LONDON. Royal Society, May 6.—Sir J. J. Thomson, president, in the chair.—R. H. Fowler; E. C. Gallop, C. N. H. Lock, and H. W. Richmond: The aerodynamics of a spinning shell. This paper deals with the motion through a gas or a body with an axis of symmetry and a spin about that axis. The range of velocities includes the velocity of sound in the gas. It has special reference to the motion of an ordinary shell through air under gravity. The problem is approached from the aerodynamical viewpoint. The force system imposed by the gas is analysed into its most important constituents by help of the theory of dimensions and by detailed wind-channel experiments. The general equations of motion are obtained in a vector notation, and reduced to tractable approximate forms in certain important special cases; in particular, when the axis of symmetry and the direction of motion of the centre of gravity nearly coincide. An approximate formal solution of these last equations is obtained, and the errors in the equations themselves and their solutions are shown to be negligible. The solutions obtained are submitted to the test of experiment and the magni tude of the more important members of the force system determined numerically as functions of the velocity of the shell up to twice the velocity of soundi At the same time the main assumptions made in the analysis are verified. The experimental method used istofiretheshell throughaseriesofcards. The shape of the holes leftin the cards determines accurately the angular motion of the axis of the shell. From this the values of the chief components of the force system are deduced. One of the principal results is to determine accurately the spin required to render the shellstable at anyvelocity. Thebehaviour of the force components as functions of the velocity appearstobe of scientificinterest, andofobvious importanceintechnicalballistics. Prof. W.E. Dalby: Researchesonthe elastic propertiesand the plastic extension of metals. This paper relates to a new type of load-extension diagram recordedautomatically by an adaptation of an instrument already described tothesociety. The extensionof the test piece is multiplied 150 times by the instrument. With thismagnification, about Tio extensionisshownon the negative, and the elastic line appears at a slope of about 60°.The shape of the elastic line can therefore be studied and the process of extensioncan be watched, so that stretching can be stopped at ah assignedvalueandtheloadremovedandthenreapplied. The removal and re-application of the load producealooponthediagram,and several such loops can be described on each negative. Looped diagrams taken from metals commonly used were shown. Comparisons of these looped diagrams show that each metal is characterised by its elastic line and loops. A succession of plates was taken from a test piece of high carbon steel stretched almost to breaking. These plates set end to end give a procession of loops, and show that the loop area tends to a maximum. The questions of time-interval between the taking of loops and heat treatment between the taking of loops are examined in relation to loop area. It is shown that in the high carbon steel and alloy steel lapse of time has little or no effect in restoring elasticity, nor is the elasticity restored by boiling in water. New data relating to the strength of materials are given bv these diagrams, viz.: (1) The area of the loop. (2) The rate of increase of the area of the loop. (3) The maximum area.—C. T. R. Wilson: Investigations on lightning discharges and on the electric field of thunderstorms. The investigations were carried out at the Solar Physics Observatory, Cambridge, by methods already described (Proceedings, 1916). Apparatus has been added to secure a photographic record of the readings of the capillarv electrometer used in the measurements. Changes in the electric field which occupy less than a tenth of a second are recorded. The sudden changes produced in the potential gradient by the passage of lightning discharges recorded in 1917 were positive in 432 cases and negative in 279. The mean value of the electric moment 2QH (Q beingthe quantitvdischarged and H the vertical height through which thischarge is displaced) of a lightning discharge is about 3 × 1016 e.s.u. × cm. or 100 coulomb-kilometres. The mean Quantity discharged is of the order of 20 coulombs. The magnitude of the potentials attained in thunderclouds is of the order of 109 volts. The rate of vertical separation of charges in a thundercloud may amount to some coulombs per second, i.e. the vertical current through the cloud is of the order of some amperes. A thundercloud or showercloud mav be regarded as an electric generator, capable of maintaining between its poles an electromotive force of the order of ioy volts. It tends to maintain an electric current from the earth to the conducting layers of the upper atmosphere or in the reverse direction, according as its polarity is – or +. The difference which must exist in the conductivity of the air above showerclouds of + and of ¢ polarity respectively, owing to the large difference between the mobilities of the negative and positive ions dragged out of the conducting layer by the field of the cloud, furnishes a possible explanation of the normal positive potential gradient at a distance from showerclouds. It is also shown that it will account for the prevailing negative sign of the potential gradients associated with showerclouds and for the preponderance of positively charged rain and positive lightning discharges, i.e. discharges which produce a positive change of potential gradient.—L. F. Richardson: The supply of energy to atmospheric eddies. Osborne Revnolds investigated the energv of eddies as a balance between income and expenditure. The income was the activity of the eddy stresses upon the corresponding rates of mean strain; the expenditure was by way of molecular viscosity. His theory refers to an incompressible liquid, but it is shown in the present paper that the same applies to an elastic fluid. In a gravitating atmosphere there is an additional channel for gain or loss, because the eddies act as thermodynamic engines, either producing or decreasing inequalities of temperature. Thev are, however, imperfect engines. It is shown that the activity contributed by the eddies by this process is
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