332 Astronomical and Nautical Collections. 
he has found that the tangent of the angle of horizontal deviation is 
proportional to the cube of the quotient of the radius of the sphere 
divided by the distance of the needle from its centre: results 
which obviously afford a confirmation of the theory here laid down. 
(He has also observed that the deviations vanish when the middle 
of the needle is in a plane passing through the centre of the sphere, 
and perpendicular to the dipping needle: but he is incorrect in 
calling this plane the plane of no attraction: there is indeed no 
plane in which the attraction of a sphere, or in general, of any 
body magnetized by the earth’s influence, becomes evanescent). | 
In order, however, to compare the theory still more precisely with 
observation, a part of the deviations, which Mr, Barlow has deter- 
mined, have been calculated from the formule of this memoir : and 
the general agreement of the results, with his observations, appears 
to leave no doubt either of the accuracy of this theory, or of that 
of the analysis which is founded on it. Without entering into the 
whole detail of this comparison, it will be sufficient to mention 
some particular cases. 
The diameter of the sphere of iron magnetized by the action of 
the earth being thirteen English inches ; and the needle, of which 
the deviations were observed, being six inches long, and its middle 
point twelve inches from the centre of the sphere; Mr. Barlow 
found, in a certain relative situation of the compass, a horizontal 
direction of 36° 15’: in the same relative position, taking into con- 
sideration the length of the needle, which is here too great to be 
neglected, the computation gives 35° 33’ for the same deviation: 
and the difference of 42’ must be partly attributed to the reaction 
of the needle on the sphere, which could not be comprehended in 
the computation, because the magnetic force of its poles is un- 
known. 
In a continuation of the same radius, the middle point of the 
needle being twenty inches from the centre, the horizontal deviation 
was reduced to 8° 52’ by observation; the calculation would make 
it 8° 42’, differing only 10’ from the experiment. 
At the same distance of twenty inches, and when the needle was 
situated near the plane in which the horizontal deviation completely 
