Chapter V), these numbers all change slowly with the lapse of time, and

on the average the right ascension of each star of the table must be increased by one twentieth of a minute for each year after 1900--i. e., in 1910 the right ascension of the first star of the table will be 0h. 38.6m. + (10/20)m. = 0h. 39.1m. The declinations also change slightly, but as they are only intended to help in finding the star on the star maps, their change may be ignored.

Having set the clock approximately to sidereal time, observe one or two more stars in the same way as above. The difference between the observed time and the right ascension, if any is found, is the "correction" of the clock. This correction ought not to exceed a minute if due care has been taken in the several operations prescribed. The relation of the clock to the right ascension of the stars is expressed in the following equation, with which the student should become thoroughly familiar:

A = T ± U

_T_ stands for the time by the clock at which the star crossed the meridian. _A_ is the right ascension of the star, and _U_ is the correction of the clock. Use the + sign in the equation whenever the clock is too slow, and the - sign when it is too fast. _U_ may be found from this equation when _A_ and _T_ are given, or _A_ may be found when _T_ and _U_ are given. It is in this way that astronomers measure the right ascensions of the stars and planets.

Determine _U_ from each star you have observed, and note how the several results agree one with another.

21. DEFINITIONS.--To define a thing or an idea is to give a description sufficient to identify it and distinguish it from every other possible thing or idea. If a definition does not come up to this standard it is insufficient. Anything beyond this requirement is certainly useless and probably mischievous.

Let the student define the following geographical terms, and let him also criticise the definitions offered by his fellow-students: Equator, poles, meridian, latitude, longitude, north, south, east, west.

Compare the following astronomical definitions with your geographical definitions, and criticise them in the same way. If you are not able to improve upon them, commit them to memory:

_The Poles_ of the heavens are those points in the sky toward which the earth's axis points. How many are there? The one near Polaris is called the north pole.

_The Celestial Equator_ is a great circle of the sky distant 90° from the poles.

_The Zenith_ is that point of the sky, overhead, toward which a plumb line points. Why is the word overhead placed in the definition? Is there more than one zenith?

_The Horizon_ is a great circle of the sky 90° distant from the zenith.

_An Hour Circle_ is any great circle of the sky which passes through the poles. Every star has its own hour circle.

_The Meridian_ is that hour circle which passes through the zenith.

_A Vertical Circle_ is any great circle that passes through the zenith. Is the meridian a vertical circle?

_The Declination_ of a star is its angular distance north or south of the celestial equator.

_The Right Ascension_ of a star is the angle included between its hour circle and the hour circle of a certain point on the equator which is called the _Vernal Equinox_. From spherical geometry we learn that this angle is to be measured either at the pole where the two hour circles intersect, as is done in the star map opposite page 124, or along the equator, as is done in the map opposite page 190. Right ascension is always measured from the vernal equinox in the direction opposite to that in which the stars appear to travel in their diurnal motion--i. e., from west toward east.

_The Altitude_ of a star is its angular distance above the horizon.

_The Azimuth_ of a star is the angle between the meridian and the vertical circle passing through the star. A star due south has an azimuth of 0°. Due west, 90°. Due north, 180°. Due east, 270°.

What is the azimuth of Polaris in degrees?

What is the azimuth of the sun at sunrise? At sunset? At noon? Are these azimuths the same on different days?

_The Hour Angle_ of a star is the angle between its hour circle and the meridian. It is measured from the meridian in the direction in which the stars appear to travel in their diurnal motion--i. e., from east toward west.

What is the hour angle of the sun at noon? What is the hour angle of Polaris when it is at the lowest point in its daily motion?

22. EXERCISES.--The student must not be satisfied with merely learning these definitions. He must learn to see these points and lines in his mind as if they were visibly painted upon the sky. To this end it will help him to note that the poles, the zenith, the meridian, the horizon, and the equator seem to stand still in the sky, always in the same place with respect to the observer, while the hour circles and the vernal equinox move with the stars and keep the same place among them. Does the apparent motion of a star change its declination or right ascension? What is the hour angle of the sun when it has the greatest altitude? Will your answer to the preceding question be true for a star? What is the altitude of the sun after sunset? In what direction is the north pole from the zenith? From the vernal equinox? Where are the points in which the meridian and equator respectively intersect the horizon?