An observer who travels north or south over the earth changes his lat.i.tude, and therefore changes the angle between his horizon plane and the axis of the earth. What effect will this have upon the position of stars in his sky? If you were to go to the earth's equator, in what part of the sky would you look for Polaris? Can Polaris be seen from Australia? From South America? If you were to go from Minnesota to Texas, in what respect would the appearance of stars in the northern sky be changed? How would the appearance of stars in the southern sky be changed?

[Ill.u.s.tration: FIG. 12.--Diurnal path of Polaris.]

EXERCISE 8.--Determine your lat.i.tude by taking the alt.i.tude of Polaris when it is at some one of the four points of its diurnal path, shown in Fig. 12. When it is at _1_ it is said to be at upper culmination, and the star ? Ursae Majoris in the handle of the Big Dipper will be directly below it. When at _2_ it is at western elongation, and the star Castor is near the meridian. When it is at _3_ it is at lower culmination, and the star Spica is on the meridian. When it is at _4_ it is at eastern elongation, and Altair is near the meridian. All of these stars are conspicuous ones, which the student should find upon the map and learn to recognize in the sky. The alt.i.tude observed at either _2_ or _4_ may be considered equal to the lat.i.tude of the place, but the alt.i.tude observed when Polaris is at the positions marked _1_ and _3_ must be corrected for the star's distance from the pole, which may be a.s.sumed equal to 1.3.

The plumb-line apparatus described at page 12 is shown in Fig. 6 slightly modified, so as to adapt it to measuring the alt.i.tudes of stars. Note that the board with the screw eye at one end has been transferred from the box to the vertical standard, and has a screw eye at each end. When the apparatus has been properly leveled, so that the plumb line hangs at the middle of the hole in the box cover, the board is to be pointed at the star by sighting through the centers of the two screw eyes, and a pencil line is to be ruled along its edge upon the face of the vertical standard. After this has been done turn the apparatus halfway around so that what was the north side now points south, level it again and revolve the board about the screw which holds it to the vertical standard, until the screw eyes again point to the star. Rule another line along the same edge of the board as before and with a protractor measure the angle between these lines. Use a bicycle lamp if you need artificial light for your work. The student who has studied plane geometry should be able to prove that one half of the angle between these lines is equal to the alt.i.tude of the star.

After you have determined your lat.i.tude from Polaris, compare the result with your position as shown upon the best map available. With a little practice and considerable care the lat.i.tude may be thus determined within one tenth of a degree, which is equivalent to about 7 miles. If you go 10 miles north or south from your first station you should find the pole higher up or lower down in the sky by an amount which can be measured with your apparatus.

19. THE MERIDIAN LINE.--To establish a true north and south line upon the ground, use the apparatus as described at page 13, and when Polaris is at upper or lower culmination drive into the ground two stakes in line with the star and the plumb line. Such a meridian line is of great convenience in observing the stars and should be laid out and permanently marked in some convenient open s.p.a.ce from which, if possible, all parts of the sky are visible. June and November are convenient months for this exercise, since Polaris then comes to culmination early in the evening.

20. TIME.--What is _the time_ at which school begins in the morning?

What do you mean by "_the time_"?

The sidereal time at any moment is the right ascension of the hour circle which at that moment coincides with the meridian. When the hour circle pa.s.sing through Sirius coincides with the meridian, the sidereal time is 6h. 40m., since that is the right ascension of Sirius, and in astronomical language Sirius is "_on the meridian_" at 6h. 40m. sidereal time. As may be seen from the map, this 6h. 40m. is the right ascension of Sirius, and if a clock be set to indicate 6h. 40m. when Sirius crosses the meridian, it will show sidereal time. If the clock is properly regulated, every other star in the heavens will come to the meridian at the moment when the time shown by the clock is equal to the right ascension of the star. A clock properly regulated for this purpose will gain about four minutes per day in comparison with ordinary clocks, and when so regulated it is called a sidereal clock. The student should be provided with such a clock for his future work, but one such clock will serve for several persons, and a nutmeg clock or a watch of the cheapest kind is quite sufficient.

[Ill.u.s.tration: THE HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, Ma.s.s.]

EXERCISE 9.--Set such a clock to sidereal time by means of the transit of a star over your meridian. For this experiment it is presupposed that a meridian line has been marked out on the ground as in -- 19, and the simplest mode of performing the experiment required is for the observer, having chosen a suitable star in the southern part of the sky, to place his eye accurately over the northern end of the meridian line and to estimate as nearly as possible the beginning and end of the period during which the star appears to stand exactly above the southern end of the line. The middle of this period may be taken as the time at which the star crossed the meridian and at this moment the sidereal time is equal to the right ascension of the star. The difference between this right ascension and the observed middle instant is the error of the clock or the amount by which its hands must be set back or forward in order to indicate true sidereal time.

A more accurate mode of performing the experiment consists in using the plumb-line apparatus carefully adjusted, as in Fig. 7, so that the line joining the wire to the center of the screw eye shall be parallel to the meridian line. Observe the time by the clock at which the star disappears behind the wire as seen through the center of the screw eye.

If the star is too high up in the sky for convenient observation, place a mirror, face up, just north of the screw eye and observe star, wire and screw eye by reflection in it.

The numerical right ascension of the observed star is needed for this experiment, and it may be measured from the star map, but it will usually be best to observe one of the stars of the table at the end of the book, and to obtain its right ascension as follows: The table gives the right ascension and declination of each star as they were at the beginning of the year 1900, but on account of the precession (see 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, lat.i.tude, 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 pa.s.ses through the poles. Every star has its own hour circle.

_The Meridian_ is that hour circle which pa.s.ses through the zenith.

_A Vertical Circle_ is any great circle that pa.s.ses 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 Alt.i.tude_ 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 pa.s.sing 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 alt.i.tude?

Will your answer to the preceding question be true for a star? What is the alt.i.tude 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?

CHAPTER III

FIXED AND WANDERING STARS

23. STAR MAPS.--Select from the map some conspicuous constellation that will be conveniently placed for observation in the evening, and make on a large scale a copy of all the stars of the constellation that are shown upon the map. At night compare this copy with the sky, and mark in upon your paper all the stars of the constellation which are not already there. Both the original drawing and the additions made to it by night should be carefully done, and for the latter purpose what is called the method of allineations may be used with advantage--i. e., the new star is in line with two already on the drawing and is midway between them, or it makes an equilateral triangle with two others, or a square with three others, etc.

A series of maps of the more prominent constellations, such as Ursa Major, Ca.s.siopea, Pegasus, Taurus, Orion, Gemini, Canis Major, Leo, Corvus, Bootes, Virgo, Hercules, Lyra, Aquila, Scorpius, should be constructed in this manner upon a uniform scale and preserved as a part of the student's work. Let the magnitude of the stars be represented on the maps as accurately as may be, and note the peculiarity of color which some stars present. For the most part their color is a very pale yellow, but occasionally one may be found of a decidedly ruddy hue--e. g., Aldebaran or Antares. Such a star map, not quite complete, is shown in Fig. 13.

So, too, a sharp eye may detect that some stars do not remain always of the same magnitude, but change their brightness from night to night, and this not on account of cloud or mist in the atmosphere, but from something in the star itself. Algol is one of the most conspicuous of these _variable stars_, as they are called.

[Ill.u.s.tration: FIG. 13.--Star map of the region about Orion.]

24. THE MOON'S MOTION AMONG THE STARS.--Whenever the moon is visible note its position among the stars by allineations, and plot it on the key map opposite page 190. Keep a record of the day and hour corresponding to each such observation. You will find, if the work is correctly done, that the positions of the moon all fall near the curved line shown on the map. This line is called the ecliptic.

After several such observations have been made and plotted, find by measurement from the map how many degrees per day the moon moves. How long would it require to make the circuit of the heavens and come back to the starting point?

On each night when you observe the moon, make on a separate piece of paper a drawing of it about 10 centimeters in diameter and show in the drawing every feature of the moon's face which you can see--e. g., the shape of the illuminated surface (phase); the direction among the stars of the line joining the horns; any spots which you can see upon the moon's face, etc. An opera gla.s.s will prove of great a.s.sistance in this work.

Use your drawings and the positions of the moon plotted upon the map to answer the following questions: Does the direction of the line joining the horns have any special relation to the ecliptic? Does the amount of illuminated surface of the moon have any relation to the moon's angular distance from the sun? Does it have any relation to the time at which the moon sets? Do the spots on the moon when visible remain always in the same place? Do they come and go? Do they change their position with relation to each other? Can you determine from these spots that the moon rotates about an axis, as the earth does? In what direction does its axis point? How long does it take to make one revolution about the axis?

Is there any day and night upon the moon?