Imágenes de páginas
PDF
EPUB

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-

ional parts in degrees of latitude

Correcting the dead reckoning

[ocr errors]
[ocr errors]

66

Case 2 & 3, to find the hypothenuse and one leg,
the other leg and its opposite angle given
Case 4 & 5, to find the angles and one leg, the
hypothenuse and the other leg given

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-
gle, the hypothenuse and the sum of the legs given
To find the sides separately and the angles, one of
the legs and the sum of hyp. and other leg given
To find the sides separately and the angles, one of
the legs and the difference between the hyp.
and other leg given

To find the sides of a rectangle, the diagonal and

the sum of the sides given

Theorems in right-angled plane trigonometry

In plane sailing to find the diff. of lat. and đẹp.

to find the distance and departure

[blocks in formation]
[ocr errors]

66

to find the difference of longitude

to find the course, (see the rule in the table,
the theorem being accidently omitted)

In Mercator's sailing-to find the course

[merged small][ocr errors][merged small][merged small][merged small]
[blocks in formation]
[ocr errors]
[ocr errors]

ERRATA.-Page 13,art. 36, for Circles of latitude are therefore,read
Parallels of latitude are therefore circles. 23,last line, for is in read
in is. 31, last line but one of article 105, for add.mer. lat. read add.
mer. diff. lat. 33, in fifth line of article 114, for 219 1-2 read 233 1-2%
34, in last line of article 116, for 86° 56' read 67° 14'. 45, in third
line of article 192, for circle one read one circle, 56, in fifth line of
article 230, erase the words being its co-sine.

DESCRIPTION AND USE

OF A

DIAGRAM OF NAVIGATION.

[graphic]
[ocr errors][merged small]

j 1. NAVIGATION, in a special sense, is the art of sailing a vessel from one place to another.

[ocr errors]

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

[graphic]

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

« AnteriorContinuar »