Let the difference of longitude be 40°; but the latitudes 56° and 80°;
And log. 2400´ }
+ log. constant } = -1.4817217
Log. sin. 68° = -1.9671659
----------
S = -1.4488876
T (tang. 22°) = .4040262
_m_ = .2109980
--------
Log. (T + _m_) (= .6150242) -1.7888921
Log. (T - _m_) (= .1830282) -1.2625181
----------
Log. 0.5263740 = D = -1.7212944
----------
S - D (= log. tangent 28° 6´) = -1.7275932
wanting of the true answer no more than 1° 4´.
And in all cases that can occur, the error of this rule will be
inconsiderable.
It is not meant, however, that it ought to take place of the easier and
better computation by a table of meridional parts: but it was thought
proper to shew, by some examples, how safely the map itself may be
depended on in the longest voyages; provided it is sufficiently large,
and the necessary rumb-lines are exactly drawn[30].
LXXIV. _A short Dissertation on Maps and Charts: In a Letter to the
Rev._ Thomas Birch, _D. D. and Secret. R. S. By Mr._ Wm. Mountaine,
_F.R.S._
[Read April 6, 1758.]
London, March 21. 1758.