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



cos&'sin(^') _ 



sin- n+ ' S sin- n+ ' <5' 

 For the point where 5+5'= 90° this becomes 



cos b' 



sin-" +, <5sin-" +, <5 / 



(25.) 



(25) is less than the value of (21) for latitude 50°. South of 

 this latitude let us suppose that b'=b in (21), which gives 



cos b sin (<54- ,5/ ) 



sin-" +1 «J sin-"+M' 



(26.) 



(26) is greater than (21) south of 50°. If therefore we show 

 that (26) is less than (25), we shall have established that (21) 

 decreases south of 50°. The denominator of (26) is greater 

 than that of 25. It will only be necessary then to show that the 

 numerator of (26) is less than that of (25). At 50°, b' =3°, and 

 cos b' = cos 3° = -99863. b may be regarded as zero. The de- 

 tails of the calculations of declination show that the variation, 

 due to a change of latitude, of 8+8' is more than twice the 

 change of latitude. Thus, while 8+8' is equal to 88^° at lati- 

 tude 50°, at latitude 60° it is equal to 66°, and at St. Louis (lat. 

 38±°) it is 113°. Thus at latitude 47°, 3° south of 50°, the nu- 

 merator of (26) is less than sin 96° = -99452. It follows therefore 

 that (21) diminishes, as we follow the meridian 93° south from 

 the latitude of 50°. North of 50° the increase of b' tends to 

 diminish (21). Dropping V, (b being equal to zero,) we have 



sin (*+*') 



sin-" +1 <5sin- n+, d' ' ( 27 ^ 



Whether 



di- 



minish, depends upon the value given to n. If we suppose »=£ 

 as approximately determined by Brewster, or f , there will be a 

 continual increase from 50° northward. But, as we have already 

 seen, the observations of temperature are best satisfied by taking 

 n=|, and at the same time *=31° and t= - 18°. Thi* will be 



more evident on inspectm 

 the formulae 



3 3 



T= 28°-(-19°) sin^sin^' -19° 



7 7 



T= 30°-(-17°) sin^sinSJ' -17 



O 



• 



8 3 



T = (31° - ( - 18°)) I sin** sin** ) - 18°. 



• 



