N A V I G 
which are defcribed lines of logarithms, of logarithmic 
fines and tangents, of meridional parts. See. He greatly- 
improved the feClor for the fame purpofes. He flowed 
alfo how to take a back-obfervation by the crofs-ftafF, 
whereby the error arifing from the eccentricity of the eye 
is avoided. He defcribed likewife another inftrument, of 
his own invention, called the crofs-bow, for taking alti¬ 
tudes of the fun or liars, with fome contrivances for the 
more ready colle&ing the latitude from the obfervation. 
The difeoveries concerning logarithms were carried to 
France in 1624. by Mr. Edmund Wingate, who publifhed 
two fmall tracts in that year at Paris. In one ofthefe he 
taught the ufe of Gunter’s fcale; and in the other, of the 
rabies of artificial fines and tangents, as modelled accord¬ 
ing to Napier’s laft form, erroneoufy attributed by Win¬ 
gate to Briggs. 
Gunter’s rule was projeCled into a circular arch by the 
Reverend Mr. William Oughtred in 1633, and its ufes 
fully fiown in a pamphlet entitled The Circles of Pro¬ 
portion where, in an appendix, are well treated feveral 
important points in navigation. It has alfo been made in 
the form of a Aiding ruler. 
The logarithmic tables were firft applied to the different 
cafes of failing by Mr. Thomas Addilbn, in his treatife 
entitled Arithmetical Navigation, printed in 1625. He 
alfo gives two traverfe-tables, with their ufes; the one 
to quarter-points of the compafs, the other to degrees. 
Mr. Henry Geilibrar.d publiflied his difeovery of the 
changes of the variation of the compafs in a fmall quarto 
pamphlet entitled “ A Difcourfe mathematical on the 
Variation of the Magnetical Needle,” printed in 1635. 
This extraordinary phenomenon he found out by com¬ 
paring the obfervations made at different times near the 
fame place by Mr. Burrough, Mr. Gunter, and himfelf, all 
perfons of great Ikill and experience in thefe matters. 
This difeovery was likewife foon known abroad ; for 
Athanafius Kircher, in his treatife entitled Mognes, firft 
printed at Rome in 164.1, informs us, that he had been 
told it by Mr. John Greaves 5 and then gives a letter of 
the famous Marinus Merfennus,containing a very dillinCt 
account of the fame. 
As altitudes of the fun are taker, on fliipboard by ob- 
ferving his elevation above the vifible horizon, to obtain 
from thence the fun’s true altitude with corre&nefs, 
Wright obferves it to be neceffary that the dip of the 
vifible horizon below the horizontal plane palling through 
the obferver’s eye fiuould be brought into the account, 
which cannot be calculated without knowing the magni¬ 
tude of the earth. Hence he was induced to propofe dif¬ 
ferent methods for finding this; but complains that the 
moft effectual w f as out of his power to execute; and there¬ 
fore contented himfelf with a rude attempt, in fome mea¬ 
fure fufficientfor his pufpofe: and the dimenfions of the 
earth deduced by him correfponded very well with the 
ufual divifions of the log-line; however, as he wrote not 
an exprefs treatife on navigation, but only for the correct¬ 
ing fuch errors as prevailed in general practice, the log¬ 
line did not fall under his notice. Mr. Richard Norwood, 
however, put in execution the method recommended by 
Mr. Wright as the moft perfect for meafuring the dimen¬ 
sions of the earth, with the true length of the degrees of 
a great circle upon it; and, in 1635, he actually meafured 
the diftance between London and York; from whence, 
and the fummer folftitial altitudes of the fun obferved on 
the meridian at both places, he found a degree on a great 
circle of the earth to contain 367,196 Englilh feet, equal 
to 57,300 French fathoms or toifes: which is very exaCt, 
as appears from many meafures that have been made fince 
thattime. .Of all this Mr. Norwood gave a full account 
in his treatife called The Seaman’s PraCtice, publifhed in 
3637. He there flows the reafon why Snellius had failed 
in his attempt: he points out alfo various ufes of his dif¬ 
eovery, particularly for correcting the grofs errors hi¬ 
therto committed in the divifions of the log-line. But 
neceffary amendments have been little attended to by 
Vol. XVI. No. 1x40. 
A T I O N. 617 
failors, whofe obftinacy in adhering to the eftabliflied 
errors has been complained of by the belt writers on na¬ 
vigation. This improvement has at length, however, 
made its way into practice ; and few navigators of reputa¬ 
tion now make ufe of the old meafure of forty-two feet 
to a knot. In that treatife alfo Mr. Norwood deferibes 
his own excellent method of fetting down and perfecting 
a fea-reckoning, by ufing a traverfe-table; which method 
he had followed and taught for many years. He flows 
alfo how to reCtify .the collide by the variation of the com¬ 
pafs being confidered; as alfo howto difeover currents, 
and to make proper allowance on tiieir account. This 
treatife, and another on trigonometry, were continually 
reprinted, as the principal books for learning feientifi- 
cally the-art of navigation. What he had delivered, efpe- 
cially in the latter of them, concerning this fubjeft, was 
contracted as a manual for failors, in a very fmall piece 
called his Epitome; which ufeful performance has gone 
through a great number of editions. No alterations were 
ever made in the Seaman’s PraCtice till the twelfth edition, 
in 1676, when the following paragraph was inferted in a 
fmaller character: “ About the year 1672, Monfieur 
Picar publified an account, in French, concerning the 
meafure of the earth, abrevia&e whereof may be feen in 
the Philofophical TranfaCtions, No. 112, wherein hecon- 
cludes one degree to contain 365,184 Englifli feet, nearly 
agreeing with Mr. Norwood’s experiment.” And this ad- 
vertifement is continued through the fubfequent editions 
as late as the year 1732. 
About the year 1645, Mr. Bond publiflied in Norwood’s 
Epitome a very great improvement in Wright’s method, 
by a property in his meridian line, whereby its divifions 
are more fcientifically afligned than the author himfelf 
was able to effeCt; which was from this theorem: That 
thefe divifions are analogous to the exceffes of the loga¬ 
rithmic tangents of half the refpeftive latitudes aug¬ 
mented by 45 degrees above the logarithm of the radius. 
This he afterwards explained more fully in the third edi¬ 
tion of Gunter’s works, printed in 1653. His rule for 
computing the meridional parts belonging to any two 
latitudes, fuppofed on the fame fide of the equator, is to 
the followung effeCf: “Take the logarithmic tangent, 
rejecting the radius, of half each latitude, augmented by 
4.5 degrees ; divide the difference of thofe numbers by 
the logarithmic tangent of 45 0 30', the radius being like¬ 
wife rejected ; and the quotient will be the meridional 
parts required, expreffed in degrees.” This rule is the 
immediate confequence from the general theorem, That 
the degrees of latitude bear to one degree (or 60 minutes, 
which in Wright’s table Hands for the meridional parts 
of one degree) the fame proportion as the logarithmic 
tangent of half any latitude augmented by 45 degrees, 
and the radius negleCted, to the like tangent of half a 
degree augmented by 45 degrees, with the radius likewife 
rejeCted. But here was farther wanting the demonftra- 
tion of this general theorem, which was at length fupplied 
by Mr. James Gregory of Aberdeen in his Exercitationes 
Geometricte, printed at London in 1668 ; and afterwards 
more concifely demonftrated, together with a fcientific 
determination of the divifor, by Dr. Halley in the Philo¬ 
fophical TranfaCtions for 1695, N° 219, from the conli- 
deration of the fpirals into which the rhumbs are franf- 
fortned in the ftereographic projection of the fphere upon 
the plane of the eq-uinoCtiai; and which is rendered ltill 
more fimple by Mr. Roger Cotes, in his Logometria, firft 
publiflied in the Philofophical TranfaCtions for 1714, 
N° 388. It is moreover added in Gunter’s book that, 
if -J&th of this divifion, which does not fenlibly differ from 
the logarithmic tangent of 45 0 1'30" (with the radius 
fubtraCted from it), be ufed, the quotient will exhibit 
the meridional parts expreffed in leagues; and this is the 
divifor let dow n in Norwood’s Epitome. After the fame 
manner the meridional parts will be found in minutes, if 
the like logarithmic tangent of 45 0 i' 30", diminiflied by' 
the radius, be taken; that is, the number ufed by others 
7 S being 
