148 APPENDIX. 



Such an example occurs in the journal on the 24th of 

 August, in lat. G3° 26' 51" N., long. 80° 51' 25" W., ^vhen 

 the variation was found to be 37° 3o' W., and dip 86° 32'. 



The relation above alluded to between the dip, variation, 

 and magnetic latitude, as first deduced from observa- 

 tion by Biot, and afterwards by deductions from the laws 

 of iron bodies by Mr. Barlow, is this, that in every part of 

 the world the tangent of the dip of the needle is equal to 

 double the tangent of the magnetic latitude of the place of 

 observation. That is, if we conceive meridians to proceed 

 from one magnetic pole of the earth to the other, and an 

 equator to be described bisecting all those meridians, from 

 which the magnetic latitudes are reckoned ; then the tan- 

 gent of the dip is equal to double the tangent of the arc 

 comprised between the magnetic equator and the place of 

 observation ; consequently, when the dip is given, the mag- 

 netic latitude and co-latitude become known, which latter 

 is the distance of the place of observation from the mag- 

 netic pole. Having thus the distance of the pole, and the 

 variation of the needle showing the direction, as referred 

 to the terrestrial meridian of the place of observation, the 

 exact situation of the pole itself becomes a matter of easy 

 computation. Thus in Fig. 1, if PP' represent the terres- 

 trial poles, and tt, ^' the magnetic poles, EQ the terrestrial 

 equator, and MQ the magnetic equator : then eZ will be the 

 terrestrial latitude, and mZ the magnetic latitude of the place 

 Z ; and consequently ttZ its magnetic co-latitude, which 

 becomes known by means of the law above-mentioned. 

 Again, wP will be the terrestrial co-latitude of the place of 

 the magnetic pole, and the angle ttPZ will be tlie difference 

 of longitude between the two meridians EP, eP, or the 

 difference of longitude between the magnetic pole and tlie 

 place of observation. 



