

1889.] T/ie Diurnal Variation of Terrestrial Magnetism. 481 



to accumulate additional data derived from the examination of other 

 parallel cases, such as the ternary alloys obtained by adding tin to 

 the immiscible pairs of metals, zinc and bismuth, aluminium and 

 lead, and aluminium and bismuth ; or by similarly employing other 

 metals instead of tin. Nothing abnormal appears to characterise the 

 solubility curves of zinc in lead-tin and of lead in zinc-tin ; in each 

 case the amount of one metal dissolved by the other increases as the 

 quantity of tin present increases, in such a way that the curves are 

 somewhat concave upwards. 



IV. " The Diurnal Variation of Terrestrial Magnetism." By 

 ARTHUR SCHUSTER, F.R.S., Professor of Physics, with an 

 Appendix by H. LAMB, F.R.S., Professor of Mathematics, 

 Owens College, Manchester. Received March 20, 1889. 



(Abstract.) 



In the year 1839 Gauss published his celebrated Memoir on 

 Terrestrial Magnetism, in which the potential on the earth's surface 

 was calculated to twenty-four terms of a series of surface harmonics. 

 It was proved in this memoir that if the horizontal components of 

 magnetic force were known all over the earth the surface potential 

 could be derived without the help of the vertical forces, and it is well 

 known now how these latter can be used to separate the terms of the 

 potential which depend on internal from those which depend 011 

 external sources. Nevertheless, Gauss made use of the vertical 

 forces in his calculations of the surface potential, in order to ensure 

 a greater degree of accuracy. He assumed for this purpose that 

 magnetic matter was distributed through the interior of the earth, 

 and mentions the fair agreement between calculated and observed 

 facts as a justification of his assumption. In the latter part of the 

 memoir it was suggested that the same method should be employed 

 in the investigation of the regular and secular variations. 



The use of harmonic analysis to separate internal from external 

 causes has never been put to a practical test, but it seems to me to 

 be specially well adapted to inquiries on the causes of the periodic 

 oscillations of the magnetic needle. 



If the magnetic effects can be fairly represented by a single term 

 in the series of harmonics as far as the horizontal forces are con- 

 cerned, there should be no doubt as to the location of the disturbing 

 cause, for the vertical force should be in the opposite direction if the 

 origin is outside from what it should be if the origin is inside the 

 earth. As the expression for the potential contains in one case the 

 distance from the earth's centre in the numerator, in the other case 

 in the denominator, and as the vertical force depends on the diffe- 



