OBSERVATIONS ON THE MAGNETIC DIP AND DECLINATION. 377 
By combining the inclinations observed in pairs of planes at right angles to one ano- 
ther, the equivalent dip for the plane of the magnetic meridian was deduced by the formula 
Cotan.? § = Cotan.? 7 ++ Cotan.? 7’ 
In which ¢ represents the inclination observed in any azimuthal plane, ¢’ that observed 
in another azimuthal plane perpendicular to the former, and 4 the equivalent dip reduced 
to the plane of the magnetic meridian. 
Here, too, are shown, in column eight, the values of 8”, deduced by the formula pre- 
viously quoted, in order to compare them directly with &’, here represented by ¢ and @’ in 
column seven, and the difference, +- or —, between & and 8” are shown in column nine 
as the true indices of the perfection of the instrument in respect to the form of the axles 
of the needles and the freedom of the dip-circle from magnetism and matter having any 
attractive or repulsive effect upon the needles. 
