TABLES.

TABLE I.

TIME OF MERIDIAN PASSAGE OF NORTH STAR ABOVE THE POLE, FOR THE YEAR 1870.

For the year 1880, add three minutes to the time; for 1890, add 7 minutes;

for 1900, add 11 minutes.

149

TABLE II.

TIME OF EXTREME ELONGATIONS OF NORTH STAR FOR THE YEAR 1870, — LAT. 40°.

For the year 1880, add 3 minutes to the time; for 1890, add 7 minutes; for 1900, add 11 minutes. Change of latitude affects the tabular time very slightly.

32

1.36
1.38

1.32

.02677

34

I.40

36

1.43

38

40

42

44

46

1.59

.03463

.02793 .02851 1.34 .02735 .02910 1.36 .02793 .02997 1.39 .02881 1.45 .03055 1.41 .02939 1.48 .03143 I.44 .03026 1.52 .03259 1.47 .03114 1.43 .02997 I.39 .02881 1.55 .03346 1.51 .03230 1.46 .03084 1.55 .03346 .03201 1.59 .03403 1.54 .03317

TABLE IV.

ROODS AND PERCHES IN DECIMAL PARTS OF AN ACRE. One Acre 4 Roods = 160 Perches=4,840 Square Yards=43,560 Square Feet.

DECIMALS OF AN ACRE IN ONE CHAIN LENGTH OF 100 FEET, AND OF VARIOUS WIDTHS.

€ When the three sides of a plane triangle are given, u but the angles.

Assume the gongest of the three sides as base; then say, conformaty with proposition a

As the base is 10 the sum of the two other sides.

So is the difference of those sides 10 the difference of the segments of the base,

Half the base added to half the sand difference gives the greater segment, and diminished by it gives the less; thus, by means of the perpendicular from the vertical angle, the original trange is divided into two, each of which falls under the first case Or they may be solved by the simpler methods applicabe to right-augied triangles.

Second Method.

2. Find any one of the angies by means of proposition 6, and the remaining angies either by a repetition of the same rule, or by the relation of sides to the sines of their opposite angles.

VIII.

RIGHT-ANGLED PLANE TRIANGLES.

1. Right angles may be solved by the rules applicable to all plane triangles; and it will be found, since a right angle is aways one of the data, that the rule usually becomes simplified in its application.

2. When two of the sides are given, the third may be found by means of the rule that the square of the hypothenuse is equal to the sum of the squares of the remaining sides.

3. Another method for solving right-angled triangles is as folows:

To find a side. Call any one of the sides radius, and write