of the Earth's magnetic Force in absolute Measure. 11 
and the equation is the same as that to which it is reduced in the former case, 
the sine of the angle of deflection being substituted for the tangent. It appears 
from the result, that this method is to be preferred to the former, not only be- 
cause the angle of deflection is greater, cet. par., but also because the variable 
part in the coefficient of the inverse fifth power of the distance is strictly 
evanescent. 
It remains now to inquire in what manner the quantity , which expresses 
the ratio of the two coefficients, may be known @ priori; and whether that 
quantity may be made to vanish, by any simple relation between the acting 
magnets. 
For this purpose we must know, at least approximately, the law of magnetic 
distribution, or the function of r by which m is represented. Almost the only 
knowledge which we possess on this subject is that derived from the researches 
of Coulomb. From these researches M. Biot has inferred, that the quantity of 
free magnetism, in each point of a bar magnetized by the method of double 
touch, may be represented by the formula 
MA (w-7— pt") 3 
» being a quantity independent of the length of the magnet, and a a function of 
pwand/. M. Biot has further shown, that when the length of the magnet is small, 
the relation between m and ris approximately expressed by the simple formula 
/T . 
1 ° 
the curve of intensities becoming, in that case, very nearly a right line passing 
through the centre of the magnet. 
Employing then this approximate formula, we have 
m= mM 
+t m +1 
— = Dh — ‘]2. 
M= \_ mrar 7 fez dr=2m'P; 
+ m’ ot! 
a ) mrdr = —§ rdr = 2 m'l'. 
ie) ——- 
The ratio of these quantities is independent of m’, and we have simpl 
q P ply 
