Inquiries concerning the Magnetkrn of the Earth. 333 
tion *5 Coulomb calculated, that, to keep the magnetised wires 
within 24< degrees of each other, 24® + 24 x 35° =: 864° of tor- 
sion were necessary; within 17 degrees of each other, 3 x 360° -f 
17° + 1*7 X 35° 169^° of torsion were necessary; and within 
12 degrees, 8 x 360° -f 12° -j~ 12 x 35° — 3312° of torsion were ne- 
cessary. At the distances 12, 17 and 24, it appears, therefore, 
that the forces of repulsion are respectively proportional to 3312, 
1692, and 864: had these numbers been 3312, 1650, and 828, 
the repulsion found by the experiment would have been accu- 
rately in the inverse duplicate ratio of the distances. The er- 
rors, 42 and 36, are not greater than might be supposed to re- 
sult from the unavoidable incorrectness of such an experiment. 
Their existence is however almost sufficiently explained, by con- 
sidering, that though the portion of each wire submitted to the 
other’s influence was very small, it did not consist of a single par- 
ticle, as the calculation demands, but of a perceptible space,'^^com- 
prehending other particles besides the one whose action was re- 
quired ; and that the force of these other particles being less ob- 
lique, and therefore stronger at greater distances, ought actual- 
ly to produce an excess similar to that found in the experi- 
ment. A result entirely analogous was obtained when the con- 
trary poles of the two wires were exposed to each other : 
and as these facts were confirmed by others, and contradicted 
by no established principle. Coulomb was warranted in conclud- 
ing, with considerable certainty, that the attraction or repul- 
sion which exists between two magnetic particles, is always 
inversely as the square of the distance : agreeing thus with the 
force of electrified substances, with the force of gravity, and 
with every other force or principle that flows from a centre in 
straight lines. It must be owned, however, that the result of 
Coulomb’s investigation is not founded on so definite and stable 
a basis, as to render all doubt unpardonable ; and the confirma- 
tion which a law of such importance in its consequences gains 
from Mr Hansteen’s examination of the subject, cannot be re- 
garded as superfluous. 
* In calculating quantities so small, the arc is .substituted for the sine, without 
serisible error. 
