§B Bowditch on Computing tlie Dip of the Magnetic JSTeedle, 



passing tbrough this axis, and any proposed place E upon tlie 

 eartii's surface, is the magnetic meridian of that place. The plane 

 passing through the earth's centre C, perpendicular to the magnet- 

 ic axis, is the magnetic equator. The magnetic latitude is count- 

 ed from this equator, and is eq^ual to the complement of the angle 



PCE. 



Upon the magnetic equator the dip is nothing or very small, and 

 at the magnetic poles is nearly equal to 90°. In any other place the 

 dip is computed upon the principle that the whole magnetic force of 

 the earth is concentrated in two magnetic points S, N, situated in 

 the magnetic axis P p, at infinitely L-mall equal distances from the 



-p 



earth's centre C. The forces of both these magnetic points are 

 supposed to be equal to each other ; the one being attractive ^ the 

 other repulsive^ both of them varying inversely as the square of 

 their distances from any attracted point E of the surface. 



Suppose the earth to be of a spherical form, and let its radius 

 CP = C E = 1, also CS = CN =^ x, the magnetic latitude of the 

 point E equal to a, and the angle PCE = it = 90° — k. Then 

 drawing the line s C w perpendicular to EC, we shall have nearly 

 S s = N w = a?, sin. A ; C » = C Ji = a?, cos. a, and as x is suppos- 

 ed to be infinitely small we shall have, by neglecting a?', a?', &c. 

 EN = CE~]V w =^ 1 — ^. sin a; E S= CE -f S s = I +a?. sin a; 

 and if the magnetic force of either of the points S, N, upon a place 

 at the distance 1 is F, the force of the point N upon E will be by 



hypothesis ^^^^^^ E. (1 + 3. x, sin. a) in the direction E N. This 



may be reduced to two other forces ; the one in the vertical direc- 

 tion E C, which will be represented very nearly by F (1 +flx, 

 slu. a) ; the other in the horizontal direction C n equal to 

 F.a7.cos. A. In like manner the repulsive force of the point 8 will be 



represented by— ^ = F (1 — -Sa? sin. k) in the direction S E, which 



Jr 



