Prof. W. A. Norton on Terrestrial Magnetism. 225 



on or near the meridian of 93° than on any other meridian. We 

 will attempt to establish the latter first. Let us suppose that 

 b— b' : and that each has the value of the smaller of the two. 

 This supposition is an unfavorable one, since it will make the 

 value of dT for other meridians than 93° greater than expression 

 (21) makes it. Upon this supposition (21) becomes 



cos 4(cos 8 sin fl 7 -f sin 8 cos 8') cos b sin (#+#') 



siir"+ x 8 sin- n+ ' & ~ sin""+ l 8 sin- n+ ' 8 n 



(22.) 



and for the point where tf + tf' = 90°, 



cos b cos 6 



. or — j — . . (23.) 



sin-"+ ' 8 sin-"+ ' 8' mn* 8 S \n 9 8' 



putting mmfj the value which accords best with the observations 

 of temperature. Now making the calculation of the declination 

 for the latitude 50°, and longitude 93° W., by formula (6), I find 

 3 =24° 40', <5'=63 56', 6=0 (very nearly), 6'= 3°, <*+<>' =88° 

 36'. The same calculation for London (latitude 51° 31') gives 

 4=37° 18', <5'=62° 29', 6 = 12° 55', 6' = 34° 17', <H <J'=99° 47'. 

 The point where 8 +8' = 90° is then in latitude 50° (nearly), on 

 the meridian 93° W. For other meridians it is north of 50°. 

 This is evidently the case for the meridian of London ; and that 

 it is true for other meridians, east or west of 93°, appears from 

 the fact, deducible from the various calculations of declination 

 and temperature, that while 8' remains the same on the same par- 

 allel of latitude, 8 diminishes towards 93°. On these meridians 

 then 8' i s a certain number of degrees less, and 8 the same num- 

 ber of degrees greater than on the meridian of 93°, at the point 

 for which <? -f- <J' = 90°. The effect of the increase of 8 upon the 

 value of expression (23) will more than compensate for that of 

 the diminution of 8' ; and the augmented val ue of b, by making 

 cos b less, will increase the difference. It appears, therefore, that 

 (23) has its maximum value in the vicinity of 93° of longitude ; 

 -on the meridian for which the angle between 8 and 8' is zero. 

 The details of the calculations of declination make it evident that 

 this mefldian, and therefore that of maximum value, lies a tew 

 de grees to the west of 93°. ' 



We have still to show that the maximum value of expression 

 W), on each meridian, is at the point where 8+8' = 90 .In lon- 

 gitude 93° this value of 8+8' occurs about in latitude oO u . t or 

 this locality an d its vicinity 6=0 (very nearly), and 6' = some 

 I °r 4o. i n going north from 6oo to 60°, b is constantly from 

 4 t0 5', and b> increases about 21°. In going south b preserves 



ab out the 



**>m the same value, while 6' diminishes j as may be seen irom 

 Je fact that at St. Louis (long. 90° 15', lat. 38° 37') the sum ot 

 the two angles b and b' does not exceed 10'. Now, let us sup- 

 P°se that 6=6' in expression (21), which will give 



8 *con d Series, Vol. IV, No. 11-Sept., 1847. 



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