A T A BL E True Course. Courfe to fteer. Miles. 20 Dungeness, S. W. by W. W. W. by S. W. 32 Beachy head, W. S. W. W. W. N. 62 Dunnofe, 33 Peverel Point, Cape la Hogue, 26 Of the True Courfe, Distance, and Courfe to be fteered by a Compafs which va- Dift. Bearing and Distance from Capes, Headlands or Highlands, Islands, Rocks, Lighthouses, &c. 8 S. Foreland by Compafs, W. N. W.is W. St. Catherine's Point, N. by W. W.is N.W. by. W. N. by E.is N. by W. Miles 23956 W. 16 Bill of Portland, S. by W. 19 32 Guernsey I. S. by W.is S. by E. 26 38 'The Start, 27 Eddeftone Lighthouse, N. by E.is N. by W. Ramhead, N. N. E. E.is N. E. 36 2 N. E. is N. Ñ. E. W. 36 to fail in the fair Way 310. you towards the French Coaft; for in fome Parts it fers S. E. and the Mid. Channel till you make the Start, you will have the Tide to fet from the English Coaft, which is in the Lat. 49° 35'N. If you fail in nel between thefe Places, is at one Third of the Width of the Channel 28 Leagues, which is 85 Miles = 1° 25; bnt the fair Way of the ChanNote, Ufhant and the Lizard bear nearly N. and S. of each other, Dist. The British Channel 290 Miles from the S. Foreland to the Lizard; The Method of finding the LATITUDE at SEA, by taking two Altitudes, either in the Forenoon or Afternoon, having the intermediate Time measured by a common Watch, with Eafe and Accuracy. independent of the Sun's Meridian Altitude. GENERAL RULES. O the Secant of the Latitude by Account, add the Secant of the Sun's Declination, (rejecting their Indexes) and call that Sum the Logarithm Ratio.* From the Natural Sine of the greatest Altitude, fubtract the Natural Sine of the leaft Altitude, and find the Logarithm of their Difference, and write it under the Logarithm Ratio, Subtract the Hours and Minutes when the Altitudes were taken from each other, and Half the Difference call Half-elapsed Time. With Half the elapfed Time enter the Tables, and from the Column of Half-elapfed Time take out the Logarithm anfwering thereto, and fet it down under the Logarithm Ratio. Add these three Logarithms together, and with their Sum enter the Tables in the Column of Middle Time, where, having found the Logarithm nearest thereto, take out the Time corresponding to it, and put it down under Half the elapfed Time. Subtract the Lefs from the Greater, and the Difference will be the Time from Noon, when the greatest Altitude was taken. With this Time enter the Tables, and from the Column of Rifing, take out the Logarithm correfponding to it; from this Logarithm fubtract the Logarithm Ratio, the Remainder will be the Logarithm of a Natural Number, which, being found in the common Table of Logarithms, and added to the Natural Sine of the greateft Altitude, will give the Natural Sine of the Sun's Meridian Altitude. Having the Meridian Altitude of the Sun at Noon, the Latitude is found by the usual Method. N. B. If the Latitude, found by the above Process, should differ widely from the Latitude by Account, it will be proper to repeat the Operation; using the Latitude laft found instead of the Latitude by Account, till the Refult gives a Latitude nearly agreeing with the Latitude ufed in the Computation. *The Arithmetical Com. of the Co-fine of any Angle is equal to the Logarithmic Se cant of that Angle, omitting the firft Figure in the Index; thus the Secant of 46° 50' is 10.16487, and omitting the first Figure 1, leaves 0.16487, the Secant lefs Radius, or The Arithmet. Com. of Co-fine 46° 50′. Being at Sea in Latitude 46° 50' North by Account, when the Sun's Declination was 11° 17' N. at 10 H. 2 M. in the Forenoon, the Sun's Altitude was 46° 55', and at 11 H. 27 M. in the Forenoon, the Second Altitude was 54° 9'. Required the true Latitude, and true Time of the Day when the greatest Altitude was taken? The Sun's gr. Alt. at 11 H. 27 M. is 54° 9' The Remainder of Diff. of Nat. Sines 8019 Log. Ratio 0.17335 The common Log. of the Diff. N. S. 8019 3.90412 In the Tables in Col. Ela. Time for 42 M. 30 S. is 0.73429 Their Sum of the Log. in Middle Time 4.81176 H. M. S. The H. M. &c. for which by the New Tables is The Diff. is the true Space of Time the Sun had to I 15 30 42 30 33 00 0 33 Finding they agree, the Watch is right. Enter the Tables with 33 M. under Col. of Rifing, and The Sum is the Natural Sine of the Sun's Meridian The Natural Sines are found in Table XVII. } 81749 The Being at Sea in Lat. 47° 19'N. by Account, when the Sun's Declination was 12o 16'N. at 10 H. 24 M. A. M. per Watch, the Sun's Alt. was 49° 9', at 1 H. 14 M. P. M. his Alt. was 51° 59′. Required the Latitude? H. M. S. 12 O 0. 10 24 0 Alt. Nat. S. Lat. 47° 19' 0:16880. I 36 0 49° 9' 75642 Sun's Dec. 12 16 0.01003 78783 Log. Ratio o Diff. N. S. 3141 Its Log. o Its Log. in Col. of half Elapf. Time is 0.44077 17883 3.49707 Here the Latitude found by Computation may be relied on, as it differs but one Mile from that ufed in the Operation. Being at Sea in Lat. 50° 40′ North per Account, when the Sun's Declination was 20° of South, at 10 H. 17 M. A. M. per Watch, the Sun's Alt. was found 17° 13', at 11 H. 17 M. A. M. per Watch, it was found 19° 41'. Required the Latitude? 35 4 El. T. 0 30 0 Its Log. from Col. half Elap. Time is 0,88430 II O In Col. of Mid. Time corresponding to 4,72032 Tr. Tim.0 31 0 From Noon, its Log. from Col. of Rif. 2,96067 T.p. W. 0 43 0 o Log. Ratio Sub. 0,22504 Lat. 49 59 N. But as this Latitude differs 41 Miles from that by Account, it will be proper to repeat the Operation, ufing the Lat. laft found inftead of the Lat. by Account. H. M. S. Elapfed Time o 30 0 Lat. 49° 59′ 0,19178 Decl. |