Astronomical and Nautical Collections. 317 
becomes = (1 + e cos? L) (1 + 2e sin? L) = 1 +e +e sin? L, 
But the radius of curvature of the meridian is equal to, the cube of 
the former normal divided by the square of the semiparameter, 
(Lyon’s Fluxions, P. 111,) or to (1 — 3e cos2 L) (1 + 2e) since 
the semiparameter is a that is, tol + 2e — 3ecos?L, neglect- 
e 
ing the square of e as inconsiderable. 
The angle at the pole on this tangent sphere will be the true dif- 
ference of the longitude on the spheroid, and the true difference of 
latitude may be found by reducing the angular difference of the leg 
and hypotenuse into linear measure, and then again into an arc of 
the curvature of the meridian; or more simply, by applying to the 
arc a correction proportional to the difference of the radii of curva- 
ture 1 +e + esin?L, and 1 + 2e — 3e cos?L, which is e—e sin? L 
— 3e cos? L = 2ecos?L, which is the excess of the radius of the 
perpendicular above that of the meridian, vanishing, as it ought to 
do, at the pole, and becoming 2e at the equator. 
If it be required to compute the effect of the deviation of the per- 
pendicular to the meridian from the plane here supposed, it may 
be found by making the actual verse sine of the portion of this 
curve in question radius, and finding the tangent of the difference 
of the curvature of the two circles here compared in an arc equal 
to the difference of latitudes found, which will be to the whole an- 
gular difference as 2e cos*L to 1. But since the verse sine in 
question is only equal to the depression of the horizon at the given 
distance, itis obvious that the tangent of so small an angle, with 
this radius, may be neglected as inconsiderable. 
iv. Extract of a Memoir on the Theory of Macnetism, read-at 
the Academy of Sciences, 2 Feb. 1824. By Mr. Poisson.—Ann. 
de Chimie, Feb. 
Ir has been customary with many natural philosophers to ex- 
plain the phenomena of electric attractions and repulsions by at- 
tributing them to two distinct fluids, possessed of the property of 
repelling the particles of the same nature, and of attracting, with an 
Vor, XVII. Z 
