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nautical Meridian are as the Differences of Longitudes 
on the Rhumb of 45* Degrees 5 confequcntly the 
logarithmic Tangents of the Half-Complements of 
Latitudes are as the lengthened Degrees on the nau- 
tical Meridian. 
Corol. 1. When the Angle between the rhumb 
Line and the Meridian is equal to 45 Degrees, then 
the Longitudes of Places on that Rhumb are exprefl'ed 
by Logarithms of Napier's Kind j whofe corrcfpond- 
ing Numbers arc natural Tangents of the Half- 
Complements of the Latitudes to Arcs expreffed in 
Parts of the Radius . 
Corol. 2. Hence, to any two Places on a Rhumb 
of 45- Degrees, the Difference of Longitude, or the 
meridional Difference of Latitude, is equal to the 
Difference of the Napierian logarithmic Tangents 
of the Half-Complements of the Latitudes of thole 
Places, eftimated in Parrs of the Radius , . 
Corol. 3. As there may be an indefinite Variety 
of Rhumbs, and therefore as many different Kinds 
of Logarithms, confequently every Species of Loga- 
rithms has its peculiar Rhumb, diftinguifhable by 
the Angle it makes with the Meridian : Therefore, 
among thefe there are two Kinds, whereto the Dif- 
ferences of Longitudes are the Differences of the 
logarithmic Tangents of the Half-Complements of 
Latitudes, eftimated in Minutes of a Degree j one of 
them belonging to Napier’s Form of logarithmic 
Tangents, and the other to Briggs's, or the common 
logarithmic Tangents. 
Art. IX, The common logarithmic Tangents are a 
Table of the ‘Differences of Longitudes, to every 
C c c c a Minute 
