N LVIQATIOK. 



[MIRCATOB'S AI 



the departure (C B) be given, then the proportion will 

 be 



A* the proper difference of latitude in to the departure, 

 > U the meridional difference of latitude to the difference 

 of longitnde. 



Such are the correct principles IIJMITI which a into sea- 

 chart U constructed ; but whether (!orrard Mercator, the 

 h (.'hart-maker, wa really in possession of tlicse 

 principles, or whether he arrived ;it their ]>ra< tical results 

 by a aerie* of happy mechanical experiments, is nut posi- 

 tively known ; ho never divulged tho methods by which 

 he proceeded, and his secret descended with him to the 

 grave. The first chart he published was in 1550 ; ami it 

 was not till the year 1500 that the true theory of its con- 

 was expounded. This was done by Edward 

 WrL-ht, Fellow of Cains College, Cambridge, who did not, 

 however, communicate his discovery to the public till 

 the year lii'.M. when his Certain Errors in A'ari<j<itinn 

 appeared ; yet tho key to tho 



entire secret U furnished by the single equation marked 



( 1 ) at page 1061 ; a property so obvious, that we cannot 



but suppose it must have been noticed by numbers of 



persons engaged in these investigations, before that time; 



but, like the common occurrence of the falling of on 



apple from a tree, it was not perceived to be the germ of 



a theory destined to change the aspect of an important 



rtment of science, till it arrested the attention of a 



."r mind. 



Edward Wright constructed his table of meridional 

 parts after tho process already described ; that is, by 

 actually adding secant after secant through every minute 

 i if the quadrant. But it was subsequently shown, by 

 Dr. II alley, that the meridional parts might be actually 

 obtained in another way we shall explain how at the 

 end of the present article. 



It is proper to remark that a table, constructed agree- 

 ably to Air. Wright's plan, will be more mathematically 

 correct the smaller the elementary portions of the 

 meridian are made ; as, for instance, if the portions, 

 inst;;iil <>f a minute, bo only half a minute in length. 

 Such a table was accordingly constructed by Oughtred, 

 and further extended by Sir Jonas Moore ; but the 

 modern table of meridional parts is based upon the 

 strictly accurate theory of Dr. ll.il Icy. Mr. Wright, 

 however, was fully sensible that, from the intervals in 

 his table being so great as 1', hia meridional parts, for 

 high latitudes, erred a little in excess, and he pointed 

 out the method of diminishing the error to any extent. 



It behoves every writer on Navigation to bring the 

 name of !'.<! :u-.l Wright prominently forward when 

 ng of what is called Murcator's Sailing. Mercator 

 has, no doubt, the merit of originating the scheme of 

 enlarging the decrees of the meridian more and more as 

 they approach the pole, or of widening the intervals 

 hvtw. cessive parallels of latitude ; he was thus 



instrumental in awakening attention to a more correct 

 way of exhibiting longitudes on a chart than was known 

 before his time ; but that he was acquainted with the 

 true principles discovered by Wright, there is strong 

 reason to doubt : for the degrees in his chart were not 

 lengthened in the due proportion which those principles 

 pointed out. 



It will occur to the reader that, when the course A 

 U a large angle, a small inaccuracy in the measure of 

 that angle may considerably affect the length of C' B'; 

 and, therefore, to diminish tho inlluenee of this error in 

 the course, it is better and safer, when it differs but 

 little from K. or W., to use the middle latitude method ; 

 there is no defect in the table of meridional parts, when 

 the proper decimals are inserted, but in the data employed 

 in connection with it. 



In moot collections of navigation tables, however, tho 

 .iU of the meridional parts are omitted, and the 

 meridional parts given only to tho nearest unit It is 

 possible, then-fore, that in taking t! between 



two numbers in tho table, there may bo an error of nearly 

 a mile in tho result. The equation 



dilf. loni;. = meriil. ditf. hit. X tan. course, 

 hows that the corresponding error in longitude will bo 



proportional to the error in tan. course. Suppose, for 

 instance, the course be 7 points, the Undent of wh 

 about 5; then tho error in longitude may potribly be 

 5 miles, which isof some consideration ; but, as observed 

 In-fore, in such a large course the middle latitude m. 

 for otlu-r reasons, should bo employed. It would, 

 ever, be an improvement if tho leading decimal belonging 

 to each meridional part were actually inserted in the 

 tables. Robertson, one of the most able and instructive 

 writers on Navigation, doct introduce the leading deci- 

 mal ;* ami so, likewise, does Dr. In man in his JVni</i.-.<Z 

 Tab'tt. An extensive table of meridional parts will also 

 bo found in the quarto collection of Table* of J. Do 

 Mi ndoza Rios. The following short table will show the 

 true meridional parts calculated agreeably to tho mathe- 

 matically-correct formula: given at the end of the present 

 article. 



We shall now re-state the proportions given iu words 

 above, and proceed to examples. 



As radius : tan. course : : Mer. diff. lat. : diff. long 

 As proper diff. lat. : departure : : Mer. diff. lat. : diff. long' 



i pies. 



1 . A ship from latitude 51 18' X., longitude 9 50' W. , 

 steers 8. 33' 8' W. , till she has run 1024 miles. Required 

 the latitude and longitude in. 



The difference of latitude is found in Example 1, page 

 1058, to be 857i miles, or 14 17' S. ; and therefore the 

 latitude in 37 V N. 



51 18' mer. parts . . 3597 5 

 37 1' . . . 2393-9 



1203-6 



.-10 



. H-8147 

 . 3-0806 



Diff. 14 17' 



As radius . 

 : tan. course, 33" 8' 

 : : mer. ditf. lat. 1204 



: diff. long. 785 '8 . 



Hence the diff. Ion?. = 13 6' \V. 

 long, left = 9 50' \V. 



.'. long, in = 22 56' 



2. A ship from latitude 49 67' N., and loDjritoda 

 5 11' W., sails between the south and west till she 

 arrives in latitude 38 27' N., and linds that she has 

 made 440 miles of departure. Required the course 



1, the distance run, and tho longitude in. 

 The course and distance are found in Kxample 2, page 

 1059; and the difference of longitude is found by tho 

 table of meridional parts, as follows : 



lat. left 49 57', mer. parts . 3470 

 lat in 38 i7' 2503 



diff. lat. 11 30* 



907 



\Ve do not understand what Robertson mr.in when he *aya " Rut a 

 table nf meridional part*, constructed by the m<>t accurate method, hu 

 only ahowrd th.it Mr. Wriirhl'a table doca nowh 



ridian part* by half a minute, and ihitonlr near the pole ; for in latitude* 

 a* far aa navigation in practicable, ti m scarcely n< i 



Slrmmt* of Ajrtj/.i'i"N, hy John RnhrrtiMn. formerly Head Master of 

 the Royal Aeademv at Portamnuth ; vol. 2. p. 1M. 



Robertson'* work ii a very valuable prrfurnmnro. and i well dearrrlng 

 a place in the eeaman'a library. It may t tip, at the 



book-null*, at a very low price. For a correct uhlo of meridional part* 

 (the decimal! omitted), the Ublea of None, Kiddie, or Rapcr may b* 



