Log. 6600´ (in 110°) 3.8195439 Constant log. -4.1015105 ---------- -1.9210544 Log. sin. 35° -1.7585913 ---------- S = ... -1.6796457 Again T = 1.4281480 _m_ = .4513202 --------- Log. (T + _m_) (= 1.8794682) 0.2740350 Log. (T - _m_) (= 0.9768278) -1.9898180 ---------- Log. 0.2842170 = D = -1.4536500 ---------- S - D (= log. tangent 59° 16´) = 0.2259957 agreeing to a minute with the solution by a table of meridional parts. EXAMPLE 2. The rest remaining, let the difference of longitude be only 40°; then Log. 2400´ (in 40°) 3.3802112 Constant log. -4.1015105 ---------- -1.4817217 Log. sin. 35° -1.7585913 ---------- S = -1.2403130 D (as before) = -1.4536500 ---------- S - D (= log. tang. 31° 27´ ½) -1.7866630 EXAMPLE 3. 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. SIR, AMONG the several improvements made in arts and sciences by ingenious men, the construction of _globes_, _maps_, or _charts_, deserves a place: not only on account of the pleasure and satisfaction that arises to speculative minds, in surveying the extent and divisions of this terraqueous globe, but also for their real use and service to navigation, trade, and commerce.