110 ON MAGNETISM. 



proper caution in interpreting these values in reference 

 to our new polar coordinates. Now, considering the 

 fictitious x as in the horizontal plane and towards the 



west, the value &x (by which -KT- and -j- are formed ), is 

 \ * ox ax J 



dV 



r. sin u . SA. ; and therefore the westerly force =- 



ax 



1 dV 



will be -- : .-7-. Considering the fictitious y as 

 r . sin u d\ 



in the horizontal plane and towards the north, By is 



dV 



r.Bu; and therefore the northerly force -=- will be 



-- .-7 And considering the fictitious z as vertical 



at the place, Bz is Br ; and therefore the vertical force 



dV. dV _, 



T~ is -- r~- Inus we have 



dz dr 



.j , 



r . sin u d\ 



The algebraist may perhaps prefer a more rigorous 

 investigation, of the following form. 



Conceiving the place of observation on the globe as 

 turned in some measure towards the spectator, the 

 origin of longitude being to the extreme left hand or 

 west; let x be measured from the Earth's center in the 

 plane of equator towards the left; y in the plane of 



