A.— MATHEMATICAL AND PHYSICAL SCIENCES. 31 



lines of force. Gunn estimates that at heights as low as 140 kilometres w 

 is very great compared with N, so that the conductivity approaches zero 

 value. Hence, in layers where the conductivity transverse to the magnetic 

 field is very small, such large circulating currents as are necessary for the 

 dynamo effect cannot flow, and where there is an apjireciable vertical 

 magnetic field there can be but negligible horizontal electric currents. 

 In the case considered by Gunn, where a charge in its spiral path can 

 execute many revolutions between successive collisions, the spiral motion 

 of the charge has the same effect as a small magnet opposed to the field, 

 so that the whole hemispherical cap is equivalent to a diamagnetic layer, 

 and to this diamagnetism Gunn attributes the diurnal variation. 



There appears to be no doubt that such a diamagnetic effect does exist, 

 and that it contributes to the diurnal variations, but it will be shown that 

 its magnitude is much too small to explain the whole of the diurnal varia- 

 tion. 



The intensity of magnetisation of the layer may be written — NKT/H 

 Avhere N is the number of ions per square centimetre column, K is Boltz- 

 mann's constant, H is the intensity of the magnetic field, and T the 

 absolute temperature. Since N and T are greater in the daytime than at 

 night, it follows that the diamagnetic effect will be greater during the day, 

 and greater in summer than in winter. Gunn assumed a height for the 

 diamagnetic layer between 150 and 180 kilometres, and assumed an 

 absolute temperature of 1,000° K. He further assumed that the number 

 of ions per cubic centimetre is proportional to the intensity of the incident 

 solar radiation plus a number of residual ions left during the night period, 

 but of course these latter take no part in the variation. With such data 

 Gunn has calculated the maximum variation of the horizontal force due 

 to the diamagnetic effect of the cap, and has got most excellent agreement 

 with the observed changes. However, Gunn had to assume a value for N 

 which is far greater than that given by Pederson, but as the latter includes 

 no figures for the other ionised layers it is not safe to draw too definite 

 conclusions. 



When the effect of gravity is taken into account, Chapman has 

 shown how, with the same value of N, the ionisation in the diamagnetic 

 layer contributes far more effectively to the diurnal variation. It is 

 shown that the less the contribution made by a charged particle to the 

 transverse conductivity (relative to the magnetic field) the greater is the 

 mean drift velocity which it experiences, and in the case of the earth's 

 magnetic field such drift currents are eastward in direction. There is, in 

 fact, a steady drift of electrons and ions in a direction perpendicular to 

 the lines of magnetic force and the gravitational field. The drift velocity 

 is greatest at the equator, and, if the ionisation is constant, the velocity 

 decreases as the pole is approached in the ratio sin 6/(1 + 3 cos^ 9). 

 Taking Pederson's value for the number of electrons and ions per cubic 

 centimetre, the equatorial current intensity has been calculated by 

 Chapman to be 4X 10"' e.m.u., which, however, is only about one-fiftieth 

 of the equatorial current intensity required to account for the variations 

 observed. However, Pederson's values may be too low. But for the 

 same ionisation values the effect is much greater than the diamagnetic 

 effect, and this naturally puts the diamagnetic effect into the position of 



