6 



Prof. W. A Norton on Terrestrial Magnetism. 



and PD, destroy each other. The same may be shown with re- 

 gard to the actions upon the south end of the needle. It follows, 

 therefore, that the needle will place itself at right angles to CPD, 

 the isogeothermal line passing through P the station of the nee- 

 dle. This is a consequence from our theory which, like the 

 formulae soon to be investigated, is to be tested by making com- 

 parisons with observations. 



Let us now deduce from the general principles which have 

 been laid down, the horizontal and vertical components of the di- 

 rective force of the needle. Fig. 3. 

 Let ApB, fig. 3, represent a 

 great circle of the earth, an- 

 swering to mPs, or nPr in fig. 

 2, Cp its radius, P the north 

 end of a magnetic needle, and ° 

 m n two particles of the earth 

 situated at equal distances to 

 the north and south of P. The 

 action of m situated to the south 

 of P, will be in the direction Pa perpendicular to mP, and that of 

 n will have the direction P6 perpendicular to nP. The force Va 

 may be decomposed into two forces having the directions PC and 

 PH ; and the force Vb may be decomposed into two having the di- 

 rections PD and PH. The sum of the two horizontal components 

 will be the effective horizontal force due to the actions of m and 

 », and the difference of the two vertical components will be the 

 effective vertical force due to the action of the same particles. 

 Since the temperature of m is higher than that of n, the compo- 

 nent directed from P to C is greater than that directed from P to 

 D, and hence the north end of the needle will be urged down- 

 ward. The horizontal force will solicit the north end of the 

 needle toward the north. The actions upon the south end of the 

 needle will be just the reverse. Now if we suppose the same pro- 

 cess of decomposition to be gone through with for each pair of 

 particles situated on AB at equal distances from P, up to a certain 

 distance at which the molecular actions become insensible, by 

 taking the sum of the individual forces along PC and PH, we 

 shall have the entire effects of the arc AB in these two directions. 

 In the same manner we may obtain the effects of any arc below 





same 



ane 



the needle. Since the curvature of the arc AB is very slight. 



par 



to p that will have any material action in the horizontal direction. 

 For arcs below the earth's surface the portion that furnishes the 

 horizontal force will be greater as the depth increases, but will 

 still, doubtless, be small in comparison with the 



more 







