[ S 62 ] 
which cuts its Rays at Angles of 45- Degrees, has 
a kind of Logarithms belonging to it, fo related to 
their correiponding Numbers, that the tmalleft Va- 
riation between the firft: and fecond Terms in the 
geometric Series, is equal to the Logarithm of the 
fecond Term, a Cypher being taken for the Loga- 
rithm of the firft. But of this kind are the hyper- 
bolical Logarithms, or thofe firft made by their 
Inventor the Lord Napier : Confequently the Loga- 
rithms to that Spiral which cuts its Rays at Angles 
of 4y Degrees, are of the Napierian Kind. 
Art. IV. The Rhumb-Lines on the Globe are ana- 
logous to the logarithmic Spiral. 
For every oblique Rhumb cuts the Meridian at 
equal Angles: And it is a Property in ftereoeraphic 
Projections, that the Lines therein interfering one 
another, form Angles equal to thofe which they re- 
prefent on the Sphere. Therefore a Projection of the 
Sphere bang made on the Plane of the Equator, 
the Meridians wiL become the Radii of the Equator, 
and the Rhumbs interfering them .t equal Angies, 
will become the proportional Spiral. 
Hence, the Arcs of the Equator, or the Differences 
of Longitude reckoned from the fame Meridian, 
are as the Logarithms of thofe Parts of tne corre- 
fponding Meridians, intercepted between the Centre 
and Rhumb-Line. 
Art. V. A Sea Chart being confirucled, wherein 
the Meridians are parade l to o.,e another , and 
the Lengths op the Degrees of Latitude increafe 
in the fame ‘Proportion as the meridional Di - 
Jiances 
