c 5 6 7 •] 
Tangents of the Half-Complements of the latitudes,' 
in Napier’s Form, are the true Di'tFuenees of Lon- 
gitudes eftimated in fexaseftmal Parts ot a Degree. 
Now Napiers Logarithms being to Briggs Sr as 
2,302^58 &c. is to 1. .1 r - 
Therefore, 2,30258 &c. : 1 :: 29088,821 &c. 
: 12633,114 &c. ; which is the Tangent df 51® 
38' 9"; and in this Angle axe the Meridians ihterL 
feded by that Rhumb, on which the Differences of 
Bricgs's logarithmic Tangents of the Half Comple- 
ments of the Latitudes, are the true Differences of 
Longitudes correlpondwg to thofe Latitudes. 
n- : , ;.v! - ;./ noi?rn:ivf//I 1 o ihou' ri 
Art. X. The \ Difference between Briggs’ s loga- 
rithmic Tangents 6 f the Half -Complements of 
the Latitudes of any two B laces, to the meri - 
dional Difference of Latitude in Minutes between 
thofe B laces, is in the conflant Ratio of 1263,3 
&c. to 1 j or of 1 to 0,0007915704 &c. 
For Briggs s logarithmic Tangents arc as the Dif- 
ferences of Longitudes on the Rhumb ( A ) of 51® 
38' 9''; whofe natural Tangent is 1263,3 &c. 
The nautical Meridian is a Scale of Longitudes on 
♦the Rhumb (B) of 45 Degrees, by Art. VI. whofe 
Tangent being equal to the Radius , may be ex- 
preffed by Unity. And the Differences of Longitude 
to equal Differences of Latitudes on different Rhumbs, 
being to each other as the Tangents of the Angles 
thofe Rhumbs make with the Meridians. Therefore, 
As the Tangent of A (51 0 g8' 9") — 1,2633, &c. 
To the Tangent of B (45°) — 1,00005 
l 
So 
