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A TRAVERSE TABLE,%
This Table is calculated for the easy and expeditious solution of the several cases of Right-angled Plane Trigonometry. It is generally esteemed a useful and requisite assistant to the Surveyor, the Navigator, and to every one, who has any concern with trigonometry in the exercise of his profession. The manner of using it must be very obvious to all, who are acquainted with the principles of that excellent branch of geometry; but to those, who have only a superficial knowledge of the subject, the following description and examples will be necessary.
In this Table, one of the acute angles—whether given, or required— if less than 45°, is found, to the nearest 15 at the top of the page ; but if more than 45°, it must be sought at the bottom, where the numbers are found in a retrograde order. And whether the angle under consideration, be at the top, or bottom, the Hypothenuse, if less than 120, is always in a Distance column; against which, in a column marked Latitude, is found the side contiguous to the angle ; and in a column, marked Departure, the side opposite the angle.
When the given numbers exceed the limits of the table, any aliquot parts, such as a half, one third, &c. may be taken ; and those found corresponding are to be doubled, trebled, &c. that is, multiplied by the same figure, that the given number is divided by.
1. Let the Hypothenuse of a right-angled triangle = 96 and one of the acute angles = 33° 45'; required the sides.
Under 33° 45' at the top of the table, and against 96 in a Distance column, are found 79.84 in a Latitude column for the side contiguous to the given angle, and 53.34 in a Departure column for the side opposite the given angle.
2. Let the sides of a right-angled triangle be = 89.23 and 66.02; required the angles and Hypothenuse.
By inspecting this table, till these two sides are found against each other in adjoining columns of Latitude and Departure, the angle op: posite the longest side is found to be 53° 30', the other 36° 30', and the Hypothenuse 111.
In this manner all the cases of Right-angled Plane Trigonometry can be readily solved.
... " The method of calculating this Table has been already investigated in the Third Section of this Treatise,