219. Liquid Measure is used in measuring wines, oils, milk, molasses, brandy, vinegar, &c., &c. The Unit of Measure is the gallon.

The gallon contains 231 cubic inches, and is the same as the old English Wine Gallon, and is equal to 8.338 lb. distilled water at its greatest density.

In calculating the capacity of cisterns, reservoirs, &c., a barrel is 31.5 gal., and 63 gal. are called a hogshead, though barrels and hogsheads as used in commerce are of different capacities, which are determined by gauging.

ANGULAR OR CIRCULAR MEASURE.

220. Circular Measure is used in measuring angles, arcs of circles, latitude and longitude, and the motions of the heavenly bodies, &c.

The Unit of Measure is the degree, which is part of the circumference of a circle.

An Angle is the difference in direction of two lines which meet (205).

221. The Vertex of an angle is the point at which its sides meet.

The Sides of an angle are the lines which form it.

The kinds of angles are Right Angles, Acute Angles, and Obtuse Angles.

A Right Angle is the angle formed by two straight lines perpendicular to each other (206).

An Acute Angle is one which is less than a right angle. An Obtuse Angle is one which is greater than a right angle.

222. A Circle is a plane figure bounded by a curved line, every part of which is equally distant from a point within called the centre.

223. The Circumference of a circle is the line which bounds it. Any part of the circumference is called an Arc.

The Diameter of a circle is a line which passes through the centre and terminates in the circumference.

The Radius is a line extending from the centre to the circumference.

224. An angle is measured by making its vertex the centre of a circle and reckoning the arc included between its sides. For this purpose the circumference is divided as in the table.

The lines CD and CA include a quarter of the circumference between them; hence their difference of direction is of 360°-90°. Such an angle is called a right angle (206), and the measuring arc is called a quadrant. The lines CD and CA are said to be perpendicular to each other (206).

The lines C B and CE include one-sixth

of a circumference

between them; hence their difference of direction is of 360°=60°, and the measuring arc is called a sextant.

An arc measuring of a circumference is called an octant.

All angles less than 90° are called acute angles, and those greater are called obtuse angles.

225. Time is a measurable portion of duration.

226. The natural measure of Time is the Solar Day, or the interval of time between two successive passages of the sun over the same meridian; but, as these intervals are of unequal length, the True Unit of Measure is a mean of those intervals, and is called a Mean Solar Day; and is 24 hours long.

227. A Solar Year is the time in which the earth makes one revolution round the sun.

228. A Civil Day is in length the same as a mean

solar day; that is, 24 hours, and in most countries begins

By an inspection of the Table the pupil will see that a solar year is 5 hr. 48 min. 49.7 sec. longer than a common year; and that 4 solar years are 4 common years + 23 hr. 15 min. 18.8 sec.

To make the

Solar and Common year correspond, 1 day is added to every fourth common year, or to every year exactly divisible by 4; and that year is called a leap year. But by adding 1 day every 4 years, too much is added by the difference between 24 hrs. and 23 hr. 15 min. 18.8 sec., or at the rate of 11 min. 10.3 sec. per year too much. In 100 yr., 18 hr. 37 min. 10 sec. too much will have been added. Hence every 100th year is called a common year; but this would be dropping too much by the difference between 24 hr. and 18 hr. 37 min. 10 sec., or 5 hr. 22 min. 50 sec. every hundred years. By calling every 400th year a leap year, it would take 3840 common years to equal 3840 solar years and 1 day. Hence,

229. Every year divisible by 4 is a leap year, except those that have 100 and not 400 for an exact divisor.

The names and order of the calendar months are, January, 1st mo.; February, 2d mo.; March, 3d mo.; April, 4th mo.; May, 5th mo.; June, 6th mo.; July, 7th mo.; August, 8th mo.; September, 9th mo.: October, 10th mo.; November, 11th mo.; December, 12th mo.