of the Earth’s magnetic Force in absolute Measure. 7 
Now let us suppose the term containing the fifth power of the distance to 
vanish, in the expression for the deflecting force. The value of @ will then be 
reduced to 
Q= pD*tanu; 
in which we may take tan wv = w tan 1’, as before. Hence there is 
4a _ Au, 
pn Fane 77h 
and the probable error is less than in the usual method in the ratio of 1 to 5-563, 
even when the latter is employed in the manner most conducive to accuracy. 
Accordingly, if by any means the coefficient of the inverse fifth power of the 
distance can be annihilated, or rendered so small that the term shall have no sensible 
influence, the accuracy of the results will be increased more than five-fold, and, 
at the same time, the observations being taken at one distance only, the labour 
of observation will be halved. 
The same advantages will be gained, if, the coefficient of the inverse fifth 
power of the distance retaining a sensible value, the ratio of the two coefficients 
may be knownd priori. Let 
Quo; 
h being a known quantity. In this case the expression for the tangent of the 
angle of deflection becomes 
tan w= s(1 +=); 
D? 
and the coefficient sought is obtained, from the result of observation at a single 
distance, by the formula 
pD’ tan ~ 
= T+ ipo" 
It is evident that the probable error of @ thus obtained, arising from an error in 
the observed deflection, is the same as in the case last considered, and therefore 
between 5 and 6 times less than in the ordinary method. 
The object of the following investigation is to point out the means of attain- 
ing these advantages. 
Let the axis of the deflecting magnet be supposed to lie in the right line 
joining the centres of the two magnets, and let the axis of the suspended magnet 
make the angle y with that line. Then, if x and y denote the forces exerted 
