DETERMINATION OK THE GAUSSIAN MAGNETIC CONSTANTS. 109 



An Account of the late Professor Jonx Couch Adams's Determination of 

 the Gaussian Magnetic Constants. By Professor W. Grylls Adams. 



I propose to give the Conference a short account of the work done by my 

 brother on the theory of terrestrial magnetism, and to give his determina- 

 tion of the Gaussian magnetic constants. This work was first taken up by 

 the late Professor John Couch Adams just fifty years ago, not long after the 

 discovery of the planet Neptune. I find from his papers, which he delivered 

 to me before his death, and which he asked me to examine to see if they 

 could be brought into form for publication, that the earliest work which he 

 did on this subject was begun in the year 1849, and that he was led to it 

 by the study of the translation of Gauss's Memoir on the Theory of Terres- 

 trial Magnetism given in Taylor's ' Scientific Memoirs ' which was published 

 in 1841. Gauss himself says in that memoir that he was stimulated to 

 undertake the work on the publication of Sabine's map of the total 

 intensity in the seventh Report of the British Association (i.e. in 1837), 

 but that the data are very scanty for the accurate determination of the 

 masmetic constants. For their accurate determination data should be 

 supplied from accurate observations of magnetic declination, horizontal 

 intensity, and dip, taken at stations uniformly distributed, as in a net- 

 work, over the surface of the Earth. 



Not only fifty years ago, when Gauss wrote, but even to the present 

 day, the progress made in the theory of terrestrial magnetism has suffered 

 from the lack of data derived from observations, because even now there 

 are few magnetic Observatories in existence, and those few are for the 

 most part grouped very close together, leaving other parts of the Earth, 

 and especially the southern hemisphere, almost entirely wanting in the 

 facts of observation without which all theories can be but visionary. 



In his calculations on the magnetic potential of the Earth and on the 

 theoretical expression of the magnetic components X, Y and Z, to the 

 north, to the west, and vertically downwards respectively, Gauss expressed 

 them for any point of the Earth's surface in series consisting of quantities 

 to which he gave the name of magnetic constants, with coefficients involving 

 Legendre's coefiicients, and which are functions of the colatitude of the 

 point. 



From the very imperfect data which he possessed. Gauss determined 

 the numerical values of the magnetic constants by his equations up to 

 terms of the fourth order — i.e. he determined the values of the first twenty- 

 four magnetic constants, three of the first order, five of the second, seven 

 of the third, and nine of the fourth order. 



No one could be more conscious of the fact than Gauss himself was 

 that his data were so meagre and so insufficient that he could by no means 

 rely on the values derived from them, and I fear that even now, at the 

 end of the nineteenth century, we must say with him that the observed 

 facts are far too scanty and that our stock of observations is still too small 

 to enable us to get out trustworthy values of the magnetic potential and 

 the magnetic elements for a given epoch. For this purpose the observa- 

 tions should be strictly contemporaneous, and we require more Observa- 

 tories where continuous records are taken. 



For Gauss's method, which was also the method followed in practice by 



