Prof. W. A. Norton on Terrestrial Magnetism. 7 
parts which act nearly in the vertical direction upon the needle. 
as we have supposed, the principle of magnetism be analogous 
in its nature to light and heat, then it must be more or less ab- 
sorbed in its passage from the lower arcs to the surface; and 
there may be a gradual decrease in the extent of the are which 
exerts a sensible action upon the needle, as the depth of the are 
increases, until at the lower surface of the stratum of sensible ac- 
tion it becomes reduced to zero. 
ormulas for the horizontal Fig. 4. 
and vertical components of the : 
directive force suited to our pres- P 
ent enquiry, may be easily inves- 
tigated. Let AB, fig. 4, be an 
isogeothermal line, and GH an 
are of a great circle crossing this line perpendicularly and passing 
through P the station of the needle. ‘The magnetic intensity of 
the particles of AB is every where the same. ‘Take any particle 
mand designate the distance Pm, in a right line, by 7. Hither 
end of a needle at P will be solicited by a force perpendicular to 
Pm, and in the vertical plane through Pm. This force will be, 
for different isogeothermal lines, directly proportional to the mag- 
netic intensity of m, and therefore to its mean annual tempera- 
ture (¢); and will, for the same isogeothermal line, vary from one 
particle to another with the distance 7. Its expression will there- 
fore be of the form At. ¢*(r); Fig. 5. 
A an indeterminate lp 
being 
constant. Now, let mp, fig. Pate 
5, represent the great  cir- a’ lr 
A G m B 
m and lying either on 
the earth’s surface or beneath 
We shall have force ;: 
any portion Gan of it by z, and PG bi 
mentary portion of GB will have for 
* The letters o F, with and without accents, are used in these investigations 
to designate dicen functions, and are therefore to be read “a function of.” 
