LONDON. Royal Society, December 6.—Sir J. J. Thomson, president, in the chair.—Prof. W. H. Young: The series of Legendre.—L. Hartshorn; The discharge of gases under high pressures. It is well known that when gas discharges through an orifice from a vessel in which the pressure is p0 into one in which it is pt, the rate of discharge is approximately constant from pi = o upwards to some critical value, but then, as £, further increases, the discharge falls off, slowly at first, after wards with greater rapidity. In the present investigation, this phenomenon is examined with greater accuracy than has hitherto been obtained. In every case it was found that the flow was constant to at least one part in 10,000 for a considerable range of £,. The critical value of pit at which the flow began to change, varied widely for different nozzles, being about 0-2 pa for the convergent and parallel ones, but as high as 0-7 p0 for certain divergent ones. Thus, the theoretical value for convergent nozzles, viz., 0-527 pa, cannot be accepted as applying even approximately to all nozzles.—Lt.-Col. A. G. Hadcock: Internal ballistics. This paper deals with the burning of the explosive in the gun and the expansion of the gas, both before and after the charge has been consumed. On firing the gun the action is threefold:-(1) The driving band on projectile is forced into the rifling grooves. (2) In subsequent burning of charge, the gas from any fraction of charge expands with consequent reduction of temperature. The still burning powder gives additional heat. The expansion is thus partly adiabatic and partly isothermal. (3) After the charge is consumed the gas expands adiabatically. From expressions given in the paper, and knowing the rate of burning of cordite under various pressures, formulas are developed for finding velocity of projectile, position in gun, and pressure of gas. The magnitude and position of maximum pressure are found by a further development of formula?.—Dr. A. Russell: The electrostatic problem of a conducting sphere in a spherical cavity. The author gives formulae by means of which the capacity, the electric force between the spheres, and the maximum electric stress on the dielectric between them can be readily computed in all cases to any required degree of accuracy. The solutions of these problems are required when determining the ratio of the measure of the electrostatic to the electromagnetic unit of charge by means of a spherical condenser for the calibration of a spherical condenser of variable capacity, for the o calibration of a high-tension voltmeter, and for the determination of the electric strengths of insulating materials.—Prof. G. N. Watson; The zeros of Bessel1 functions. The paper contains a statement and discussion of some general theorems concerning the zeros of Bessel functions; the theorems are true for functions of any order, and, unlike results previously known, are of particular interest in the case of functions of high order. It appears that comparatively general considerations of a non-arithmetical type yield fairly precise information concerning the position and numbers of the zeros of the Bessel functions of the first kind. It is doubtful whether results of this character could be obtained without making use of the method of steepest descents which has been prominent in various recent investigations.