CONTENTS. Case 1, to find the difference of lat. and departure 16 2, to find the distance and departure 3, to find the distance and difference of lat. 4, to find the course and departure "to find how many miles make a degree of 2, to find the difference of longitude 3, to find the parallel of latitude Case 1, to find the course and distance 2, to find the course, distance and diff. lon. 3, to find the diff. lat. dep. and diff. Ion. 4, to find the distance, dep. and diff. lon. 5, to find the course, dep. and diff. lon. 6, to find the distance, diff. lat. and diff. lon. 7, to find the course, diff. lat. and diff. lon To find the meridional parts by the Diagram Case 1, to find the course and distance 2, to find the course, distance, and diff. lon, 3, to find the diff. lat. and diff. lon. 4, to find the distance and diff. lon. 5, to find the course and diff. lon. 6, to find the distance, diff. lat. and diff. lon. 21 30 CONTENTS. Case 7, to find the course, diff. lat. and diff. lon. 8, to find the distance and diff. of lat. To find by the Diagram the value of merid- Application of the Diagram of Navigation to 46 right-angled plane trigonometry 66 Case 2 & 3, to find the hypothenuse and one leg, Problems which may be performed by the diagram 48 To find the diagonal of a square To find the diagonal of a rectangle To find each leg and the angles of a plane trian- To find the sides of a rectangle, the diagonal and Theorems in right-angled plane trigonometry to find the course and difference of lat. 66 to find the course and distance In parallel sailing-to find the meridian distance 66 to find the difference of longitude to find the course, (see the rule in the table, ERRATA.-Page 13,art. 36, for Circles of latitude are therefore,read DESCRIPTION AND USE OF A DIAGRAM OF NAVIGATION. j 1. NAVIGATION, in a special sense, is the art of sailing a vessel from one place to another. 2. That part of Navigation called Nautical Astronomy comprehends observations of the heavenly bodies, by suitable instruments, whereby the ship's place may be known with more certainty. Description of the Diagram of Navigation 3. The Diagram of Navigation is a geometrical canon of sines, tangents, and secants, corresponding to any given radius. 4. It is in the form of a Quadrant, or quarter circle, and exhibits a series of right-angled plane triangles, whose sides and angles are measured by marginal fig ures. 5. It has two sides perpendicular to each other, and a graduated Arc. 6. The sides are divided into equal parts; to which parts are drawn lines parallel to the sides; which lines, 2 intersecting at right angles, form the plane of the Diainto equal squares. gram 7. The equal parts into which the sides are divided are numbered at every decimal division, and every fifth line being larger than those which are intermediate, any line may be readily traced to its margin, where its value is given. 8. The Arc is divided into eight parts, corresponding to the eight points of the quarter compass; which are numbered from left to right; and each point is subdivided into half and quarter points. 9. The Arc is also divided into ninety degrees; which are numbered at every division of five degrees, from left to right, and also from right to left; and each degree is subdivided into tenths. 10. The Arc may be divided into any given number of equal parts. 11. On the centre angle of the Diagram is fitted a moveable INDEX; one edge of which (that which coincides with the pivot on which it moves) is graduated to the equal parts of the sides. 12. From the centre angle to the arc are drawn rhumb lines for the points of the compass, as a guide to catch the eye readily on these points, and as shewing how the index forms the hypothenuse, or longest side of a right-angled triangle. 13. The divisions on the sides, and on the index may be valued as the figures express, or in any other convenient numbers resulting from multiplication or division, as in any scale of equal parts. Thus 100 may be used as, as 10, as 100, as 1000, as 10,000, &c.The subdivisions being always in a decimal ratio to the number assumed. 14. To the main arc of the diagram is annexed an arc of expanded degrees of latitude for the meridional parts used in Mercator's sailing. This arc is also divided into degrees and tenths, and is numbered at every division of five degrees, beginning at 10° and ending at 62°. The process of obtaining the meridional parts |