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XIV. A Rule for finding the meridional Parts 
to any Spheroid, with the fame Ex affine fs as 
in a Sphere, by Colin Mac Laurin, F. R. S. 
Communicated by Andrew Mitchel, Efift 
F.R.S. 
I T was demonftrated long ago, that in a Sphere the 
Nautical Meridian Line is a Scale of logarithmic 
Tangents of the half Complements of the Latitudes, 
The fame may be computed with no lefs Exadnefs 
to any Spheroid by the following Rule. 
Let the Semidiameter of the Equator be to the 
Diftance of the Focus of the generating Ellipfe from 
the Centre as m to i. Let A reprefent the Latitude 
for which the meridional Parts are required, s the 
Sine of this Latitude, the Radius being Unit 5 find 
the Ark B, whofe Sine is s -\ take the logarithmic 
Tangent of half the Complement of B from the 
common Tables ; fubtrad this logarithmic Tangent 
from 10.000000, or the logarithmic Tangent of 45 0 } 
multiply the Remainder by and 
the Produd fubtraded from the meridional Parts in 
the Sphere, computed in the ufual manner for the 
Latitude A, will give the meridional Parts expreffed 
in Minutes for the fame Latitude in the Spheroid, 
provided it is oblate. When the Spheroid is oblong, 
the Difference of the meridional Parts in the Sphere 
and Spheroid for the fame Latitude, is then deter- 
mined 
