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the sim’s declination for lour years, in order to find the latitude jfrom his meridian-altitude'; directions to find the same by-certain |stars ; of the course of the sun and moon ; the length of the days; jof time and its divisions; the method of finding tlie hour of theday and night; and lastly, a description of the sea-chart, on which, Ito discover where the ship is, they made use of a small table, that jshe ved, upon the alteration of one degree of the latitude, how jman v leagues were rim in each rhumb, together with the depnr- !ttire from the meridian. Besides, some instruments were describ-ed, especially by Cortes ; such as one to find the place and de-clination of the sun, with the days, and place of the moon ; cer- |tain dials, the astrolabe, and cross-staff; with a complex machine ito discover the hour and latitude at once. About the same limewere made proposals for finding the longitude by observations onthe moon. In 1530, Gemma Frisius advised the keeping of thetime by means of small clocks or watches, then, as he says, new lyinvented. lie also contrived a new sort of cross-staff, and an in-strument called the nautical quadrant; which last was muchpraised by William Cunningham, in his Astronomical Glass,printed in i 559. In 1537, Peter Nunez, or Nonius, published abook in the Portuguese language, to explain a difficulty in navi-gation proposed to him by the commander, Don Martin AlphonsoL)e Susa. In this he exposes the errors of the plane chart, andgives the solution of several curious astronomical problems;among which is that of determining the latitude from two observa-tions of the sun’s altitude, and intermediate azimuth being given.He invented a method of dividing a quadrant by means of con- :centric circles, which, after being much improved by Dr. Halley,is used at present, and is called a nonius. In 157’L Mr. WilliamBourne published a treatise, in which, by considering the irregu-larities iu the moon’s motion, he shews the errors of the sailors infinding her age by the cpact, and also in determining the hourfrom observing on what point of the compass the sun and moonappeared. Also he describes the way by which our sailors esti-mate the rale of a ship in her course, by the log. This was sonamed from the piece of wood or log that iloats in tho water, whilethe time is reckoned during which the line that is fastened to it isveering out. The author of this contrivance is not known ; nei-ther was it taken notice of till 1607, in an East India voyage, pub-lished by Purchas : but from this time it became famous, and wasmuch taken notice of by almost all writers on navigation in everycountry ; and it still continues to be used as at first, though manyattempts have been made to improve it, and contrivances pro-posed to supply its place ; many of which have succeeded in quiet |water, but proved useless in a stormy sea. See Log. Several jimprovements were soon made ; but many errors were still found j]tn the practice of sailing, especially’ such as were the consequences 1of using the plain chart. Methods of removing these errors hadindeed been sought after; and Gerard Mercator seems to havebeen the first who found the true method of doing this so as toanswer the purposes of seamen. His method was to represent theparallels both of latitude and longitude by parallel straight lines,but gradually to augment the former as they approached the pole.Thus the rhumbs, which otherwise ought to have been curves,were now also extended into straight lines; and thus a straightline drawn between any two places marked upon the chart wouldmake an angle with the meridians, expressing the rhumb leadingfrom the one to the other. But though, in 1569, Mercator pub- ilished an universal map constructed in this manner, it doth not jappear that he was acquainted with the principles on which thisproceeded; and it is now generally believed, that the true prin-ciples on which the construction of what is called Mercator ’s chartdepends, were first discovered by an Englishman, Mr. Edward jWright. For some time after the appearance ot Mercator ’s map, jit was not rightly understood, and it was even thought to he en- jtirely useless, if not detrimental. However, about 1592, its utility |began to be perceived ; and seven years after Mr. W right printed :his famous treatise intituled “ The Correction of certain Errors inNavigation,” where lie. fully explained the reason of extending thelength of the parallels of latitude, and the uses of it to navigators. In1610 a second edition of Mr. Wright’s book was published withimprovements. An excellent method w r as proposed of determin- ]ing the magnitude of the earth; at the same time it was judiciously iproposed to make our common measures in some proportion to a |idegree on its surface, that they might not depend on the uncertain I
length of a barley-corn. Some of his other improvements were,“ The table of latitudes for dividing the meridian computed tominutes;” whereas it had only been divided to every tenth mi-nute. lie also published a description of an instrument which hecalls the sea-ring; and by which the variation of the compass,altitude of the sun, and time of the day, may be determinedat once in any place, provided the latitude is known. Heshewed also how to correct the errors arising from the eccentricityof the eye in observing by the cross-staff. He made a totatamendment in the tables of the declinations and places of the sunand stars from his own observations made with a six-foot quadrantin the years 1594, 95, 96, and 97. These improvements soon be-came known abroad. In 1608, a treatise intituled llypomneinataMathematics was published by Simon Stevin , ior the use of 1’rinceMaurice. In that part relating to navigation, the author havingtreated of sailing on a great circle, and shewn how to draw therhumbs on a globe mechanically, sets down Wright’s two tablesoflatilude and of rhumbs, in order to describe these lines moreaccurately, pretending even to have discovered an error inWright’s table. Blit all Stevin ’s objections were fully answeredby the author himself, who shewed that they arose from the grossway of calculating made use of by the former. Though the me-thod discovered by Wright, for finding the change of longitude bya ship sailing on a rhumb, is the proper way of performingit, Hand-son proposes two ways of approximation to it without the assistance ofWright’s division of the meridian-line. The first was computedby the arithmetical mean between the cosines of botli latitudes;the other by-the same mean between the secants, as an alternate,when Wright’s book was not at hand ; though this latter is widerfrom the truth than the first. By the same calculations also heshewed how much eacli of these compenditims deviates from thetruth; also how widely the computations on the erroneous prin-ciples of the plane chart differ from them all. The method, how-ever, generally used by our sailors is commonly called the middlolatitude : which, though it errs more than that by the arithmeticalmean between the two co-sines, is preferred on account of itsbeing less operose: yet in high latitudes it is more eligible to usethat of the arithmetical mean between the logarithmic co-sines,equivalent to the geometrical mean between the co-sinrs them-selves ; a method since proposed by Mr. John Bassat. The com-putation by the middle latitude will always fall short of the truechange of longitude; that by the geometrical mean will alwaysexceed; but that by the arithmetical mean falls short in latitudesabove 45°,and exceeds in less latitudes. However,none of these me-thods will differ much from the truth when the change of latitude issmall. About this time logarithms were invented by John Napier ,Baron of Merchiston in Scotland , and proved of the utmost serviceto the art of navigation. They were first applied by Mr. EdwardGunter in 1620. He constructed a table of artificial sines andtangents to every minute of the quadrant. These were appliedaccording to Wright’s table of meridional parts, and have beenfound extremely useful in other branches of the mathematics. Hecontrived also a most excellent ruler, commonly called Gunter’sscale, on w hich were inscribed the logarithmic lines for numbers,and for sines and tangents of arches. He also greatly improvedthe sector and other instruments for the same purposes. SeeGunter. Mr. Itichard Norwood, put in execution the methodrecommended by Mr. Wright as the most perfect for measuringthe dimensions of the earth, with the true length of the degrees ofa great circle upon it; and, in 1635, he actually measured the dis-tance between London and \ ork ; from whence, and the summersolstitial altitudes of the sun observed on the meridian at bothplaces, he found a degree on a great circle of the earth to contain367,196 English feet, equal to 57,300 French fathoms or toises:which is very exact, as appears from many measures that havebeen made since that time. Of all this Mr. Norwood gave a fullaccount in his treatise, called, The Seaman’s Practice,'publishedin 1637. In the twelfth edition of this work, published in 1676,when the following paragraph was inserted in a smaller character:“About 1672, M. Picarl published an account in French , con-cerning the measure of the earth, a breviate whereof may be seenin the Philosophical Transactions , No. 112; wherein he concludesone degree to contain 365,184 English feet, nearly agreeing withMr. Norwood’s experiment;” and this advertisement iscontinuedin the subsequent editions as late as 1732, About 1645, Mr.
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