334 Astronomical and Nautical Collections. 
instance, and the differences between the calculation and the ob- 
servations are not sufficiently great to induce us to abandon them. 
Besides, if there were any slight difference of intensity among these 
actions, depending on the difference of the materials of which the 
sphere and the needle are formed, the observations in question 
could scarcely have been sufficiently accurate to determine so de- 
licate a point. 
The author terminates the abstract of this admirable memoir with 
aremark which he thinks may be of some advantage in practice. 
The horizontal deviation of the needle, produced by the influ- 
ence of the magnetized sphere, and the relation of the number of: 
oscillations which it makes when so influenced to the number of 
its spontaneous oscillations, comprehend, in their analytical ex- 
pressions, that of the dip at the place and time of observation: so 
that by making the deviation and the ratio of the variations equal 
to the values obtained by observation for a known situation of the 
needle, we may obtain two equations, either of which might serve to 
compute the dip. If we employ the ratio of the oscillations, we 
have the advantage of being able to obtain it by observation, with 
sufficient accuracy, from a needle so small ‘as to be incapable of 
sensibly affecting the magnetism of the sphere. The equation to be 
resolved, in order to obtain the dip, will contain the diameter of the 
sphere, and the distance from its centre; both which may be mea- 
sured with great precision: it will also comprehend the two angles 
which determine the line of direction of the needle from the sphere: 
but when the needle is near the point which affords the maximum of 
action, a small error in the direction of this line will have little in- 
fluence on the magnitude of the dip, which may be determined by 
the method here described with more accuracy and ae than by 
direct observation. 
A second memoir is intended to contain a determination of the 
mode of distribution of magnetism in needles of steel magnetized to 
saturation, and in needles of iron magnetized by induction, by 
means of the same general theorems that have been demonstrated 
in the present essay ; and from these distributions the phenomena 
of their mutual attractions and repulsions will be deduced, upon 
similar principles. 
