224 



Prof. W. A. Norton on Terrestrial Magnetism. 



perpendicular to the isothermal line. It has already been seen 

 that the general expression for the variation of temperature an- 

 swering to an indefinitely small change of place is, 



dT 



Cn (cos 8 sind' rftf-f- cos & sin 8d8') 

 sin- n+l *sin-" + '^ 



(19.) 



Fig, 11. 



Let C, fig. 11, be the geographical pole, 

 A, A' the two cold poles, A being the 

 American pole, BL the direction of the 

 isogeothermal line at B, Bn an arc per- 

 pendicular to BL and nw, nv arcs perpen- 

 dicular to AB and A'B. Let Bn = k and 

 denote the angles ABn and A'Bn by b 

 and V. Then dS =Bu= Bn cos ABn = k 

 cos b\ and d8'=Bv=Bn cos A'Bn= k 



cos b 



Substituting in equation (19), 



cTT 



And d T oc 



Cn(cos 8 sin d'k cos b +cos 8 f sin 8 k co s b') 



sin~ w+ M sin" n+1 (T 

 cos 8 sin 9' cos 6+ cos 9 ' sin 8 cos b 1 



sin~"+ » 8 sin~"'+ ' 8 / 



(20.) 



(21.) 



Now the calculations of the declination which have been made, 

 show that b and b' diminish (along with the angle ABA') and 

 thus cos b and cos b' increase as we follow the same parallel of 

 latitude from the meridian of Paris, westward, as far as longitude 

 90° to 100°, (for example, for London 6 = 12 "" 



O fit/ 



00', b 



.„. „, „ XVJ ^lm IM1 . ^ , ui inereaDouts. Umitt 



cos 6', the numerator becomes cos 8 sin 8' -f sin 8 cos 8' 



, , „__ w „_34°17', 



and for longitude 93° W., and latitude 50°, 6= 'and 6'= 3°): 

 also that *' remains the same while 8 diminishes, and that 8' is 

 greater than 8, and is nearly equal to the colatitude of the place 

 +25°. The tendency of the changes of cos b and cos V is to 

 make the expression (21) for dT greater in proportion as we draw 

 nearer to the meridian 93°. or thprohr^to Omittin^ cos b and 



___. , m . sin{8+ 8 '} 



This will be the greatest when 8 +$' ==90° • and since 8' remains 

 the same on the same parallel of latitude and 8 diminishes with 

 the angle ABA', as we go westward towards the meridian 93°, 

 it is plain that 8+d' will be equal to 90° at the lowest latitude 

 on, or near, the meridian where the angle ABA' is equal to zero. 

 At this point the numerator of the fractional expression (21) ® 

 greater than at the same latitude, or at any latitude, on any other 

 meridian ; for it is only on this meridian that cos b and cos b 

 may be regarded as equal to unity. It is only necessary then, to 

 establish that on each meridian the greatest value of dT obtains 

 where *+*=90° and that a greater value obtains at this point 



