109 



COJIPASS CORRECTION. 



COMPASS CORRECTION. 



HO 



exist in our system. In such a cause, it behoves every man of science 

 who would assist the navigator to cast aside all prejudices and mere 

 " customs," and, taking the simple facts of the case, attempt a total 

 revision of the subject of compass correction. 



But what of the check referred to, as deduced from celestial 

 observation ? The question of correction must be viewed under two 

 aspects, namely, the accuracy and labour in the means employed. As 

 a question of spherical trigonometry, its accuracy is mathematically 

 sufficient ; and, as regards labour, there are two ways of working, 

 namely, by logarithmic calculation and by constrttction. The calcu- 

 lation of an azimuth is the resolution of a spheric triangle, in which 

 certain things are given to find others : as in the following example, in 

 which it was possible to use the horizon. 



Suppose a ship to be in latitude 51 30' N., when the altitude of the 

 sun's centre was 40 25', the sun's declination at the same moment 

 being 20 2' N. : required the sun's true bearing and the error of the 

 compass, the bearing of the sun by compass being S. 79 39' \V. : 



Bum 161 63 



I Sum 80 



Diff. between Sum and F. disU 10 



56i 

 58J 



cosine 

 cosine . 



9-19711 

 9-99193 



The true azimuth . S. 69' 39' W. = Log sine square 9-51336 

 By compass . . . B. 79 39 W. 



Error of compasf . . 100 West. 



Or supposing the horizon obscured, and an altitude impracticable, 

 take the following example : 



A ship in latitude 10 20* N.; sun's declination, 22 14' S.; the time 

 of day, Ih. 44m. 17s. ; the sun's bearing, N. 162 3' West : required the 

 true azimuth and compass error ? 



cotangent 0-6354S 



cot. 3-6354S 



90 0' 

 Sun's declination 22 14 



Polar distance .112 11 



90 s 0' 

 Co. Lat. 10 20 



79 40 



Sum . 

 Difference 



t Sum 

 \ Diff. 



191 54 

 32 34 



93 57 

 IB 17 



secant 0-98439 

 cos. . 0-98221 



88* 34' tan. . 1-60209 

 180 00 



co. sec. 0-00235 

 sine . 9-44776 



tan. | 

 60' 37' / 



0-09359 



Supplement 



Sum, N. 

 N. 



91 20 

 50 37 



142 



162 



3 W. = True azimuth. 



3 W. = Sun's bearing by compass. 



20 W. Error of compass. 



Such are the calculations in each case, and they are shortened when 

 altitude and time are both known. Better even would it be to use in this 

 manner a few extra logarithms daily, than to depend on a correcting- 

 card. But there is another and more simple method, not generally 

 known, of solving a spheric triangle with sufficient accuracy for an 

 azimuth, where the nearest degree is enough, because one cannot steer 

 a ship to within less than a degree or two : it is by construction of the 

 gpheric triangle. This process, however, would have its inconve- 

 niences, although it requires only a plane scale and a pair of dividers 

 or compaxsea. But these inconveniences have of late been totally 

 obviated by the invention of the spherograph [SPHEROGRAPH], in which, 

 having any three elements of a spheric triangle, the others are found 

 without any calculation, and in a very few seconds ; indeed, the Astro- 

 nomer-Royal has given his written opinion that "far Ike special purpose 

 of determining azimuths to correct a compass, he thinks the spheroyraph w 

 excel/' 



In anticipation of the word SPJIEROHRAPH, a sketch of the instru- 

 ment as it appears when finding an azimuth will in this place be 

 sufficiently illustrative. 



In the annexed figure the sun is represented as being just on the 

 horizon, the dark lines of the drawing represent the upper sphere, and 

 the dotted ones those of the under sphere as stem through, the upper 

 transparent one, both sphere.* being moveable on the centre C. 



Suppose the latitude, say 50 N., to be represented by PR (equal to 

 the height of the north pole of the heavens above the north part of 



the horizon), and the oblique circle P o s to represent the hour circle 

 for 7 P.M., and the small circle D o M to represent the sun in its 

 distance from the equator (EQ), or, as it is called, the declination. For 

 all nautical purposes the line D Q) o M may be called the sun's path in 

 the heavens for that day. Now, the part of the circle n must have been 

 moved on its centre c so as to place it 50 (the required latitude) 

 from P : on the under sphere no other movement is required : but we see 

 at a glance that the sun 'would be at M at midnight, at o when rising 

 or setting, and at D when on its meridian. Hence, the degrees being 

 all printed on the spherograph so as to enable all distances to be read 

 off, no further measure or construction could be required, and we 

 should in this instance find that c o on the horizon would measure the 

 rising amplitude and o B the rising azimuth ; and c being the east 

 and R the north part of the horizon of the instrument, the sun 

 would rise at about N.E. by E. Suppose it were required to correct 

 the compass at any time of the day, say at 9 A.M., I should select the 

 9 A.M. hour circle pfg s, as drawn on the under sphere of the sphero- 

 graph, and notice where it crosses the parallel of declination DM at ff) ; 

 and any vertical circle (suppose Z0N) which, passing through the 

 intersection, cuts the horizon (as at x), would show the bearing in 

 azimuth as measured at H X ; and as H is at the south part of the horizon 

 and c is at the east, c x would be very nearly east by south : if the 

 compass showed by it that the sun was at the same time (for instance) 

 E.S.E., the compass would have an error of one point. 



It seems then that a possibility exists of totally avoiding accidents 

 dependent on compass errors, and by a means sanctioned and approved 

 by the Astronomer Royal ; and although changes in magnetic condition 

 cannot be foreseen and prevented, we in reality seem to be able, 6y 

 merely turning a transparent card on its centre, and at any time, or at 

 any part of the world, and by a process which occupies about ten 

 seconds of time, when any heavenly body is visible, and without 

 requiring any observation fur altitude, to place an effectual check upon 

 a compass. 



In order therefore to put the question in a plain and available 

 form for mariners, the following is proposed as a system applicable at 

 all times to any compass, and on board any ship, be her magnetic 

 condition whatsoever it may : and as this method of ascertaining a true 

 azimuth from celestial observation is totally independent of the horizon, 

 it is available in a few seconds whenever any heavenly body is visible, 

 even in hazy weather, and is therefore much more convenient and 

 expeditious, as it must be more accurate, than any swinging of a 

 ship: 



1. As a mariner always knows his latitude and declination to the 

 nearest degree, and his apparent time to the nearest minute or 

 two, let him, when desirous of merely checking his compass, 

 find at once the sun's true azimuth [BEARINO] by the sphero- 

 graph (or by construction or calculation, at pleasure), and 

 compare the result with his compass bearing of the sun's centre. 

 If his ship be at anchor, and he wishes to examine into her 

 general local attraction, let him, while she is stringing with the tide, 

 take the bearings of the ship's head as she comes to the several 

 points of the compass, noting against each observation the 

 apparent time at which it was taken : then let him seek against 

 each of tho.-ic times in the spherograph the corresponding true 

 azimuth of the sun (the whole is done by one movement of the 

 upper card of the sph<>rograph on its centre), and by comparison 

 the whole condition of the ship fur that day or period is shown, 

 and that too without the usual labour and expense and deten- 

 tion of the vessel during compass correction. As many as 300 



