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



haps any other known temperature. We shall see hereafter that 

 it is not necessary to suppose that the molecular magnetic force 

 becomes zero at the magnetic poles, in order to explain the fact 

 of the horizontal intensity becoming reduced to zero there. 



Vertical Intensity. 



The formula obtained for the vertical intensity is, 



Ver. intensity = C(t-f) . . (16.) 

 C being a constant, and t, t', the mean annual temperatures at 

 two places situated at certain equal distances north and south of 

 the given place, in a direction perpendicular to the isogeothermal 

 line, or rather line of equal molecular magnetic intensity, t and 

 f in the formula are in general the measures of the molecular mag- 

 netic intensities ; and it is assumed that the temperatures may be 

 taken as these measures. Since the temperatures t and V cannot 

 in general be readily obtained from existing observations, we will 

 seek for the law of variation of t - 1'. It has already been seen 

 that the diminution of temperature from the equator northward, 

 on the western continent, is as 1 - cos 21at. - C. Now, for a 

 small number of degrees north and south of the given place, C 

 may be considered as constant ; and hence the difference of tem- 

 perature of two places situated the same number of degrees, say 

 5°, to the north and south of the given place, is proportional to 

 cos 2(lat. - 5°) - cos 2(lat. + 5°). This is equivalent to the gen- 

 erally received law that the temperature varies, for a moderate 

 distance, as the square of the cosine of the latitude. F° r 

 cos 2 lat. <s, 1 +cos 21at, and hence, putting rfand d' equal to the van- 



temperature 



in question, and I 



( 



(l-fcos2/), ^(l+cos2Z)-(l+cos2(/+5°)). Whence 

 d+d'v cos 2(1-5°) - cos 2( I + 5° ). This is the measure of the 

 variation of temperature on a meridian passing through the place- 



per 



l th 



perpend 



proportion 



[C 



meridian to unity. For, let P, Fig. 9, be the Fig. *»■ 



given place, IPV the meridian through P, AB 

 and CD two parallel isogeothermal lines at equal 

 distances from P, and Im a perpendicular to AB 

 and CD. The variation of temperature for a 

 given distance will be as much greater in the 



as 



less than IV. But Im : IV : : cos Vim : 1. We 

 may take for the approximate value of Vim the declination of «* 

 magnetic needle. If therefore we denote this by d, we have, by 

 substitution in formula (16), 



