210 C. F. GAUSS ON THE GENERAL THEORY OF 



given in Art. 22, consists in the unknown values being broken 

 into groups, each of which is determined by itself, whereby the 

 calculation is greatly facilitated ; whereas, in the other mode of 

 proceeding, the intermingung of all the unknown quantities 

 renders their separation extremely difficult. On the other hand, 

 the disadvantage of the second method is, that, instead of being 

 founded on direct observation, it rests on graphical representa- 

 tions, which, in districts where we do possess observations, re- 

 present them but rudely, and which, in districts where observa- 

 tions are wanting, are only conjectural, and, to a certain degree, 

 arbitrary, and may therefore differ considerably from the truth. 

 However, we must either postpone all attempts, till such time as 

 we shall be provided with far more complete and trustworthy 

 data than we now possess, or, with our present very scanty 

 means, make a first attempt, from which we are entitled to ex- 

 pect little more than a rough approximation. A close compari- 

 son of the results of calculation with those of actual observa- 

 tion in all parts of the earth, furnishes a certain standard by 

 which our success may be estimated. And if this test shall 

 show that the first attempt has not entirely failed, it will power- 

 fully assist suitable preparations for future fresh attempts by 

 either method. 



25. 



Several years ago I repeatedly began attempts of this kind, 

 from all of which the great inadequacy of the data at my com- 

 mand forced me to desist. I might earlier have concluded such 

 an essay if I had obtained the fulfilment of my often-expressed 

 wish for a general map representing the horizontal intensity. 

 This want could not be supplied by the combination of the im- 

 perfect general maps of dip and of total intensity, then existing. 



The appearance of Sabine's Map of the Total Intensity (in the 

 Seventh Report of the British Association for the Advancement 

 of Science) has stimulated me to undertake and complete a new 

 attempt, which must be regarded, however, only in the Ught 

 mentioned in the foregoing article. The data employed in the 

 calcidations are for twelve points on seven parallels. They are 

 taken for the intensity from the above-mentioned map ; for the 

 declination from Barlow's map {Phil. Trans. 1 833) ; and for the 

 inclination from Horner's map {Physikalisches Worterbuch, 

 Band vi.). Considerable portions of these maps still remain blank. 



