24 



NA TURE 



[\0VEiVIBER 5, I< 



ologists and other men of science who were confronted by 

 phenomena in which the characteristics of wave motion 

 appeared prominent. First there were the large-scale 

 oscillations of the atmosphere, shown in the oscillation 

 of barometric pressure. These waves were not mainly 

 gravitational. The principal periods of their free oscilla- 

 tion are 22, 16, . . hours. If we take into account the 

 rotation of the earth, the character of the oscillation and 

 the periods are modified. Laplace's theorv of the tides, 

 which has been very much improved by Hough, applies 

 to an ocean covering the globe, and the only difficulty 

 that arises when we wish to apply this to the atmosphere 

 comes from differences of temperature. If we neglect 

 these differences and apply Hough's theory to the atmo- 

 sphere, the second type of oscillation has a period of about 

 twelve hours. If we examine the facts as recorded by 

 the barometer, we find the well-known diurnal oscillation 

 irregular in amplitude and phase, and depending in a 

 marked way on the height above sea-level, and, secondly, 

 the semi-diurnal oscillation, extremely regular in amplitude 

 for places in the same latitude and 'in phase for places in 

 the same longitude. 



The first thing that suggests itself is that this is a tide 

 caused by the sun's attraction ; but the corresponding lunar 

 tide ought to be more marked, whereas, actually, the 

 lunar tide is almost absent. Moreover, the phase is wrong 

 m sign, and it is too big. Lord Kelvin was the first to 

 suggest that the semi-diurnal tide was a temperature 

 effect. The daily variation of temperature is not harmonic 

 and when it is analysed there is a definite component with 

 a half-day period. The objection to attributing the semi- 

 diurnal pressure variation to this is that the latter is 

 extremely regular, while the temperature variation changes 

 considerably with the locality. IMargules has shown that 

 on a rotating earth the period of free oscillation of the 

 atmosphere lies very near to twelve hours, and con- 

 sequently a forced oscillation of this period would be 

 magnified. 



Passing on to local oscillations, Prof. Lamb said these 

 were probably mainly gravitational. The atmosphere 

 might be treated as an incompressible fluid because of 

 the relatively large value of the velocity of sound. 



If we have two fluids of densities p and p', with a hori- 

 zontal surface of separation, the velocity of waves at this 



surface is f&L £ZZ'. Waves of this type occurring in 



>- 27r p + p 

 the atmosphere would not appreciably affect the barometer 

 at a place some distance below the surface of separation 

 owing to the fact that the intensity of the disturbance 

 diminishes exponentially. Only in the case of very lone 

 vyaves should we expect the oscillation to be shown on 

 the barometric curve. 



If the upper fluid is the denser, the amplitude of the 

 disturbance increases rapidly, and we mav get a series 

 of filaments as the result of disturbance. So long ago as 

 1857 Stanley Jevons conceived the possibility of cirrus 

 clouds arising m this way, and made experiments with 

 liquids in verification. 



If the change of density is not abrupt, but takes place 

 across a transition layer, the character of the motion may 

 change. It is probable that the structure of the disturb- 

 ance will be larger. If we have difference of velocity as 

 well as of density, the wave-velocity at the surface of 

 separation is given by 



p + p \ 2Tr p + p' (p + p'f 



. p)- 



If X is small, the expression under the root becomes 

 negative, indicating that the condition of affairs is un- 

 stable. This instability is more effective than viscosity in 

 reducing an abrupt change of velocity to a gradual change 

 taking place across a transition layer. The question then 

 arises as to whether we get rid of the instabilitv when 

 the change becomes a gradual one. Helmholtz 'investi- 

 gated the problem of waves at a surface of separation in 

 the atmosphere. He concluded that, instead of instability, 

 we might have waves of permanent type of finite ampli- 

 tude. The question of the stability of 'these waves is still 

 an open one. 



In the application to the atmosphere it is deduced that 

 NO. 2036, VOL. 79] 



at the crests of the waves there may be sufficient con- 

 densation through the expansion and cooling of the air to 

 make the crests visible. Before this can be settled we 

 need a picture of what really does happen when we cross 

 a layer where these wave-like clouds are formed. Mathe- 

 maticians have gone nearly as far as they are able without 

 precise information on such points. 



Dr. Shaw then showed some lantern-slides illustrating 

 wave motion in the atmosphere recorded by the micro- 

 barograph. In some cases a large sudden increase or 

 decrease in the pressure was followed by a series of waves 

 falling off rapidly in intensity. In other cases similar 

 sudden changes were unaccompanied by waves, while in 

 others still waves were formed without any sudden change 

 occurring. He suggested the possibility of a current of 

 air in rapid motion acquiring a dynamical stability as the 

 result of the motion in such a way that a disturbance of 

 the current might produce an oscillation of the current 

 as a whole in a horizontal direction. 



Mr. Wedderburn gave the results of observations of 

 temperature in Loch Ness, showing how temperature 

 oscillations arose from the circulation of the water. He 

 showed the results of experiments on the circulation of 

 water in a vessel of parabolic cross-section over which 

 a strong current of air was passing. The liquid circulated 

 in two distinct systems with a definite surface of separa- 

 tion. 



Sir William White spoke on ocean waves and on the 

 importance of the new experimental tank to be set up at 

 the National Physical Laboratory. 



Prof. Lamb's paper has been ordered to be printed in 

 full in the report. 



.At the conclusion of this discussion the section again 

 trifurcated. 



In the department of mathematics, Sir Robert Ball 

 opened the meeting with an account of the physical appli- 

 cations of the theory of screws, and referred specially to 

 the excellent work done by the late Prof. C. J. Joly on 

 quaternions, in which the present paper had its origin. 

 Sir Robert showed that the theory of linear vector func- 

 tions was really identical with that of the composition of 

 screws, and that the whole subject became thereby much 

 simplified, and the formulas far more concisely expressed. 



Dr. T. W. Nicholson read a paper on the inductance of 

 two parallel wires. The author stated that the ordinary 

 formula is inaccurate when the currents are of high fre- 

 quency ; in the present paper new formulae are given 

 which give a correct result for frequencies as high as lo'. 



Prof. F. Purser contributed a paper on the rtther stress 

 of gravitation. Maxwell had selected as a particular solu- 

 tion of the fundamental equations a pressure R'/Stt along 

 the lines of gravitating force, and an equal tension per- 

 pendicular to these lines, R being the resultant force of 

 gravitation on unit mass, but there are difficulties in 

 accounting for these by corresponding strains. Prof. 

 Purser shows that the difficulties are removed if we con- 

 sider that we are not bound to Maxwell's special solution, 

 but may take such a solution as may be deduced from a 

 state of strain according to the laws for (say) a homo- 

 geneous isotropic fether. 



Several papers were taken as read in the absence of the 

 authors. 



The proceedings in the department of general physics 

 commenced with a paper by Sir W. de W. Abney, K.C.B., 

 on a new three-colour camera, in which the stereoscopic 

 effect arising when three images are taken simultaneously 

 by three lenses lying side by side is reduced to a minimum. 

 Incidentally, it was pointed out that in this camera the 

 mirrors are made of steel varnished with celluloid dis- 

 solved in acetone. Dr. Harker directed attention to 

 Cowper-Coles's use of metallic cobalt, and Prof. W. F. 

 Barrett, who was in the chair, strongly recommended 

 galena for the purpose. 



Sir Oliver Lodge described a new method for measuring 

 large inductances containing iron which has been devised 

 by him in collaboration with Mr. Benjamin Davies. A 

 special galvanometer, consisting of a well-damped coil 

 moving dead heat in a strong magnetic field, is connected 

 in series with the inductance and a specially designed 

 alternator giving a simple harmonic current. A switch 

 enables the inductance to be suddenly replaced by a non- 



