KECKONIXO AT SEA. 



RECKONING AT SEA. 



When ihip CTIMSDS the MU towards the pUoe of iu destination, its 

 path, on account of the various windu, currenU, Ac., by which it in 

 impelled, U always indirect, and generally consists of numeral* zig-zags, 

 whose portions are lines of a few mile* in length. The length of each of 

 then knee, and the angle which it makoa with the terrestrial meridian 

 paving through one of its extremities (all necessary corrections having 

 been made) are the data obtained by the l-*j-li*t and comptut ; and tli 

 earth being supposed to be a sphere, those linos might lie considered I 

 as arcs of great circles. Hence the rule* of spherical trigoninm try 

 might be employed to find tin- length of an arc joining the two ex- \ 

 tremities of Uie series of indirect lines, and the angle which it 

 makes with the meridian passing through either of those extremities ; 

 and, from these, the geographical position of the ship. But, because j 

 this process U considered laborious, others possessing greater facilities 

 are, according to circumstances, employed, and these will be described 

 after it has been shown what are the corrections which the observed 

 elements require before they can be used in the computations. 



The reckoning may be said to commence when the ship is on the 

 point of quitting a harbour or road ; and the first circumstances to be 

 recorded are the observed bearing and the estimated distance of some 

 remarkable object on the coast whose geographical position is known, 

 together with the bearing of the ship's line of motion at the time, 

 and her velocity on that line. 



Let it be here observed that the said object on the coast is called the 

 point of drparturt, and that the angle which the line of a ship's motion 

 at any time makes with the meridian passing through the actual 

 position of the ship is callcd.her courst. Xow, while the angle indicated 

 by the compass remains the same, the ship's path, except when it 

 coincides with the meridian, or with a line tending due east and west, 

 is a portion of that which is called the laxodromic curve [Kni'Mii- , 

 LINE] ; vet, to the extent of a few miles, it is the custom to consider 

 it as a right line, and, therefore, as making a constant angle with the 

 meridian passing through one of its extremities. The deviation of the 

 magnetic from the true meridian (the declination or variation of the 

 needle) differing in different places, the amount of that variation 

 (ascertained by celestial observations as often as possible) must be 

 added to or subtracted from the angles observed with the compass, in 

 order to have the bearing, or course, from the true meridian. But 

 while a ship is sailing with the wind in a direction oblique to the line 

 of her keel, she is compelled, by the force of the wind and the resist- 

 ance of the water against her side, to move in the direction of a line 

 which makes some angle with her keel on the side opposite to that 

 from which the wind is blowing ; this angle is called the ler-icay, and 

 as it differs for different ships, it must always be determined by trial 

 in some one of the ways proposed iu treatises on navigation. The esti- 

 mated amount of the lee-way is a second correction, which must be 

 applied to the course observed with the compass, in order to obtain 

 the correct angle with the meridian. 



The velocity of the ship is ascertained by mean* of tin- 1 

 which at once indicates the number of geographical 

 (equatorial minutes) she has passed over in an hour ; ami oonasqusntlY, 

 supposing her motion to be uniform, the space through which the -hip 

 has sailed on a particular course iu a given number of hours is known. 

 This is technically called the diftanee. 



Again, when a ship is sailing either in a current of the ocean, or in a 

 tide near a shore, her velocity aiul the direction of her motion will In- 

 affected by those of the current or tide. Kirst, if the nhip in impelled 

 by the wind in the same direction as tho current is moving, it \.- 

 evident that the velocity given by the log will be only the ili: 

 between the snip's real velocity and that of the current, an. I 

 quently the Utter must be added to the velocity given by the log in 

 order to have the true velocity. On the other hand, if the hi]> i> 

 ini]>elled by the wind in a direction contrary to that of the current, tho 

 velocity f the latter must be subtracted from that given by the ! 

 order to obtain the true velocity of the ship. Again, if the <li 

 of the current is oblique to the line of the ship's motion accoi 1 

 the compass, the tine path an. 1 velocity "f the hip will, by the com- 

 petition of motioiu, be the diagonal of a parallelogram formed on lines 

 representing the observed directions and velocities of the .-hip ami 

 current; consequently, since this rule is the same em that by which i 

 found a path of the ship which shall be equivalent in length ami 

 tion to any two successive paths whose lengths and directions arc 

 given, it i- evident that among the registered courses and veloci' . 

 a .-hip it will be onlyuiecessary to insert the observed direct! 

 velocity of the current, as if the ship had actually m 

 direction, and with that velocity during the time that she continued to 

 sail in the current. The like remark may be made respecting the 

 deviation of a ship from the course on which she appears by the com- 

 pass to have sailed, in consequence of a swell of the sea, by which . lie 

 may be driven in some other direction. This direction must be 

 observed, and the velocity estimated according to the judgment of the 

 seaman. 



Now, in order to show how all the corrections may be applied to the 

 observed elements, let it be supposed that at the noon of some day a 

 remarkable object A on the shore was observed by the compass to 

 bear W. by N., and that its estimated distance from the ship 

 miles. At the same moment let the ship begin to Rail on a . 

 which is S.W. by the compass; and let the velocity 1-y the 1 

 knots, or 3 miles per hour. Also let the following table exprea the 

 several memoranda in the order iu which they may be suppus .1 to 

 en made in the course of one day; that is, according to the 

 practice of seamen, between the noon of one day and the noon of tin- 

 next. 



The bearing of the ship from the point of departure being corrected 

 for the variation of the needle becomes N. 78 15' E. ; the dist 

 20 miles. 



The first course corrected in like manner becomes S. 21 W. ; and 

 the distance run between noon and 10 P.M. is 43-5 miles. 



The third course corrected for lee-way and variation becomes S. 60 

 34' E. ; and the distance run between 10 r.M. and 8 A.M. is 50'5 miles. 



The fourth course corrected in like manner becomes S. 12 45' E. ; 

 and the distance run between 8 AM. and noon is 25 miles. 



The direction of the swell corrected for the variation of the needle 

 becomes N. 43 30' E.; and the distance is 36 mile*. Lastly, the 

 direction of the current corrected also for the variation become- S. |i; 

 30' E. ; and the distance is 24 miles. 



These corrected courses and distances are then insetted in ord 

 in the first and second columns of the following table ; 



Now, if the navigation is comprehended within about ten degrees on 

 each side of the equator, such a zone. of the earth may be supposed to 

 be projected on the interior surface of a circumscribing cylinder, and 

 then developed on a plane; in which state the meridians and the 

 parallels of latitude become right lines parallel to themselves respec- 

 tively, and the length of a degree of longitude on every parallel equal 

 to that of a degree on the equator or on the meridians. This is called 

 the plane chart, and the projection of a ship's path on it is called plane 



Let the several directions in which the ship luu moved, and the 



distances passed over in each direction, be represented in the subjoined 

 diagram, the construction of which, agreeably to the nature of the 

 plane chart, is as follows : 



Draw the lines A 1, A 2, A 3, &c., making with \p, tho meridian at 

 the point of departure, angles equal to the several courses as they 

 occur successively in the preceding table (col. 1), and draw the lines 

 be, cd, Ice., parallel to A 2, A 3, &c., respectively ; the distances A'I, l:c, 

 cd, &.C., being laid down according to the successive numi 

 by a scale of equal part.H representing geographical mile.- (or equatorial 

 minutes). At the end of the day the ship is arrived at the point </ ; 



