A.— MATHEMATICAL AND PHYSICAL SCIENCES. 27 



second, but the results obtained differ very appreciably from those calcu- 

 lated on the theory, i.e. an effect proportional to co^r'. 



As theory after theory breaks down when the calculated magnetic 

 effects are compared with those actually observed on the earth, we are 

 forced to conclude that our knowledge of the cause of the earth's magnetism 

 is little more than conjecture, for of the theories put forward all that have 

 been put to a practical test have been found wanting in some respect. 

 Larmor's theory of internal rotation in a meridianal plane cannot be put 

 to a laboratory test, and other theories based on slight departures from 

 the accepted laws of electrodynamics are equally difficult to decide in the 

 laboratory. It is possible that when we know the cause of terrestrial 

 magnetism we shall know also the cause of gravitation. But it may be 

 that we shall have to wait for many generations before the results of 

 observations may confirm a theory. Swann, in putting forward his 

 modifications to the accepted laws of electrodynamics, remarks that the 

 positive electricity of the earth would, according to his theory, gradually 

 disappear, but the disappearance of one half of 1 per cent, of it would 

 take a hundred million million million years, which is rather a long time. 



Vertical Electric Currents. 



There is, however, a possibility that a small portion of the earth's 

 magnetic field may be due to vertical electric earth-air currents, which 

 can easily be distinguished from currents circulating in the upper 

 atmosphere or in regions beyond. If all electric currents are parallel to 

 the earth's surface in the form of current sheets or the circuits are such 

 that no portion of the earth's surface is included in them, then the line 

 integral of the horizontal magnetic force around any closed area on the 

 earth must be zero, since no element of current is enclosed by the area. 

 If, however, an electric circuit cuts the earth's surface, the resulting 

 magnetic intensity may be regarded as due in part to a current sheet 

 parallel to the earth's surface and in part to a vertical current. In such 

 case the line integral of the horizontal magnetic force taken round a 

 closed area will not vanish but be equal to iv: times the enclosed current, 

 and from its magnitude and sign the intensity and direction of the earth- 

 air electric current within the closed area may be calculated. Gauss 

 first applied such a test and found the line integral around a triangular 

 area to be zero within the limits of the errors of observation. 



Adolf Schmidt developed the work of Gauss, and on the basis of the 

 Neumayer magnetic charts of 1885 found evidence for the existence of 

 such earth-air electric currents. Schmidt's first estimate of the magnitude 

 of such vertical currents, namely, 0.16 ampere per square kilometre, was 

 no doubt excessive, and he concluded that the estimate was erroneous 

 because of systematic errors in the charts. 



Riicker chose areas in Great Britain, where the magnetic forces were 

 well known, and failed to find any evidence of such vertical currents. 

 Dyson and Furner made an examination of data available in 1922, and 

 Conclude that although there is some evidence, such currents are not 

 indicated with any certainty. On the other hand, Bauer has made 

 many calculations, and on all occasions has been forced to conclude that 

 Buch vertical currents do exist. In 1896 he computed line integrals, taking 



