astronomical day begins at noon and ends at noon, its hours being reckoned from 0 to 24h; the civil day begins at midnight and ends at midnight, its hours being reckoned through twice 12: the commencement of the astronomical day is placed 12 hours later than that of the civil day.

According to the point of definition chosen, the Astronomical Day is either a Sidereal Day, an Apparent Solar Day, or a Mean Solar Day; the term when used alone is usually understood to refer to the Mean Solar Day.

ANNUAL TIME.

Year: The period in which the earth makes a revolution in her orbit round the sun, as indicated by the corresponding apparent revolution of the sun in the ecliptic.

Sidereal Year: The period between the sun leaving some fixed point in the ecliptic, such as a fixed star, and returning to that point again.

Solar Year, called also the Equinoctial or Tropical Year: The period between the sun leaving the first point of Aries and returning to that point again.

Mean Solar Year: The average length of a long succession of solar years.

Civil Year: The year used for practical purposes, consisting of an integral number of days.

CHAPTER III.

DIAGRAMS.

HAVING given the definitions in general terms, it remains to illustrate them by diagrams. The following examples will be sufficient to show how this should be done.

I. EXPLANATION OF THE THREE SYSTEMS OF GREAT CIRCLE CO-ORDINATES FOR THE SURFACE OF THE CELESTIAL SPHERE.

OFG represents the primary great circle,

C its pole,

O the point of origin ;

FCG is the secondary great circle passing through the

point X;

then the point X is defined by the co-ordinates OF and

FX.

If the primary great circle be the equinoctial, then OF is the right ascension, and FX the declination of X.

If the primary great circle be the ecliptic, then OF is the longitude, and FX the latitude of X.

If the primary great circle be the horizon, then OF is the azimuth, and FX the altitude of X.

When the definition of any particular element is required to be explained, the figure should have the letters we are accustomed to use for the system involved. Thus :

(1.) Define the right ascension and declination of a heavenly body, and illustrate your definitions by a figure. Having given the definitions, proceed :

xx represents the equinoctial,

then x is the right ascension of X, xX is the declination of X.

P

X

(2.) Define the longitude and latitude of a heavenly body, and illustrate your definitions by a figure. Having given the definitions, proceed : kk' represents the ecliptic,

kKk the circle of latitude passing through X ; then k is the longitude of X,

kX is the latitude of X.

(3.) Define the azimuth and altitude of a heavenly body, and illustrate your definitions by a figure.

Having given the definitions, proceed :

Saa' represents the horizon,

Z its pole,

S the south point (the north pole of the heavens being elevated),

aZa' the circle of altitude passing through X;

then Sa is the azimuth of X,

aX is the altitude of X.

The annexed diagram, which is a projection on the

horizon, exhibits all the three systems of great circle co-ordinates together.