: Certain linear differential equations of astronomical interest. This paper is written to exemplify the application of a general method for the solution of linear differential equations given by the author some years ago. The method furnishes solutions in a form valid for an indefinitely extended region. It is here applied(1) to establish a result as to the convergence of the solution of a particular equation, apparently in disagreement with a conclusion reached by Poincare in his “Methodes Nouvelles de la Mecanique Celeste“;(2) to place the general method given by Laplace for the absorption of the time in astronomical series under trigonometrical signs in connection with the ordinary theory of characteristic exponents;(3) to discuss in general terms the oscillations of a dynamical system about any given possible state of motion;(4) to furnish a regular calculus for the solution of the equation used by G. W. Hill for the motion of the moon's perigee, and similar equations. The earlier part of the paper discusses particular equations from a less formal point of view, and has seemed necessary in order to place the matter in proper light. One particular problem discussed is that of the stability of three bodies of any masses moving in ellipses at the angular points of an equilateral triangle, a matter of which the discussion has recently been revived.—Prof. Karl Pearson: The partial correlation-ratio. The general theory of mutiple correlation has been long established, and is summed up in the discussion of two constants-the partial correlation coefficient and the multiple correlation coefficient. If there be m variates, 1,2,3. . . m, then the partial correlation coefficient of the (tn -2)nd order is related to the multiple correlation coefficients of the (m – 1)th and (m – 2)nd orders by the equation:—