In order to procure a practically useful treatise on Gauging, the article on this subject has been entirely written by a practical man, an intelligent Supervisor of Excise.

All the other articles, both in Parts I. and II., have been written by an eminent Mathematician in the Scottish metropolis, who is also distinguished as a public Lecturer on the science.

For the convenience of Teachers, and the use of such Students as do not enjoy the benefit of an instructor, a KEY has been published simultaneously with the work. Besides the solutions at length of all the Exercises in the book, there is appended to it a valuable Supplement, containing demonstrations not given in the work, and much other useful matter.

Of Logarithms,

CONTENTS OF PART II.

Description of Tables of Logarithms,

Logarithmic Arithmetic,

Explanation of Tables of Log. Sines, Tangents, &c.,

Difference of Latitude and Departure,

Tables of Interest and Annuities,

TRIGONOMETRY,

Definitions,

Solution of Right-angled Triangles,

Solution of Oblique-angled Triangles,

Demonstration of useful Theorems,

To find the Angles when the sides are given,

Expressions for the Sine and Cosine of the sum and difference

of two Angles,

Page

1

2

6

11

15

16

19

19

22

24

29

32

33

34

37

42

46

48

49

53

54

56

ib.

58

To find the Diameter and Circumference of a Circle, the one

To find the Area included between two Arcs of different Circles, having a common Chord,

76

To find the Area of a Figure bounded by a curve and straight

lines,

77

MENSURATION OF SOLIDS,

To find the Solidity of a Prism,

To find the Surface and Solidity of a Cylinder,
To find the Surface and Solidity of a Pyramid,
To find the Surface and Solidity of a Cone,

To find the Surface and Solidity of the Frustum of a Pyramid

or Cone,

To find the Solidity of a Wedge,

78

79

80

81

82

To find the Solidity of a Prismoid,

To find the Curve Surface of a Sphere, or any Segment or Zone of it,

88

89

90

91

Circular Spindle,

To find the Solid Content of the Middle Frustum or Zone of a

To find the Solidity and Surface of a Circular Ring,
To find the Surface and Solidity of each of the Regular Bodies, 94

To measure a Field of three sides,

To measure a Field of four sides,

97

ib.

102

Page

To measure a Field of more than four sides,

104

To survey a piece of Land in the form of an irregular belt,

107

To measure a Lake or Wood without entering it,

108

To find the breadth of a River without crossing it,

109

To find the Surface, and draw a Plan, of hilly or sloping

ground,

115

To deduce the true angle at a station from angles measured near it,

116

To find the length of a line on the level of the sea corresponding to a line measured at an elevated level,

117

Given the Specific Gravity and Solidity of a Body, to find its
Weight,

126

Given the Specific Gravity and Weight of a Body, to find its
Solidity,

127

To find the Specific Gravity of a Body, its Weight and Solid
Content being given, .

ib.

To find the Specific Gravity of a Body without knowing its So

To find the quantity of each ingredient in a given compound of two ingredients,

ib.

GAUGING,

131

Description of the Sliding Rule,

132

To find the content of Solids of greater depth than one inch,
Gauging open Vessels,

137

139

To Gauge a Malt Cistern, &c.,

ib.

To Gauge a Vessel in the form of a Frustum of a Pyramid or

To Gauge, Fix, and Tabulate a Vessel, which is nearly circular, 141

To Gauge and Tabulate an Irregular Oval Vessel by means of

Ordinates,

To Gauge a Still,

Malt Gauging,

Cask Gauging,

Ullaging of Casks,

Miscellaneous Questions in Gauging,

General Exercises,

TABLES.

Logarithmic Sines, Tangents, and Secants, for every point and quarter point of the Compass,

Logarithms of all numbers, from 1 to 100,

Logarithms of all numbers, from 100 to 1,000,000,
Logarithmic Sines, Tangents, and Secants, for every degree
and minute of the Quadrant,

Natural Sines and Cosines for every degree and Minute of the