History. entitled the Haven-finding Art. In this ancient tract is acquainted with the principles upon which this proceeded; History . also described the method by which our sailors estimate and it is now generally believed, that the true principles on , deed, to the proportion between the distances of the paral- fine a system of such maps to one and the same scale, but In the year 1581 Michael Coignet, a native of Antwerp, to plan them out by a different measure, as occasion might published a treatise, in which he animadverted on Medina. require ; with this precaution, however, that the degrees of In this he showed, that as the rhumbs are spirals, making longitude in each should bear some proportion to those of endless revolutions about the poles, numerous errors must latitude, and this proportion was to be deduced from that arise from their being represented by straight lines on the which the magnitude of the respective parallels bore to a sea charts; but although he hoped to find a remedy for great circle of the sphere. He added, that, in particular these errors, he was of opinion that the proposals of Nonius maps, if this proportion be observed with regard to the were scarcely practicable, and therefore in a great measure middle parallel , the inconvenience will not be great, aluseless. In treating of the sun's declination, he took notice though the meridians should be straight lines parallel to of the gradual decrease in the obliquity of the ecliptic; he each other. But here he is understood only to mean, that also described the cross staff with three transverse pieces, the maps should in some measure represent the figures of which he admitted were then in common use amongst the the countries for which they are drawn. In this sense sailors. He likewise described some instruments of bis Mercator, who drew maps for Ptolemy's tables, understood own invention ; but all of them are now laid aside, except- him; thinking it, however, an improvement not to reguing perhaps his nocturnal. He constructed a sea table to late the meridians by one parallel, but by two, one distant be used by such as sailed beyond the sixtieth degree of from the northern, the other from the southern extremity latitude; and at the end of the book is delivered a method of the map, by a fourth part of the whole depth; by which of sailing upon a parallel of latitude by means of a ring dial means, in his maps, although the meridians are straight and a twenty-four hour glass. The same year the discovery lines, yet they are generally drawn inclining to each other of the dipping-needle was made by Robert Norman. towards the poles. With regard to Cortes, he speaks only In his publication on that subject he maintains, in opposition of the number of degrees of latitude, and not of the extent to Cortes, that the variation of the compass was caused by of them; nay, he gives express directions that they should some point on the surface of the earth, and not in the hea- all be laid down by equal measurement in a scale of vens; and he also made considerable improvements on the leagues adapted to the map. construction of compasses themselves, showing especially For some time after the appearance of Mercator's map the danger of not fixing, on account of the variation, the it was not rightly understood, and it was even thought to wire directly under the fleur de lis, as compasses made in be entirely useless, if not detrimental. However, about different countries have it placed differently. To this per- the year 1592 its utility began to be perceived ; and seven formance of Norman's is prefixed a discourse on the varia- years afterwards Wright printed his famous treatise ention of the magnetical needle, by William Burrough, in titled The Correction of certain Errors in Navigation, which he shows how to determine the variation in many where he fully explained the reason of extending the length different ways, and also points out many errors in the prac- of the parallels of latitude, and the uses thereof to navitice of navigation at that time, speaking in very severe gators. In 1610 a second edition of Wright's book was terms concerning those who had published upon it. published, with improvements. An excellent method was During this time the Spaniards continued to publish trea- proposed of determining the magnitude of the earth; and at tises on the art. In 1585 an excellent Compendium was the same time it was judiciously proposed to make our compublished by Roderico Zamorano, and contributed greatly mon measures in some proportion to a degree on its surface, towards the improvement of the art, particularly in the sea that they might not depend on the uncertain length of a charts. Globes of an improved kind, and of a much larger barleycorn. Amongst his other improvements may be mensize than those formerly used, were now constructed, and tioned the Table of Latitudes for Dividing the Meridian many improvements were made in other instruments; never- computed to Minutes, whereas it had been only divided to theless, the plane chart continued still to be followed, though every tenth minute. He also published a description of an its errors were frequently complained of. Methods of re- instrument which he calls the sea rings, by which the varimoving these errors had indeed been sought after ; and ation of the compass, the altitude of the sun, and the time Gerard Mercator seems to have been the first who found of the day, may at once readily be determined in any place, the true method of effecting this, so as to answer the pur- provided the latitude is known. He also showed how to poses of seamen. He represented the degrees both of lati- correct the errors arising from the eccentricity of the eye in tude and longitude by parallel straight lines, but gradually observing by the cross staff. In the years 1594, 1596, augmented the space between the former as they approached 1596, and 1597, he amended the tables of the declinations the pole. Thus the rhumbs, which otherwise ought to have and places of the sun and stars from his own observations been curves, were now also extended into straight lines; made with a six-feet quadrant, a sea quadrant to take altiand thus a straight line drawn between any two places tudes by a forward or backward observation, and likewise marked upon the cliart formed an angle with the meridians, with a contrivance for the ready finding of the latitude by expressing the rhumb leading from the one to the other. the height of the pole-star, when not upon the meridian. But although in 1569 Mercator published a universal map To this edition was subjoined a translation of Zamorano's constructed in this manner. it does not appear that he was Compendium, above mentioned, in which he corrected some History mistakes in the original, adding a large table of the varia- and tangents to every minute of the quadrant, which he History. tion of the compass observed in different parts of the published in 1620. In this work he applied to navigation, known by the name of Gunter's Scale,' on which are de- year at Paris. In one of these he taught the use of Gunter's In 1624 the learned Willebrordus Snellius, professor of scale; and in the other, that of the tables of artificial sines mathematics at Leyden, published a treatise of naviga- and tangents, as modelled according to Napier's last form, tion on Wright's plan, but somewhat obscurely; and as he erroneously attributed by Wingate to Briggs. did not particularly mention all the discoveries of Wright, Gunter's scale was projected into a circular arch by the the latter was thought by some to have taken the hint of all Reverend William Oughtred in 1633; and its uses were his discoveries from Snellius. But this supposition has been fully shown in a pamphlet entitled the Circles of Proporlong ago refuted; and Wright's title to the honour of those tion, where, in an appendix, several important points in discoveries remains unchallenged. navigation are well treated. It has also been made in the Having shown how to find the place of the ship upon form of a sliding ruler. his chart, Wright observed that the same might be per- The logarithmic tables were first applied to the different formed more accurately by calculation ; but considering, cases of sailing, by Thomas Addison, in his treatise enas he says, that the latitudes, and especially the courses titled Arithmetical Navigation, printed in the year 1625. at sea, could not be determined so precisely, he forbore He also gave two traverse tables, with their uses; the one setting down particular examples; as the mariner may be to quarter points of the compass, and the other to degrees. allowed to save himself this trouble, and only to mark out Henry Gellibrand published his discovery of the changes upon his chart the ship’s way, after the manner then usually of the variation of the compass, in a small quarto pamphlet, practised. However, in 1614, Raphe Handson, amongst entitled A Discourse Mathematical on the Variation of the the nautical questions which he subjoined to a translation Magnetical Needle, printed in 1635. This extraordinary of Pitiscus's Trigonometry, solved very distinctly every phenomenon he found out by comparing the observations case of navigation, by applying arithmetical calculations to which had been made at different times near the same Wright's Tables of Latitudes, or of Meridional Parts, as it place by Burrough, Gunter, and himself, all persons of has since been called. Although the method discovered by great skill and experience in these matters. This discovery Wright for finding the change of longitude by a ship sail- was likewise soon known abroad; for Athanasius Kircher, ing on a rhumb is the proper way of performing it, Hand- in his treatise entitled Magnes, first printed at Rome in son also proposes two methods of approximation without the year 1641, informs us that he had been told of it by the assistance of Wright's division of the meridian line. John Greaves, and then gives a letter of the famous The first was computed by the arithmetical mean between Marinus Mersennus, containing a very distinct account of the cosines of both latitudes ; and the other by the same the same. mean between the secants, as an alternative when Wright's As altitudes of the sun are taken on shipboard by obbook was not at hand; although this latter is wider of the serving his elevation above the visible horizon, to obtain truth than the former. By the same calculations also he from these the sun's true altitude with correctness, Wright showed how much each of these compends deviates from observed it to be necessary that the dip of the visible horithe truth, and also how widely the computations on the zon below the horizontal plane passing through the oberroneous principles of the plane chart differ from them server's eye should be brought into the account, which all. The method generally used by our sailors, however, cannot be calculated without knowing the magnitude of the is commonly called the middle latitude, which, although it earth. Hence he was induced to propose different methods errs more than that by the arithmetical mean between the for finding this ; but he complains that the most effectual two cosines, is preferred on account of its being less oper- was out of his power to execute, and therefore he contented ose ; yet in high latitudes it is more eligible to use that himself with a rude attempt, in some measure sufficient for of the arithmetical mean between the logarithmic cosines, his purpose. The dimensions of the earth deduced by him equivalent to the geometrical mean between the cosines corresponded very well with the usual divisions of the logthemselves—a method since proposed by John Bassat. line; nevertheless, as he did not write an express treatise The computation by the middle latitude will always fall on navigation, but only for correcting such errors as preshort of the true change of longitude, that by the geome- vailed in general practice, the log-line did not fall under trical mean will always exceed; but that by the arithme- his notice. Richard Norwood, however, put in execution tical mean falls short in latitudes of about 45°, and exceeds the method recommended by Wright as the most perfect in lesser latitudes. However, none of these methods will for measuring the dimensions of the earth, with the true differ much from the truth when the change of latitude is length of the degrees of a great circle upon it; and in sufficiently small. 1635 he actually measured the distance between London About this period logarithms were invented by John and York; from which measurement, and the summer solNapier, Baron of Merchiston in Scotland, and proved of stitial altitudes of the sun observed on the meridian at both the utmost service to the art of navigation. From these places, he found a degree on a great circle of the earth Edmund Gunter constructed a table of logarithmic sines to contain 367,196 English feet, equal to 57,300 French See GUNTER'S SCALE. History. History. fathoms or toises; which is very exact, as appears from Transactions for 1695 (No. 219), from the consideration many measurements that have been made since that time. of the spirals into which the rhumbs are transformed in the this wonderful phenomenon seems hitherto to have eluded We are indebted to Dr Practice of purpose were found to answer so well that he obtained the The works which have latterly appeared on navigation are PreliminNaviga- parliamentary reward. These have been improved by Ar- those on the longitude and navigation by Mackay, Inman, ary Printion. nold, Earnshaw, and many others, so as now to be almost Riddle, Norie, Jeans, and others; and these contain every ciples. in common use. necessary requisite to form the practical navigator. PRACTICE OF NAVIGATION BOOK I. Hemispheres, according as the North or the South Pole lies within them. The first meridian, which is a great circle passing The longitude of a place is the arc of the equator inter- On the supposition that the earth is a sphere, the length ship from one port to another by help of rules, in which the of all arcs of great circles upon it subtending an angle of , by means of observations on the heavenly bodies ; and tude, reduced to minutes and parts of minutes, also repre- In the practice of navigation, the latitude and longitude P F M M G L E K к ус B R T Chap. I.—PRELIMINARY PRINCIPLES. TERMS USED IN NAVIGATION; AND GENERAL EXPLANA- 1. Latitude and Longitude. Fig. 1. 2. Definitions of Terms used in Navigation, and Explanations. PAQ, PBR, PCS......PFV be meridians supposed very . . AC; AC; Prelimin- two meridians between whico they respectively lie; or, in Or in logarithms, log. true diff. lat.=log. dist. + L cos course – 10, 2. Given course (BAC) and true difference of latitude AC=AB x sec BAC BC=AB x tan BAC; or dist.=true diff. lat. x sec course · (111.) of this meridian intercepted between any two consecutive dep.=true diff. lat. x tan course · (iv.) AC=BC x cosec BAC AB=BC x cot BAC; or dist. = dep. x cosec course (v.) intercepted between the same meridians are not equal, but and true diff. lat.=dep. x cot course (VI.) 4. Given distance and true difference of latitude, to find course and departure. AB Cos BAC= or cosine course = true diff. lat., dist. (VII.) dep.=dist. x sin course by (11.) 5. Given the distance and departure, to find the course In navigation, each of the triangles ABH, BCI, &c., is and true difference of latitude. considered as a plane triangle; and as each of them is BC Sin BAC= or sin course = dep. - distance . (viii.) And then we have true diff. lat.=dist. x cos course. 6. Given the true difference of latitude and departure, CK : DK : CD:: AH : BH : AB to find the course and distance. BC Tan BAC = or tan course=departure = true diff. lat. . (1x.) dist. true diff. lat. x sec course by (111.); :: AH: BH : AB. Length of Arc of 1° of Parallels of Latitude. We have already stated that the lengths of the parallels of latitude diminish as the lati- tude increases. In fact, it des Let EQ be the equator, PCP the polar diameter of the earth the course. passing through C, and LML'any Take AB (fig. 2)=the true diff. lat. parallel of latitude. Let the angle Draw BC at right angles to it=de ECL, or the latitude, bel, and let parture. Join AC. Then AC is the LM and EF be the arcs of the P' parallel and of the equator in- Fig. 3. PEP and PFP'. Then angle ECF=angle LOM, because of latitude, departure, distance, and they both measure the angle between the planes of the two meridians. Hence Fig. 2. arc LM: arc EF::OL:CE:: OL:CL, because CE = CL; 1. Given course (BAC) and distance (AC), to find true OL or arc LM=arc EF X = arc EF x sin OCL CL = arc EF x cos LCE=arc EF * cos l. Hence if FE be the length of an arc lo of longitude at the i.e., true diff. lat. (in miles) = dist. x cos course . (1.) equator, or 60 miles, LM the length of an arc 1° of longitude and departure = dist. x sin course (11.) in latitude 1-= 60 x cos l. AB; . = L' L B с С E F |