amount of the dip of the magnetic needle, in London, &c. 3 
were considered by them merely as approximations ; since it 
could not have been otherwise overlooked, that the arith- 
metical mean is in no case the result which is strictly de- 
ducible from the arcs, and that, in many instances, it must 
differ considerably from the more correct deduction ; whilst 
the adoption of this method in general practice, has charged 
the results with an error, which might haves been avoided ; 
the amount of which can only now be known, when the 
details of the observation have been given, and furnish the 
means of re-computation. 
The perfect balancing of the needle is sometimes at- 
tempted by a cross of wires affixed to the axis, as described 
in the Philosophical Transactions for 1772, Article 35; but 
this contrivance is more ingenious than useful in practice, 
and introduces a liability to errors, of far more importance 
than the inconveniencies which it was designed to obviate. 
The adjustment of the balance, after the needle is magnetised, 
is in itself a troublesome, tedious, and uncertain operation, 
and is far too subject to derangement to be confided in, when 
the instrument has been removed from station to station ; 
moreover, the inaccuracies occasioned by friction, are aug- 
mented by the additional weight of the mechanism on the 
one arm of the axis, and of a counterweight on the other. 
The errors of an imperfect balance are reducible by calcu- 
lation, but those of friction are not so; whether they may 
arise from the axis not being truly cylindrical, or from the 
inequalities of its surface producing a resistance on the planes, 
which the moving force of the needle is not fully adequate to 
overcome. It may be, therefore, justly remarked, that the 
true and unimpeded motion of the axis, and the consequent 
