Showing papers in "Philosophical Transactions of the Royal Society A in 1930"

On the Stresses in the Neighbourhood of a Circular Hole in a Strip under Tension

Abstract: The problem of determining the stresses in a plate under tension when the material is pierced by one or more circular holes is one of both theoretical interest and practical importance. Provided that the plate may be regarded as infinitely extended in two dimensions, the solution for a single hole is easily found and is well known. The presence of the hole leads to the occurrence of stresses equal to three times the tension at infinity, these maximum stresses occurring at the edge of the hole and on the diameter perpendicular to the direction of the applied tension. More general stress systems, corresponding to the presence of tractions at the edge of the hole, may be studied by similar methods, not only when the plate is infinite but also when there is a second circular boundary concentric with the first. A number of special solutions for the infinite plate have recently been published by BICKLEY. The solution for a semi-infinite plate with one circular hole was obtained by JEFFREY, using bipolar co-ordinates,§ which may be applied also to the case of an infinite plate pierced by two holes

The Electric and Magnetic State of the Interior of the Earth, as Inferred from Terrestrial Magnetic Variations

Abstract: 1.1. By spherical harmonic analysis it is possible, as was shown by GAUSS, to distinguish between the parts of the earth’s magnetic field, at any time, which originate respectively within and above the earth’s surface. In this way GAUSS confirmed and extended GILBERT’s conclusion that the field is almost entirely of internal origin. 1.2. Sir ARTHUR SCHUSTER applied the method to the field of the daily magnetic variation at the earth’s surface, and found that the major part is of external origin, but that there is also a part produced within the earth. He attributed the latter to electric currents induced in the earth by the outer varying field, which he regarded as primary. In co-operation with Prof. H. LAMB he showed that the relation between the two parts of the field is consistent with this hypothesis ; the calculations referred to currents induced in a uniformly conducting sphere. They showed that the conducting sphere must be distinctly smaller than the earth, that is, it is an inner core, and not the whole earth, which is effective.

Microseisms Associated with Disturbed Weather in the Indian Seas

Abstract: Seismologists have often noted the appearance of pronounced microseisms in seismic records when the weather has been disturbed over a neighbouring sea. For instance, the late Dr. KLOTZ suggested a relationship between disturbed weather in the north Atlantic and the largest microseismic movements at Ottawa. Dr. HARRISON, writing in ' Nature,’ November 1, 1924, in continuation of a note* by the present writer, pointed out that well-marked microseisms in the Omori charts at Calcutta invariably confirmed other evidence in the case of the early stages of dangerous cyclones, and were sometimes noticed when the storm centre was so much as 1000 miles south of Calcutta. He did not, however, recall any instance in which microseisms were associated with ordinary rough weather or with an advance of the monsoon. On the other hand, “ investigation at Eskdalemuir of the possible connection between microseismical amplitude and the state of the sea at different points of the British coasts have yielded results of an inconclusive kind. For example, the correlation between the state of the sea and the Microseismic movements of a type, which were quite characteristic of the south-west monsoon period, made their first appearance in the seismograms generally in May with the advance of the monsoon in the south-east Arabian Sea, becoming more and more pronounced as the monsoon currents approached Bombay. They became less marked or disappeared during a temporary break in the monsoon and reappeared with the strengthening of the currents. They were more or less steady vibrations having periods ranging from 4 to 10 seconds.

The Polytopes with Regular-Prismatic Vertex Figures

Abstract: The regular polytopes in two and three dimensions (polygons and polyhedra) and the “Archimedean solids ” have been known since ancient times. To these, KEPLER and POINSOT added the regular star-polyhedra. About the middle of last century, L. SCHLAFLI* discovered the (convex) regular polytopes in more dimensions. As he was ignorant of two of the four KEPLER-POINSOT polyhedra, his enumeration of the analogous star-polytopes in four dimensions remained to be completed by E. HESS. Recently, D. M. Y. SOMMERVILLE interpreted the (convex) regular polytopes as partitions of elliptic space, and considered the analogous partitions of hyperbolic space. Some particular processes, for constructing “ uniform ” polytopes analogous to the Archimedean solids, were discovered by Mrs. BOOLE STOTT and discussed in great detail (with the help of co-ordinates) by Prof. SCHOUTE. Further, E. L. ELTE completely enumerated all the uniform polytopes having a certain “ degree of regularity,” these including seven new ones (in six, seven and eight dimensions).

On the problem of hydrodynamic stability. I. uniform shearing motion in a viscous fluid

Abstract: 1. Except in a few very simple cases, the equations which govern the motion of a viscous fluid have so far defied analysis. Their difficulty comes mainly from the fact that they are not linear, so that the principle of superposition cannot be employed, as in many branches of mathematical physics, to construct solutions by the method of series or of singularities. For the same reason the flow pattern in the neighbourhood of a moving body must alter when the speed of the body is changed, and it follows that any exact determination of the pattern will be restricted to some definite speed. As a matter of fact, no precise determination of this kind exists, except in cases where the motion is indefinitely slow. But the form of the equations gives no reason for doubting the possibility of “steady” motion (in which the velocities are functions only of position) in every case of flow past fixed and rigid boundaries. Now in experiment it is found (unless the velocities are very small) that eddying or periodic motions always occur. Thus the conclusion seems inevitable that a steady motion may become unstable as the rate of flow is increased, in the sense that accidental disturbances, if of suitable type, will persist.

The International Temperature Scale between 0 degrees and 100 degrees C

Abstract: The aim of the work set out in the following paper is to secure as accurate as possible a knowledge of the difference between the scales defined by the platinum resistance thermometer and the mercury in verre dur thermometer. The readings of the former are reduced by the customary quadratic equation of CALLENDAR, and the latter by using the corrections to the constant volume hydrogen scale, as determined by CHAPPUIS.* The reasons for undertaking the intercomparison may be set out briefly as follows :— In 1887 the International Committee of Weights and Measures adopted as the standard scale of temperature that of the constant volume hydrogen thermometer set up by CHAPPUIS at the Bureau International at Sevres. In order to make this scale available to investigators elsewhere, primary standard mercury in verre dur thermometers were prepared by TONNELOT of Paris to the specification of the Bureau International, and CHAPPUIS made a careful comparison between eight of these mercury thermometers and his hydrogen thermometer over the range — 24° C. to 100° C.