and 





228 Prof. W. A. Norton on Terrestrial Magnetism. 



suppositions we obtain from (21) for the meridian 93° the ex- 



cos ft 7 sin (<*+ 5/ ) 

 pression sin .. + iJsill -+T«/ ' 



cos b sin (*+*') - T r , . . -, « . , 



pression s i n -H- T j s i n -M- ij> ' Now for the same latltude d 1S less 



for 93°, or thereabouts, than for any other meridian, while 8' is 

 the same ; and therefore south of the point of maximum on 93°, 



sin (3+d') 

 or of latitude 50°, the numerator of the fraction grsq-t^ s «j -*hJ/ 



is greater and denominator less, and therefore the fraction itself 

 greater upon this meridian than any other. Again near this me- 

 ridian b' for 10° south of 50° is less than 2° ; and some 15° from 

 it the value of b exceeds this amount. The maximum value of 

 (21) for the meridian of 93° is then greater than its value at the 

 same latitude (50°) on any other meridian, or at any lower lati- 

 tude. We have also before 



th 



90°, or 



any where to the north of this. It only remains then to show that 

 it is greater than any value between this point and 50°. The ex- 

 pression for the maximum value in question is • -«+i d&ii^w' 



and that for the value of (21) between the two points just men- 



cos b sin (8 -fd') 

 tioned is sul -+ l( s s i n -"+. J/ * We have already seen that the de- 



nominator of the first fraction is less than that of the second for 

 each of the two points in question. As the denominator of the 

 second gradually decreases from one point to the other, it follows 

 therefore that it is continually greater than that of the first. 

 Hence between these points the second fraction is less than the 

 first. 



We conclude therefore that the pole of maximum intensity 

 situated about in latitude 50°, and longitude 93° to 100°. 



In what precedes, it has been supposed that expression (21) IS 

 rigorously true, but in its investigation no account was taken . o» 

 the motion of the fictitious cold poles. The error from tins 

 cause is trifling, except at considerable distances from the cola 

 poles, and cannot vitiate the result just obtained. Our conclu- 

 sions with respect to the situations of the points of greatest in- 

 tensity on distant meridians, may not be strictly correct, from this 



is 



cause. 



necessar 



value of n for all parts of the earth. It is not improbable that it 



necessar 



n for different quarters of the earth, varying from f to 1. I u * aC 



