Page:Encyclopædia Britannica, Ninth Edition, v. 17.djvu/277

Rh NAVIGATION 265 Log of H.M.S. &quot;North Star.&quot; H. K. A Course. Lee way. Wind. 2 2 ts 1 Q 1 o tj

Is =s Remarks, &c. Tuesday, May 9th, 1882. Direction. Force. 1 2 3 4 5 6 7 8 9 10 11 12 Moored in Plymouth Sound. Single anchor. Working ont. A.M. 6. Unmoored, and shortened in on SB. to 30 fathoms. 9.30. Made all plain sail. Weighed and worked ont of Plymouth Sound. Noon. Tacked. Calm.

or 29-86 54 Vble. 2 og South. 4 be 30-0 55 SWS. Vble. 6 bv 30-0&quot;. 57 Course, made good. Distance. Latitude. Longitude. Variation Allowed True Bearings and Distance. Made Through Good, the Water. D.R. D.R. Obs. Current. 20 25 Wly. Eddystone Lighthouse, S 34&quot; E., 1 mile. 1 2 3 4 5 6 7 8 9 10 11 12 7 8 6 7 7 7 7 8 4 3 7 8 4 6 6 4 &quot;2 6 8 8 swjs. s b v iw. South. SSE. S Southerly. 6 be 5JE. 58 P.M. Tide set W. by S. (true) 5 miles, during the afternoon. 4. Lizard Lighthouses, N.W., 12 miles. (Ship s headS.W. by W.) ,, Taken aback, by shift of wind. Braced round on the star board tack. 8.30. W illiam Jones fell from the main-rigging and broke his arm. 11. Tacked. Midnight. Two sail in sight.

SSE. 6 og 8JE. 30-0 58 i Westerly. 5 oq 7E. J WSW. 7 bcp

29-90 56 J SW. 4} W i 7 bcq 2W. 29-85 54 45 Remarks, &c. Wednesday, May 10th, 1882. 1 2 3 4 5 6 7 8 9 10 11 12 8 8 8 7 7 6 6 5 2 7 10 5 5 2 5 5 2 WNV. NW.

SW. 7 be 2 W. A.M. 2.20. Exchanged numbers with the s.s. &quot; Fox,&quot; bound to London. 7. Variation by azimuth (head N.W.) 24-25 westerly. 10. Trimmed sails. Xoon. Set port studding sails. ... j ... i WSW. 6 om 4 W. 29-80 50 i 5 od b&quot; Vble. SE. 3 6 7 or be bcv - J 29 : 9 54 4(9 Course, made good. S56JW. Distance. Latitude. Longitude. Variation True Bearings and Distance. Allowed. Made Through Good. the Water. D.R. 49 7 54&quot; D.R. 6-42 Obs. 49 8 13&quot; Obs. Current. Entrance to Strait of Belle Isle. 20 25 W. N. 85 9 W. 1858 miles. Do. By great circle sailing, N. C6 3 W. 1824-2 miles. 114-1 174-3 1 2 3 P.M. &quot;With middle latitude 49 40 and departure 95 1, enter the traverse table. Taking the complement of middle latitude as a course, and the departure in its column, the difference of longitude = 147 is found in the distance column ; which being west is added to the Eddy- stone s westerly longitude. To find the Course and Distance Made Good by Infection. Difference of latitude 63 1 and departure 95 1 will be found opposite 56^ and under 114 ; therefore it is S. 56J &quot;W. 114 miles from the Eddystone. To do the same more exactly by logarithms, the multiplication and division of the quantities being performed by the addition and subtraction of their logarithms. First, required the difference of longitude. dep. 95 ! xrad. cos mid. lat. 49 40 95-1 log + 10... 11-978180 49 40 log cos 9-811061 Or Diff. long. 146-9 log 2 167119 dep. 95 1 x sec 49 40 = diff.long. rad. 95-1 log 1-978180 49 40 log sec -10 0188939 Diff. long. 146-9 log 2-167119 The proportions which sines, tangents, and secants bear to the- course, distance, difference, latitude, and departure, and these to each other, form the principal points in plane trigonometry connected with navigation, which can be easily demonstrated by two figures. If the hypothenuse AB be made radius, as in fig. 12, the whole will be con tained within the circle, and the sides are in proportion to the sines of their opposite angles ; but if the base be made the radius, as in fig. 13, the other side BC is entirely without the circle, touching only at the point C ; it is therefore a tangent subtending the angle A, and the hypothenuse AB be comes the secant of the angle A. In like manner BC may be made radius, then AC would become the tangent of angle B. PJO-. 13. To find the course and distance made good by calculations. Making BC the radius, XVIL 34