72 NOTES TO BOOK XII. 



at any given time, if known, can be expressed by charts of 

 the earth's surface, on which are drawn the isodynamic, 

 isogonal, and isoclinal curves. The second of these kinds 

 of charts contain the "Halleian lines 1 ' spoken of in page 

 62. Moreover the magnetic elements at each place are to 

 be observed in such a manner as to determine both their 

 periodical variations, (the changes which occur in the 

 poriod of a day, and of a year,) the secular changes, as the 

 gradual increase or diminution of the declination at the 

 same place for many years ; and the irregular fluctuations 

 which, as we have said, are simultaneous over a large part, 

 or the whole, of the earth's surface. 



When these Facts have been ascertained over the 

 whole extent of the earth's surface, we shall still have to 

 enquire what is the Cause of the changes in the forces 

 which these phenomena disclose. But as a basis for all 

 speculation on that subject, we must know the law of the 

 phenomena, and of the forces which immediately produce 

 them. I have already said that Euler tried to account for 

 the Halleian lines by means of two magnetic " poles," but 

 that M. Hansteen conceived it necessary to assume four. 

 But an entirely new light has been thrown upon this sub- 

 ject by the beautiful investigations of Gauss, in his Theory 

 of Terrestrial Magnetism, published in 1839. He remarks 

 that the term " poles," as used by his predecessors, in- 

 volves an assumption arbitrary, and, as it is now found, 

 false ; namely, that certain definite points, two, four, or 

 more, acting according to the laws of ordinary magnetical 

 poles, will explain the phenomena. He starts from a more 

 comprehensive assumption, that magnetism is distributed 

 throughout the mass of the earth in an unknown manner. 

 On this assumption he obtains a function V, by the dif- 



