m NAVIGATION. 
would make an angle with the meridians, expreffmg the 
rhumb leading from the one to the other. But though, 
in 1569, Mercator publiflied an univerfal map conftrudted 
in this manner, it doth not appear that he was acquaint¬ 
ed with the principles on which this proceeded ; and it 
is now generally believed, that the true principles on 
which the conftrudtion of what is called Mercator's chart 
depends, were firft difeovered by an Englifhman, Mr. 
Edward Wright. 
Mr. Wright fuppofes, but, according to the general 
opinion, without fufficient grounds, that this enlargement 
of the degrees of latitude was known and mentioned by 
Ptolemy, and that the fame thing had alfo been fpoken of 
by Cortes. The expreflions of Ptolemy alluded to, relate 
indeed to the proportion between the diftances of the 
parallels and meridians ; but, inftead of propofing any 
gradual enlargement of the parallels of latitude in a gene¬ 
ral chart, he l'peaks only of particular maps; and advifes 
not to confine a fyftem of fuch maps to one and the fame 
fcale, but to plan them out by a different meafure, as 
occafion might require : only with this precaution, that 
the degrees of longitude in each fliould bear fome pro¬ 
portion to thofe of latitude; and this proportion is to be 
deduced from that which the magnitude of the refpedtive 
parallels bears to a great circle of the fphere. He adds, 
that in particular maps, if this proportion be obferved 
with regard to the middle parallel, the inconvenience will 
not be great, though the meridians fhould be ftraight 
lines parallel to each other. Here he is faid only to 
mean, that the maps fhould in fome meafure reprefent the 
figures of the countries for which they are drawn. In 
this fenfe Mercator, who drew maps for Ptolemy’s tables, 
underftood him; thinking it, however, an improvement 
not to regulate the meridians by one parallel, but by two; 
one diftant from the northern, the other from the fouth- 
ern, extremity of the map by a fourth part of the whole 
depth ; by which means, in his maps, though the meridi¬ 
ans are ftraight lines, yet they are generally drawn inclin¬ 
ing to each other towards the poles. With regard to 
Cortes, he fpeaks only of the number of degrees of lati¬ 
tude, and not of the extent of them ; nay, he gives exprefs 
directions that they fliould all be laid down by equal mea- 
furement on a fcale of leagues adapted to the map. 
For fome time after the appearance of Mercator’s map, 
it was not rightly underftood; and it was even thought 
to be entirely ufelefs, if not detrimental. However, 
about the year 1592, its utility began to be perceived ; 
and, feven years after, Mr. Wright printed his famous 
treatife entitled, The Correction of certain Errors in 
Navigation ; where he fully explained the reafon of ex¬ 
tending the length of the parallels of latitude, and the 
ufes of it to navigators. In 1610, a fecond edition of Mr. 
Wright’s book was publifhed with improvements. An 
excellent method was propofed of determining the mag¬ 
nitude of the earth ; at the fame time it was judicioufiy 
propofed to make our common meafures in fome propor¬ 
tion to a degree on its furface, that they might not de¬ 
pend on the uncertain length of a barley-corn. Some of 
his other improvements were, “ The table of latitudes 
for dividing the meridian computed to minutes;” where¬ 
as it had been only divided to every tenth minute. He 
alfo publiflied a defeription of an inftrument which he 
calls the fea-rings; and by which the variation of the 
compafs, altitude of the fun, and time of the day, may 
be determined readily at once in any place, provided the 
latitude is known. He ftiowed alfo how to correfit the 
errors arifing from the eccentricity of the eye in obferving 
by the crofs-ftaft'. He made a total amendment in the 
tables of the declinations and places of the fun and ftars 
from his own obfervations made with a fix-foot quadrant 
in the years 159+, 5, 6, and 7. A fea-quadrant to take 
altitudes by a forward or backward observation ; and 
likewife with a contrivance for the ready finding the lati¬ 
tude by the height of the pole-ftar, when not upon the 
meridian. To this edition was fubjoined a tranflation of 
Zamorano’s Compendium above mentioned, in which he 
corrected fome miftakes in the original; adding a large 
table of the variation of the compafs, obferved in very 
different parts of the world, to fhow that it was not occa- 
fioned by any magnetical pole. 
Thefe improvements foon became known abroad. In 
1608, a treatife, entitled Hjpomnemata Mathcmatica, was 
publifhed by Simon Stevin,for the ufeof Prince Maurice. 
In that part relating to navigation, the author, having 
treated of failing on a great circle, and fhown how to draw 
the rhumbs on a globe mechanically, fets down Wright’s 
two tables of latitudes and of rhumbs, in order to def'eribe 
thefe lines more accurately, pretending even to have 
difeovered an error in Wright’s table. But all Stevin’s 
objedtions were fully anfwered by the author himfelf, who 
fhowed that they arofe from the grofs way of calculating 
made life of by. the former. 
In 1624, the learned Wellebrordus Snellius, profefFor 
of mathematics at Leyden, publifhed a treatife of naviga¬ 
tion on Wright’s plan, but fomewhat obfeurely ; and, as 
he did not particularly mention all the difeoveries of 
Wright, the latter was thought by fome to have taken the 
hint of all his difeoveries from Snellius. But this fup- 
pofition is long ago refuted ; and Wright enjoys the ho¬ 
nour of thofe difeoveries which is jultly his due. 
Mr. Wright, having fhown how to find the place of the 
fhip on his chart, obferved that the fame might be per¬ 
formed more accurately by calculation ; but, confidering, 
as he fays, that the latitudes, and efpecially the courfes 
at fea, could not be determined fo precifely, he forbore 
fetting down particular examples; as the mariner may be 
allowed to fave himfelf this trouble, and only mark out 
upon his chart the (hip’s way, after the manner then 
ulually pradtifed. However, in 1614, Mr. Raphe Handfon, 
among his Nautical Queftions, fubjoined to a tranflation 
of Pitifcus’s Trigonometry, folved very diftindtly every 
cafe of navigation, by applying arithmetical calculations 
to Wright’s Table of Latitudes, or of Meridional Parts* 
as it hasfince been called. Though the method difeovered 
by Wright for finding the change of longitude by a fhip 
failing on a rhumb is the proper way of performing it, 
Handfon alfo propofes two ways of approximation to it 
without the aftiltance of Wright’s diviiion of the meridian 
line. The firft was computed by the arithmetical mean 
between the cofines of both latitudes; the other by the 
fame mean between the fecants, as an alternative when 
Wright’s book was not at hand ; though this latter is 
wider from the truth than the firft. By the fame calcu¬ 
lations, alfo, he fhowed how much each of thefe compen- 
diums deviates from the truth, and alfo how widely the 
computations on the erroneous principles of the plane 
chart ■ differ from them all. The method, however, 
moftly ufea by our tailors is commonly called the middle 
latitude; which, though it errs more than that by the 
arithmetical mean between the two coiines, is preferred 
on account of its being lets operofe : yet in high latitudes 
it is more eligible to ufe that of the arithmetical mean 
between the logarithmic cofines, equivalent to the geo¬ 
metrical mean between the cofines themfelves; a method 
fince propofed by Mr. John Bafiht. The computation by 
the middle latitude will always fall fhort of the true 
ehange of longitude ; that by the geometrical mean will 
always exceed; but that by the arithmetical mean falls 
fhort in latitudes above 45 degrees, and exceeds in (mailer 
latitudes. However, none of thefe methods will differ 
much from the truth when the change of latitude is fufti- 
ciently fmall. 
About this time logarithms were invented by John 
Napier, baron of Merchifton in Scotland, and proved of 
the utmoft fervice to the art-of navigation. From which 
Mr. Edmund Gunter conftrufted a table of logarithmic 
fines and tangents to every minute of the quadrant, 
which he publiflied in ioio. In this work he applied to 
navigation, and other branches of mathematics, his admir¬ 
able" ruler known by the name of hunter's Jcdc; on 
which 
