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t tides made on thofe Rhumbs , when the meridi- 
onal Differences of Latitudes are equal or , are 
reciprocally proportional to unequal meridional 
Differences of Latitudes on thofe Rhumbs , when 
the Differences of Longitudes are equal. 
For the meridional Difference of Latitude, is to 
the Difference of Longitude; as Radius is to the Tan- 
gent of the Angle of the Courfe, or of the Angle 
which the Rhumb makes with the Meridian. There- 
fore, when the meridional Differences of Latitudes 
are equal, the Differences of Longitudes are as the 
Tangents of the Courfes : But, when the Differences 
of Longitudes are equal, the meridional Differences 
of Latitudes are reciprocally as the Tangents of the 
Courfes. 
Art. VIII. The logarithmic Tangents of the Half- 
Complements of the Latitudes , are analogous to 
the lengthen’d Degrees in the nautical Meridian 
Line , in a Mercator s Chart. 
For, in the ftereogr^phic Projection of the Sphere 
on the Plane of the Equator, the Latitudes of Places 
are projected by the Half-Tangents of the Comple- 
ments of thofe Latitudes, which Half-Tangents are the 
Rays of a proportional Spiral : Now, if a Series of 
fuccellive Latitudes be taken on any Rhumb, the 
correfponding Differences of Longitudes will be Lo- 
garithms to the Rays of the Spiral, or to the Tangents 
of the Half-Complements of thofe Latitudes : There- 
fore' the Differences of Longitudes are as the loga- 
rithmic T angents of the Hal f-Complements of the La- 
titudes : But(^r/.VI.) the lengthened Degrees on the 
nautical 
