Degrees A Table of Meridional Parts. 120 75 90 105 135 150.165 3 180 195 210 225 15 910 926 942 957 16 973 988 IC04 1020 17 1035 10511067 1082 18 1098 1114 1130 1146 19 1161 1177 1193 1209 20 1225 1241 1257 1273 21 1289 1305 1321 1338 22 1354 1370 1386 1402 23 1419 1435 14511468 24 1484 15091517 1533 25 1550 1567 1583 1600 26 1616 1633 1650 1667 27 1684 1700 1717 1734 28 1751 1768 1785 1802 29 1819 1837 1854 1871 30 1888 1906 1923 1941 - Centefines. 25 50 75 31 1950 1976 1993 2011 32 2028 2046 2064 2082 33 2100 2117 2135 2153 34 2171 2190 2208 2226 35 2244 2263 2281 2300 36 2318 2337 2355 2374 37 2393 2411 2430 2449 38 2468 2487 2507 2526 39 2549 2564 2584 2603 40 2523 2642 2662 2682 41 2702 2722 2742 2762 42 2782 2802 2822 2843 43 2863 2884 2904 2925 44 2946 2967 2988 3009 45 3030 3051 3073 3094 46 3116 3137 3159 3181 47 3203 3225 3247 3269 48 3292 3314 3337 3359 49 3382 3405 3428 3451| 50 3475 3498 3522 3545 51 3567 3593 3617 3641 52 3665 3690 3714 3739 53 3764 3789 3814 3839 54 3865 3890 3916 3940 55 3968 3994 4021 4047 56 4974 4101 4128 4155 57 4183 4211 4238 4266) 58 4295 4323 4352 4380 59 4409 4439 4463 4498 60 4528 4558 4588 4619 61 4650 4681 4712 4744 Hhh 2 4744 A The Ufe of the Table of Meridional Parts. What Meridional Parts do answer to 26 deg. of Latitude: Latitude 26. oo Deg 24. 25 Deg47. 50 Deg63.00 Deg 2. What Degrees and Cetefims do anfwer to. 11. 25 Deg. 679 Merid. Parts.Anfwer5c. 50 Deg. 3522 M. P. 9488 M. P. 283.75 Dég. For the Refolving of the following Problems, which (in kind) Fig. will be the fame with thofe in Plain Sailing as to the Trigonometri. LXIX. sal Work. But in the performance of them, I will fet the places propofed down upon a Sea-Chart, made according to the Projection of Mercator, where the Degrees of Latitude are enlarged according as they tend nearer and nearer to the Pole: And on the out-fide of fuch a Chart, I have defcribed a Plain Sea-Chart alfo,where the Meridians and Parallels of Latitude are every where of an equal distance; and fo wrought the Questions according to both Charts, by which the difference will more plainly appear: And the Chart which I have here made to work the following Examples upon, begins (at the bottom of it) at about 49.50 deg. of Latitude, and extends upwards to 55. 50 deg. of Latitude; and at the Top and Bottom to Six Degrees Difference of Longitude: But the Parallels of Latitude in the Plain Chart, (which are diftinguifhed by Pricked Lines) ex-~ tend to above 59 deg. of Latitude within the fame Bounds. PROB. I. The Latitudes of two Places, and their difference of Longitude being known; To find, (1) The Rumb leading from one to the other: And (2) Their. Diftance upon that Rumb: according to Mercators Chart. By Trigonometrical Calculation L the Fig. the Chart, draw the Line A C, which is the Rumb (or Course) LXIX. from A to C: And thus have you upon your Chart conftituted a Right-angled Plain Triangle ABC, in which you have given, (1) B C, the Difference of Longitude 6.50 deg. which you muft Reduce into Miles (or Minutes) of Longitude by multiplying them by 60, (as in Plain Sailing) and they make 330. 00 Miles.- (2) A B, the Difference of Latitude 5. co deg. which must be Reduced into Meridional Parts thus: The Meridional Parts for 50. 00 d. are For 55.00 Their Difference 3475 2968 493 Which are the Meridional Parts anfwering to the 5. co deg. Diffe rence of Latitude of the two Places A and C: And by thefe you may find; (1.) The Rumb BAC. (2) The Meridional Diftance upon the Rumb A C. By Trigonometrical Calculation. As the Merid. Dif. of Latitude A B, 493 M. P. Is to the Dif. of Longitude B C 330 Miles So is the Radius, Tangent 45 deg. To the Tangent of BA C, 33. 80 degrees. 2.692847 12.518514 IO. 9.825667 Which is the Rumb, leading from A to C: whofe Complement 56. 20 deg. is the Angle B C A, or the Complement of the Rumb: (2.) For the Meridional Diftance on the Rumb A C. As the Co-fine of the Rumb: B CA, 56. 20 d. 9.919592 Is to the Merid. Differ. of Latitude AB 493 M. R. 12.692847 So is Radius Sine 90 deg. IO. To the Merid. Diftance A C, 593.27 M. P. 2.773255 Now to find the Meridional Degrees anfwerable to thefe Meridi onal Parts, you must Firft, Subftract the MPO of AB, from the M P of A C, their Difference is Ico. 27 M.P. the half whereof is 50.13 M. P. Secondly, Add this half Difference 50. 13, to the Meridional Parts of the Greater Latitude 55. co deg. viz. 3968, and it makes 4018. 13, which are the Merid. Parts anfwering to 55. 50 deg. of Alfo, fubftract this half Difference 50. 13, from the Merid. Parts of the Leffer Latitude 50.co deg. viz. 3475, and the Remainder Latitude. -- Remainder will be 3424. 87, which are the Merid. Parts anfwering Fig. to 49.38 deg. of Latitude. Thirdly, The Difference of thefe two Latitudes laft found, viza, 55. 50 de. and 49. 38 deg. is 6. 12 deg. And that is the trie Distance upon the Rumb between A and C, in Degrees. And according to this Method, may all the other Problems (before wrought by the Plain Sea-Chart) be performed by Tri. Calculation; by the fame Canons: Only remember, to Reduce the Difference of Latitudes and Diftance on the Rumb, înto Meridional Parts, but the Difference of Longitude into Miles, as in the other. Now that you may fee the Difference between thefe two ways; See the Figure of the Chart, wherein the two Places are laid down by the Plain Chart; as in the Triangle AOS, which Triangle be ing refolved (as is before fhewed) you will find (1) The Rumb OAS, to be 47. 73 deg. Differing from the truth 13. 93 deg.. (2) The Distance upon the Rumb AS, to be 7. 43 de. Differing from the other I. 31. And let thus much fuffice for Sailing according to Mercator.. There is a third way of Sailing, which differs not much from this way of Mercator's, but may be performed without Reductien or ufe of Meridional Parts; which is called Sailing by the Middle Latitude: of which a little. L.XIX.. I III. Of Sailing by the Middle Latitude. Shall exemplefie this way of Sailing by Four of the moft ufual Problems in Navigation: And they fhall be the fame as in the foregoing whereby the Difference will the better appear... PROB. I The Longitude and Latitude of two Places, A and C, Given (1) The Rumb BA C. (2) The Distance upon the Rumb: AC. LET |