REPORT ON THE MAGNETISM OF THE EARTH. 121 



Humboldt was the first who determined that the intensity of 

 the whole magnetic force is different at different positions on 

 the earth's surface. Having made observations on the times of 

 vibration of the same dipping needle, at various stations in the 

 vicinity of the equator, and approaching to the northern pole, 

 he found that the intensity of the terrestrial force decreases in 

 approaching the equator ; but no precise law, according to which 

 the intensity depends upon the distance from the equator, can 

 be determined from these observations. Numbei'less observa- 

 tions have since been made in both hemispheres, with every 

 precaution to ensure accuracy in the results, but they do not in 

 general accord with the theoretical formulae with which they 

 have been compared. 



On the hypothesis of two magnetic poles not far removed 

 from the centre of the earth, if 8 represent the dip, \ the mag- 

 netic latitude of the place of observation, I the intensity of the 

 force in the direction of the dip, and m a constant, then 



1 = 



and therefore, 



\/{4-3 sin2 8)' 

 tan S = 2 tan A ; 



I=|^(3sin^A+ 1); 



or if i is the angular distance from the magnetic pole, or the 

 complement of the latitude, 



1 := '± ^ {3 cosH + I). 



By comparing his own observations with the first of these 

 formulae, Captain Sabine came to the conclusion that they were 

 " decisive against the supposed relation of the force to the ob- 

 served dip, and equally so against any other relation whatso- 

 ever, in which the respective phaenomena might be supposed to 

 vary in correspondence with each other." Comparing them, 

 however, with the last formula, he concludes that " the accord- 

 ance of the experimental results with the general law proposed 

 for their representation, cannot be contemplated as otherwise 

 than most striking and remarkable." How the same set of 

 observations should be in remarkable accordance with the one 

 formula and at variance with the other, when these formulae are 

 dependent on each other, it is difficult to conceive ; but the 

 conclusion drawn by Captain Sabine from his observations, at 

 least shows the danger of relying upon any single set of obser- 

 vations as confirmatory or subversive of theoretical views. I 



