682 BEPORT— 1893. 



6. On the Period of Vibration of Electrical Disturbances upon the Earth. 

 By Professor G. F. FitzGeeald, Sc.D., M.A., F.E.S., F.T.C.D. 



Professor J. J. Thomson and Mr. 0. Heaviside have calculated the period of 

 vibration on a sphere alone in space and found it about '059 second. The fact 

 that the upper regions of the atmosphere conduct makes it possible that there is a 

 period of vibration due to the vibrations similar to those on a sphere surrounded 

 by a concentric spherical shell. In calculating this case it is not necessary to con- 

 sider propagation in time for an approximate result, and it was pointed out that a 

 roughly approximate result could be obtained by equating the electric force at the 

 centre of the earth to a simply harmonic distribution of electricity on its sur- 

 face and on that of a concentric shell, to the electric force due to the rate of varia- 

 tion of the Vector potential of the electric currents calculated on the assumption of 

 a simply periodic variation of the electric distribution. It appears that the dis- 

 placement currents between the outer and inner shells are the only contributors to 

 the Vector potential. The value of the time of vibration obtained by this very 

 simple approximation is 



rp_ /2Kfumogalb 



Applying this to the case of the earth with a conducting layer at a height of 100 

 kilometres (much higher than is probable) it appears that a period of vibration of 

 about one second would be possible. A variation in the height of the conducting 

 layer produces only a small effect upon this if the height be small compared with 

 the diameter of the earth. In the case of the sun the period of vibration would 

 be about a hundred times as great. An approximate estimate was made as to the 

 electric density at the pole required to produce a horizontal force at the equator 

 equal to about the hundredth part of the earth's horizontal force, and it was found 

 to be eight electrostatic units per square centimetre. Anything very much greater 

 than this should produce a measurable reduction of barometric pressure. Atten- 

 tion was called to the desirability of having a sufficient number of magnetic 

 stations in a ring round the magnetic pole to be able to determine whether there 

 were simultaneous, easterly or westerly, waves of disturbance of horizontal force. 

 Such a simultaneous disturbance, of which there was some evidence from the pre- 

 sent sparsely distributed observatories, would mean that there was an earth current 

 which was running through the earth in such a way that it must be continued by 

 auroral discharges in the upper regions of the air. 



7. The Moon^s Atmosphere and the Kinetic Theory of Gases. 

 By G. H. Brtan, M.A. 



[The possibility of applying the kinetic theory of gases to explain the absence 

 of any perceptible atmosphere round the Moon seems to have been contemplated 

 ever since the earliest days of the kinetic theory itself. Mr. S. Tolver Preston 

 claims to have been the first to suggest this explanation (' Nature,' Nov. 7, 1878) ; 

 but the idea was thought of long before then, for "Waterston, in his now well- 

 known paper on 'The Physics of Media' (' Phil. Trans. R.S.,' 1892 [A]), specially 

 considers the problem of the Moon's atmosphere. His investigation would, how- 

 ever, require all the molecules of a gas to have the same velocity, which we now 

 know to be incorrect, and it leads to the conclusion that the existence of a lunar 

 atmosphere would be possible at ordinary temperatures.] 



Now, according to the well-known 'error' law of distribution of velocity 

 among the molecules of a gas, there must always be some molecules moving with 

 sufficiently great speeds to overcome the attraction of any body, however powerful, 

 and some whose speed is too small to enable them to escape from the attraction of 

 any body, however feeble. On this assumption no planet would theoretically 

 have an absolutely permanent atmosphere. If, however, the proportion of mole- 

 cules which escape is relatively exceedingly small, the atmosphere of the planet 

 may be regarded as practically permanent. In order, therefore, to test the relative 



