is a key which contains the names of the more important constellations and the names of the brighter stars in their constellations. These names are for the most part a Greek letter prefixed to the genitive case of the Latin name of the constellation. (See the Greek alphabet printed at the end of the book.)

9. Magnitudes of the stars.—Nearly nineteen centuries ago St. Paul noted that "one star differeth from another star in glory," and no more apt words can be found to mark the difference of brightness which the stars present. Even prior to St. Paul's day the ancient Greek astronomers had divided the stars in respect of brightness into six groups, which the modern astronomers still use, calling each group a magnitude. Thus a few of the brightest stars are said to be of the first magnitude, the great mass of faint ones which are just visible to the unaided eye are said to be of the sixth magnitude, and intermediate degrees of brilliancy are represented by the intermediate magnitudes, second, third, fourth, and fifth. The student must not be misled by the word magnitude. It has no reference to the size of the stars, but only to their brightness, and on the star maps of this book the larger and smaller circles by which the stars are represented indicate only the brightness of the stars according to the system of magnitudes. Following the indications of these maps, the student should, in learning the principal stars and constellations, learn also to recognize how bright is a star of the second, fourth, or other magnitude.

10. Observing the stars.—Find on the map and in the sky the stars α Ursæ Minoris, α Ursæ Majoris, β Ursæ Majoris. What geometrical figure will fit on to these stars? In addition to its regular name, α Ursæ Minoris is frequently called by the special name Polaris, or the pole star. Why are the other two stars called "the Pointers"? What letter of the alphabet do the five bright stars in Cassiopeia suggest?

Exercise 6.—Stand in such a position that Polaris is just hidden behind the corner of a building or some other vertical line, and mark upon the key map as accurately as possible the position of this line with respect to the other stars, showing which stars are to the right and which are to the left of it. Record the time (date, hour, and minute) at which this observation was made. An hour or two later repeat the observation at the same place, draw the line and note the time, and you will find that the line last drawn upon the map does not agree with the first one. The stars have changed their positions, and with respect to the vertical line the Pointers are now in a different direction from Polaris. Measure with a protractor the angle between the two lines drawn in the map, and use this angle and the recorded times of the observation to find how many degrees per hour this direction is changing. It should be about 15° per hour. If the observation were repeated 12 hours after the first recorded time, what would be the position of the vertical line among the stars? What would it be 24 hours later? A week later? Repeat the observation on the next clear night, and allowing for the number of whole revolutions made by the stars between the two dates, again determine from the time interval a more accurate value of the rate at which the stars move.

The motion of the stars which the student has here detected is called their "diurnal" motion. What is the significance of the word diurnal?

In the preceding paragraph there is introduced a method of great importance in astronomical practice—i. e., determining something—in this case the rate per hour, from observations separated by a long interval of time, in order to get a more accurate value than could be found from a short interval. Why is it more accurate? To determine the rate at which the planet Mars rotates about its axis, astronomers use observations separated by an interval of more than 200 years, during which the planet made more than 75,000 revolutions upon its axis. If we were to write out in algebraic form an equation for determining the length of one revolution of Mars about its axis, the large number, 75,000, would appear in the equation as a divisor, and in the final result would greatly reduce whatever errors existed in the observations employed.

Repeat Exercise 6 night after night, and note whether the stars come back to the same position at the same hour and minute every night.