6 Prof. W. A. Norton on Terrestrial Magnetism. 
and PD, destroy each other, 'The same may be shown with re- 
ard to the actions upon the south end of the needle. _ It follows, 
therefore, that the needle will place itself at right angles to CPD, 
the isogeothermal line passing through P the station of the nee- 
dle. This is a consequence from our theory which, like the 
formule soon to be investigated, is to be tested by making com- 
parisons with observations. 
Let us now deduce from the general principles which have 
been laid down, the horizontal and vertical components of the di- 
rective force of the needle. Fig. 3. 
Let ApB, fig. 3, represent a 8) pp 
great circle of the earth, an- 
swering to mPs, or nPr in fig. 
2, Cp its radius, P the north i : 
end of a magnetic needle, and 
m n two particles of the earth 
situated at equal distances to 
the north and south of P. The 
action of m situated to the south 
of P, will be in the direction Pa perpendicular to mP, and that of 
n will have the direction Pd perpendicular to nP. The force Pa 
may be decomposed into two forces having the directions PC and 
PH; and the force Po may be decomposed into two having the di- 
rections PD and PH. 'The sum of the two horizontal components 
cess of decomposition to be gone through with for each pair of 
distance at which the molecular actions become insensible, by 
taking the sum of the individual forces along PC and PH, we 
shall have the entire effects of the are AB in these two directions. 
In the same manner we may obtain the effects of any are below 
AB and situated in the same plane; and thus the entire effect of 
all the matter situated in this plane which exerts any action upo? 
the needle. Since the curvature of the arc AB is very y 
and P is very near to it, it is only the particles situated quite nea 
to p that will have any material action in the horizontal direction 
For arcs below the earth’s surface the portion that furnishes the 
horizontal force will be greater as the depth increases, but W 
still, doubtless, be small in comparison with the more distant 
