Description and use of the sector

To find the logarithm of any num-

ber and the contrary

Multiplication by logarithms

Division by logarithms

Involution by logarithms

Evolution by logarithms

The rule of three by logarithms

To calculate compound interest

by logarithms

To find the log. sine, tangent, &c.

corresponding to any number

of degrees and minutes

To find the degrees, minutes, and

seconds corresponding to any

log. sine, tangent, &c.

To find the arithmetical comple-

ment of any logarithm

Plane trigonometry

Table of solutions of the various

cases of trigonometry

Right-angled plane trigonometry

Questions to exercise the learner in

right-angled plane trigonometry

Oblique trigonometry

A short introduction to astronomy

and geography

Explanations of the terms used in

astronomy and geography

Examples in geography

Plane Sailing

A table of the angles which every

pojat of the compass makes

with the meridian

A table of solutions of the several

cases of plane sailing

Questions to exercise the learner

in plane sailing

Traverse sailing

Parallel sailing

Theorems for solving the several
cases of parallel sailing

A table showing how many miles

of meridian distance correspond

1 Questions to exercise the learner

4 in parallel sailing

Middle latitude sailing

7Theorems in middle latitude sail-

ing

67

13 Table of solutions of the several

17 cases of middle latitude sailing 63

20 Questions to exercise the learner

21 in middle latitude sailing

Mercator's sailing

24 To find the meridional parts cor-

responding to any degree and

minute

26

29 Table of solutions of the various
31 cases of Mercator's sailing
31 To work a compound course by
middle latitude or Mercator's

32

32 sailing

32 Construction and use of Merca-

tor's chart

33 Of the log-line and half-minute

glass

Description and use of a quadrant

33 of reflection

34

34

To adjust a quadrant

To take an altitude by a fore ob-
servation

To take the sun's altitude by a

back observation

35 Advice to seamen in the choice of

a quadrant

36 Description and use of a sextant

37 of reflection

To adjust a sextant

40 To measure the angular distance

40 of the sun from the moon

To measure the angular distance

of the moon from a star

Verification of the mirrors and co-

47, loured glasses

44

50 Description and uses of the circle

of reflection

51

Adjustments of the circle of reflec-

tion

52 To observe the meridian altitude

of an object by a circle

53 To measure the angular distance

of the sun from the moon by a

circle

58

76

77

77

.100

102

103

59 To measure the angular distance of

the moon from a star by a circle 104

Verification of the mirrors and

coloured glasses

63

64

100

<

On parallax, refraction, and dip

of the horizon

107

Page.

of two different objects,

taken within a few minutes of.

each other, by one observer

SIGNS AND ABBREVIATIONS USED IN THIS WORK.

Is the sign of addition, and denotes that whatever number or quantity follows the sign, must be added to those that go before it, thus 9+8 signifies that 8 is to be added to 9. Or A+B implies that the quantities represented by A and B are to be added. The sign + is called the positive sign.

The sign of subtraction; and denotes that the number following it must be subtracted from those going before it, thus 7-5, signifies that 5 must be subtracted from 7. The sign — is called the negative sign.

X Is the sign of multiplication, and shows that the numbers placed before and after it are to be multiplied, thus, 7 x 9 signifies 7 multiplied by 9, which makes 63; and 7× 8 × 2 signifies the continued product of 7 by 8 and by 2, which makes 112. Multiplication is also denoted by placing a point between the quantities to be multiplied; thus A.B signifies that A is to be multiplied by B.

Is the sign of division, and signifies that the number that stands before it is to be divided by the number following it, as 72+12 shows that 72 is to be divided by 12. Division may also be denoted by placing two points between the numbers, thus, 72: 12 represents 72 divided by 12

72

or by placing the numbers thus, which signifies 72 divided by 12.

() or

12

Either of these marks is used for connecting numbers to

gether, thus, 3+4×6, or (3+4)×6, signifies that the sum of 3 and 4 is to be multiplied by 6.

Is the sign of equality, and shows that the numbers or quantities placed before it are equal to those following it: thus & × 12=96. Or 8 mul

tiplied by 12 are equal to 96, and 7+2×4=36.

:::: Is the sign of proportion, and is marked thus, 7: 14 :: 10: 20, that is, as 7 is to 14, so is 10 to 20. Or A: B:: C: D, that is, as A is to B, so is C to D.

• Signifies degrees; thus, 450 represents 45 degrees. .

'Signifies minutes; thus, 24' or 24 minutes,

"

Signifies seconds; thus, 44", or 44 seconds.

Signifies thirds or sixtieth parts of seconds; thus, 44", or 44 thirds.

S. Signifies sine. N. S. Signifies Natural sine.

Sec. Signifies Secant.

Tan. Signifies Tangent.

Co-sine, Co-tangent, or Co-secant of an arch signifies the sine, tangent or secant of the complement of that arch respectively.

<Signifies Angle; with an s at top Angles, <s

Ad Angled,

A Signifies Triangle. 's Triangles.

Signifies a square.

or

the Sun. O or the Moon. *a Star. L. L. Lower Limb. U. L. Upper Limb. N. L. Nearest Limb. S. D. Semi-diameter. P. L. Proportional Logarithm. N. A. Nautical Almanac. Z. D. Zenith Distance. D. R. Dead Reckoning.