Skip to main content

Full text of "A text-book of astronomy"

See other formats




LQ Q^ 


<J O 

i | 















THE present work is not a compendium of astronomy 
or an outline course of popular reading in that science. It 
has been prepared as a text-book, and the author has pur- 
posely omitted from it much matter interesting as well as 
important to a complete view of the science, and has en- 
deavored to concentrate attention upon those parts of the 
subject that possess special educational value. From this 
point of view matter which permits of experimental treat- 
ment with simple apparatus is of peculiar value and is 
given a prominence in the text beyond its just due in a 
well-balanced exposition of the elements of astronomy, 
while topics, such as the results of spectrum analysis, 
which depend upon elaborate apparatus, are in the experi- 
mental part of the work accorded much less space than 
their intrinsic importance would justify. 

Teacher and student are alike urged to magnify the 
observational side of the subject and to strive to obtain in 
their work the maximum degree of precision of which their 
apparatus is capable. The instruments required are few 
and easily obtained. With exception of a watch and a pro- 
tractor, all of the apparatus needed may be built by any 
one of fair mechanical talent who will follow the illustra- 
tions and descriptions of the text. In order that proper 
opportunity for observations may be had, the study should 
be pursued during the milder portion of the year, between 
April and November in northern latitudes, using clear 


54. in 34 


weather for a direct study of the sky and cloudy days for 
book work. 

The illustrations contained in the present work are 
worthy of as careful study as is the text, and many of 
them are intended as an aid to experimental work and 
accurate measurement, e. g., the star maps, the diagrams 
of the planetary orbits, pictures of the moon, sun, etc. If 
the school possesses a projection lantern, a set of astro- 
nomical slides to be used in connection with it may be 
made of great advantage, if the pictures are studied as an 
auxiliary to Nature. Mere display and scenic effect are of 
little value. 

A brief bibliography of popular literature upon astron- 
omy may be found at the end of this book, and it will be 
well if at least a part of these works can be placed in the 
school library and systematically used for supplementary 
reading. An added interest may be given to the study if 
one or more of the popular periodicals which deal with 
astronomy are taken regularly by the school and kept 
within easy reach of the students. From time to time 
the teacher may well assign topics treated in these peri- 
odicals to be read by individual students and presented 
to the class in the form of an essay. 

The author is under obligations to many of his profes- 
sional friends who have contributed illustrative matter for 
his text, and his thanks are in an especial manner due to 
the editors of the Astrophysical Journal, Astronomy and 
Astrophysics, and Popular Astronomy for permission to 
reproduce here plates which have appeared in those peri- 
odicals, and to Dr. Charles Boynton, who has kindly read 
and criticised the proofs. 






The measurement of angles and time. 


Finding the stars Their apparent motion Latitude Direc- 
tion of the meridian Sidereal time Definitions. 


Apparent motion of the sun, moon, and planets Orbits of the 
planets How to find the planets. 

IV. CELESTIAL MECHANICS . . ..... . .46 

Kepler's laws Newton's laws of motion The law of gravita- 
tion Orbital motion Perturbations Masses of the planets 
Discovery of Neptune The tides. 

V. THE EARTH AS A PLANET . . . .^ -. . . 70 

Size Mass Precession The warming of the earth The 
atmosphere Twilight. 

VI. THE MEASUREMENT OF TIME '. -..". . . . . 86 

Solar and sidereal time Longitude The calendar Chro- 

VII. ECLIPSES . . . .".... .101 

Their cause and nature Eclipse limits Eclipse maps .Re- 
currence and prediction of eclipses. 


The clock Radiant energy Mirrors and lenses The tele- 
scopeCameraSpectroscopePrinciples of spectrum analysis. 

IX. THE MOON . . . . . . "... . . .150 

Numerical data Phases Motion Librations Lunar topog- 
raphy Physical condition. 



X. THE SUN . _.-'. . . -, . * .. . 178 

Numerical data Chemical nature Temperature Visible 
and invisible parts Photosphere Spots Faculae Chromo- 
sphere Prominences Corona The sun-spot period The sun's 
rotation Mechanical theory oi the sun. 

XI. THE PLANETS . ...... . . . 212 

Arrangement of the solar system Bode's law Physical con- 
dition of the planets Jupiter Saturn Uranus and Neptune 
Venus Mercury Mars The asteroids. 

XII. COMETS AND METEORS . . . " . . . . . 251 

Motion, size, and mass of comets Meteors Their number 
and distribution Meteor showers Relation of comets and me- 
teors Periodic comets Comet families and groups Comet tails 
Physical nature of comets Collisions. 

XIII. THE FIXED STARS . . . i . . ... .291 

Number of the stars Brightness Distance Proper motion 
Motion in line of sight Double stars Variable stars New 

XIV. STARS AND NEBULA . V *. ; . . . . 330 

Stellar colors and spectra Classes of stars Clusters Nebu- 
lae Their spectra and physical condition The Milky Way 
Construction of the heavens Extent of the stellar system. 

XV. GROWTH AND DECAY . . . . . . ... . . 358 

Logical bases and limitations Development of the sun The 
nebular hypothesis Tidal friction Roche's limit Development 
of the moon Development of stars and nebulae The future. 

APPENDIX : . . . " . . v . . . ; . .'. . 383 
INDEX 387 



I. Northern Constellations . . .... . 124 

II. Equatorial Constellations . '. , _. . , . . 190 

III. Map of Mars . . ... : . . . V .. 246 

IV. The Pleiades . . ~ . ... . . . V . . 344 

Protractor :'.'-. In pocket at back of book 



A Total Solar Eclipse . . . .."-'/ / . Frontispiece 

The Harvard College Observatory, Cambridge. Mass. . . . 24 

Isaac Xewton . ... ... .. * . . . . 46 

Galileo Galilei . . . ." ..',". . . . 52 

The Lick Observatory, Mount Hamilton, Cal. . ... 60 

The Yerkes Observatory, Williams Bay, Wis 100 

The Moon, one day after First Quarter . . . ... 150 

William Herschel . . . ..... . .234 

Pierre Simon Laplace . . . 364 




1. Accurate measurement. Accurate measurement is the 
foundation of exact science, and at the very beginning of 
his study in astronomy the student should learn something 
of the astronomer's kind of measurement. He should prac- 
tice measuring the stars with all possible care, and should 
seek to attain the most accurate results of which his instru- 
ments and apparatus are capable. The ordinary affairs of 
life furnish abundant illustration of some of these measure- 
ments, such as finding the length of a board in inches or 
the weight of a load of coal in pounds and measurements 
of both length and weight are of importance in astronomy, 
but of far greater astronomical importance than these are 
the measurement of angles and the measurement of time. 
A kitchen clock or a cheap watch is usually thought of as 
a machine to tell the " time of day," but it may be used to 
time a horse or a bicycler upon a race course, and then it 
becomes an instrument to measure the amount of time 
required for covering the length of the course. Astrono- 
mers use a clock in both of these ways to tell the time at 
which something happens or is done, and to measure the 
amount of time required for something ; and in using a 
clock for either purpose the student should learn to take 
the time from it to the nearest second or better, if it has a 



seconds hand,' 6r' to 1 'a small fraction of a minute, by esti- 
mating the position of the minute hand between the min- 
ute marks on the dial. Estimate the fraction in tenths of 
a minute, not in halves or quarters. 

EXERCISE 1. If several watches are available, let one 
person tap sharply upon a desk with a pencil and let each 
of the others note the time by the minute hand to the 
nearest tenth of a minute 'and record the observations as 
follows : 

2h. 44.5m. First tap. 2h. 46.4m. 1.9m. 
2h. 44.9m. Second tap. 2h. 46.7m. 1.8m. 
2h. 40.6m. Third tap. 2h. 48.6m. 2.0m. 

The letters h and m are used as abbreviations for hour and 
minute. The first and second columns of the table are the 
record made by one student, and second and third the rec- 
ord made by another. After all the observations have been 
made and recorded they should be brought together and 
compared by taking the differences between the times re- 
corded for each tap, as is shown in the last column. This 
difference shows how much faster one watch is than the 
other, and the agreement or disagreement of these differ- 
ences shows the degree of accuracy of the observations. 
Keep up this practice until tenths of a minute can be esti- 
mated with fair precision. 

2. Angles and their use. An angle is the amount of 
opening or difference of direction between two lines that 
cross each other. At twelve o'clock the hour and minute 
hand of a watch point in the same direction and the angle 
between them is zero. At one o'clock the minute hand is 
again at XII, but the hour hand has moved to I, one 
twelfth part of the circumference of the dial, and the angle 
between the hands is one twelfth of a circumference. It is 
customary to imagine the circumference of a dial to be cut 
up into 360 equal parts i. e., each minute space of an ordi- 
nary dial to be subdivided into six equal parts, each of 


which is called a degree, and the measurement of an angle 
consists in finding how many of these degrees are included 
in the opening between its sides. At one o'clock the angle 
between the hands of a watch is thirty degrees, which is 
usually written 30, at three o'clock it is 90, at six o'clock 
180, etc. 

A watch may be used to measure angles. How? But 
a more convenient instrument is the protractor, which is 
shown in Fig. 1, applied to the angle ABC and showing 
that A BC = 85 as near- 
ly as the protractor scale 
can be read. 

The student should 
have and use a protrac- 
tor, such as is fur- 
nished with this book, 
for the numerous exer- 
cises which are to follow. 


neatly a triangle with FIG. I.-A protractor. 

sides about 100 millimeters long, measure each of its an- 
gles and take their sum. No matter what may be the 
shape of the triangle, this sum should be very nearly 180 
exactly 180 if the work were perfect but perfection 
can seldom be attained and one of the first lessons to 
be learned in any science which deals with measurement 
is, that however careful we may be in our work some 
minute error will cling to it and our results can be only 
approximately correct. This, however, should not be 
taken as an excuse for careless work, but rather as a stim- 
ulus to extra effort in order that the unavoidable errors 
may be made as small as possible. In the present case 
the measured angles may be improved a little by adding 
(algebraically) to each of them one third of the amount by 
which their sum falls short of 180, as in the following 
example : 


Measured angles. Correction. Corrected angles. 

A 73^4 +0.1 73.5 

B 49.3 +0.1 49.4 

C 57.0 +0.1 57.1 

Sum 179.7 180.0 

Defect +0.3 

This process is in very common use among astronomers, 
and is called " adjusting " the observations. 

3. Triangles. The instruments used by astronomers for 
the measurement of angles are usually provided with a 
telescope, which may be pointed at different objects, and 
with a scale, like that of the protractor, to measure the 
angle through which the telescope is turned in passing 
from one object to another. In this way it is possible to 
measure the angle between lines drawn from the instru- 
ment to two distant ob- 
jects, such as two church 
steeples or the sun and 
moon, and this is usually 
called the angle between 
the objects. By meas- 
uring angles in this way 
it is possible to deter- 
mine the distance to an 

inaccessible point, as shown in Fig. 2. A surveyor at A 
desires to know the distance to C\ on the opposite side of a 
river which he can not cross. He measures with a tape line 
along his own side of the stream the distance A B 100 
yards and then, with a suitable instrument, measures the 
angle at A between the points C and B, and the angle at 
B between <?and A, finding BAC = 73.4, A B C= 49.3. 
To determine the distance A C he draws upon paper a line 
100 millimeters long, and marks the ends a and b ; with a 
protractor he constructs at a the angle ~b a c = 73.4, and at 
b the anglr abc = 49.3, and marks by c the point where 


the two lines thus drawn meet. With the millimeter scale 
he now measures the distance a c = 90.2 millimeters, which 
determines the distance A C across the river to be 90.2 
yards, since the triangle on paper has been made simi- 
lar to the one across the river, and millimeters on the one 
correspond to yards on the other. What is the proposition 
of geometry upon which this depends? The measured 
distance A B in the surveyor's problem is called a base line. 
EXERCISE 3. With a foot rule and a protractor meas- 
ure a base line and the angles necessary to determine the 
length of the schoolroom. After the length has been thus 
found, measure it directly with the foot rule and compare 

FIG. 3. Finding the moon's distance from the earth. 

the measured length with the one found from the angles. 
If any part of the work has been carelessly done, the stu- 
dent need not expect the results to agree. 

In the same manner, by sighting at the moon from 
widely different parts of the earth, as in Fig. 3, the moon's 
distance from us is found to be about a quarter of a million 
miles. What is the base line in this case ? 

4. The horizon altitudes. In their observations astron- 
omers and sailors make much use of the plane of the hori- 
zon, and practically any flat and level surface, such as that 
of a smooth pond, may be regarded as a part of this plane 
and used as such. A very common observation relating to 


the plane of the horizon is called " taking the sun's alti- 
tude," and consists in measuring the angle between the 
sun's rays and the plane of the horizon upon which they 
fall. This angle between a line and a plane appears slightly 
different from the angle between two lines, but is really the 
same thing, since it means the angle between the sun's rays 
and a line drawn in the plane of the horizon toward the 
point directly under the sun. Compare this with the defi- 
nition given in the geographies, " The latitude of a point 
on the earth's surface is its angular distance north or south 
of the equator," and note that the latitude is the angle 
between the plane of the equator and a line drawn from 
the earth's center to the given point on its surface. 

A convenient method of obtaining a part of the plane 
of the horizon for use in observation is as follows : Place 
a slate or a pane of glass upon a table in the sunshine. 
Slightly moisten its whole surface and then pour a little 
more water upon it near the center. If the water runs 
toward one side, thrust the edge of a thin wooden wedge 
under this side and block it up until the water shows no 
tendency to run one way rather than another ; it is then 
level and a part of the plane of the horizon. Get several 
wedges ready before commencing the experiment. After 
they have been properly placed, drive a pin or tack behind 
each one so that it may not slip. 

5. Taking the sun's altitude. EXERCISE 4. Prepare a 
piece of board 20 centimeters or more square, planed 
smooth on one face and one edge. Drive a pin perpen- 
dicularly into the face of the board, near the middle of the 
planed edge. Set the board on edge on the horizon plane 
and turn it edgewise toward the sun so that a shadow of 
the pin is cast on the plane. Stick another pin into the 
board, near its upper edge, so that its shadow shall fall 
exactly upon the shadow of the first pin, and with a watch 
or clock observe the time at which the two shadows coin- 
cide. Without lifting the board from the plane, turn it 


around so that the opposite edge is directed toward the sun 
and set a third pin just as the second one was placed, and 
again take the time. Remove the pins and draw fine pencil 
lines, connecting the holes, as shown in Fig. 4, and with 
the protractor measure the an- 
gle thus marked. The student 
who has studied elementary ge- 
ometry should be able to dem- 
onstrate that at the mean of the 
two recorded times the sun's alti- 
tude was equal to one half of the 

angle measured in the figure. FlG - 4. -Taking the sun's 

When the board is turned 

edgewise toward the sun so that its shadow is as thin as 
possible, rule a pencil line alongside it on the horizon plane. 
The angle which this line makes with a line pointing due 
south is called the sun's azimuth. When the sun is south, 
its azimuth is zero ; when west, it is 90 ; when east, 
270, etc. 

EXERCISE 5. Let a number of different students take 
the sun's altitude during both the morning and afternoon 
session and note the time of each observation, to the near- 
est minute. Verify the setting of the plane of the horizon 
from time to time, to make sure that no change has occurred 
in it. 

6. Graphical representations. Make a graph (drawing) 
of all the observations, similar to Fig. 5, and find by bisect- 
ing a set of chords g to #, e to e^ d to d, drawn parallel to 
B B, the time at which the sun's altitude was greatest. In 
Fig. 5 we see from the intersection of M M with B B that 
this time was llh. 50m. 

The method of graphs which is here introduced is of 
great importance in physical science, and the student 
should carefully observe in Fig. 5 that the line B B is a 
scale of times, which may be made long or short, provided 
only the intervals between consecutive hours 9 to 10, 10 to 


11, 11 to 12, etc., are equal. The distance of each little 
circle from B B is taken proportional to the sun's altitude, 
and may be upon any desired scale e. g., a millimeter to 
a degree provided the same scale is used for all observa- 

d ,-ff> -&- ~-^-.,d 



B 9 10 11 -trl.2 1 SB 

FIG. 5. A graph of the sun's altitude. 

tions. Each circle is placed accurately over that part of 
the base line which corresponds to the time at which the 
altitude was taken. Square ruled paper is very convenient, 
although not necessary, for such diagrams. It is especially 
to be noted that from the few observations which are rep- 
resented in the figure a smooth curve has been drawn 
through the circles which represent the sun's altitude, and 
this curve shows the altitude of the sun at every moment 
between 9 A. M. and 3 P. M. In Fig. 5 the sun's altitude at 
noon was 57. What was it at half past two ? 

7. Diameter of a distant object. By sighting over a pro- 
tractor, measure the angle between imaginary lines drawn 
from it to the opposite sides of a window. Carry the pro- 
tractor farther away from the window and repeat the ex- 
periment, to see how much the angle changes. The angle 
thus measured is called " the angle subtended " by the win- 
dow at the place where the measurement was made. If 
this place was squarely in front of the window we may 
draw upon paper an angle equal to the measured one and 
lay off from the vertex along its sides a distance propor- 
tional to the distance of the window e. g., a millimeter for 


each centimeter of real distance. If a cross line be now 
drawn connecting the points thus found, its length will be 
proportional to the width of the window, and the width 
may be read oil to scale, a centimeter for every millimeter 
in the length of the cross line. 

The astronomer who measures with an appropriate in- 
strument the angle subtended by the moon may in an 
entirely similar manner find the moon's diameter and has, 
in fact, found it to be 2,163 miles. Can the same method 
be used to find the diameter of the sun ? A planet ? The 
earth ? 





8. The stars. From the very beginning of his study in 
astronomy, and as frequently as possible, the student should 
practice watching the stars by night, to become acquainted 
with the constellations and their movements. As an intro- 
duction to this study he may face toward the north, and 
compare the stars which he sees in that part of the sky with 
the map of the northern heavens, given on Plate I, oppo- 
site page 124. Turn the map around, upside down if 
necessary, until the stars upon it match the brighter ones 
in the sky. Note how the stars are grouped in such con- 
spicuous constellations as the Big Dipper (Ursa Major), the 
Little Dipper (Ursa Minor), and Cassiopea. These three 
constellations should be learned so that they can be recog- 
nized at any time. 

The names of the stars. Facing the star map is a key 
which contains the names of the more important constella- 
tions and the names of the brighter stars in their constella- 
tions. These names are for the most part a Greek letter 
prefixed to the genitive case of the Latin name of the con- 
stellation. (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 diff ereth 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 
at the beginning and end 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 magni- 
tudes. Following the indications of these maps, the stu- 
dent should, in learning the principal stars and constella- 
tions, 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 a Ursae Minoris, a Ursae Majoris, ft Ursae Ma- 
joris. What geometrical figure will fit on to these stars ? 
In addition to its regular name, a Ursae Minoris is frequent- 
ly 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 Cassiopea 

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. Kecord 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 verti- 
cal 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 ? Kepeat the observation on the next 
clear night, and allowing for the number of whole revolu- 
tions made by the stars between the two dates, again deter- 
mine 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 de- 
tected is called their u diurnal " motion. What is the sig- 
nificance of the word diurnal ? 

In the preceding paragraph there is introduced a method 
of great importance in astronomical practice i. e., determin- 
ing something in this case the rate per hour, from obser- 
vations 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, astron- 
omers 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. 

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

11. The plumb-line apparatus. This experiment, and 
many others, may be conveniently and accurately made 
with no other apparatus than a plumb line, and a device 



for sighting past it. In Figs. 6 and 7 there is shown a 
simple form of such apparatus, consisting essentially of a 
board which rests in a horizontal position upon the points 
of three screws that pass through it. This board carries 

FIG. 6. 

The plumb-line apparatus. 

FIG. 7. 

a small box, to one side of which is nailed in vertical posi- 
tion another board 5 or 6 feet long to carry the plumb line. 
This consists of a wire or fish line with any heavy weight 
e. g., a brick or flatiron tied to its lower end and immersed 
in a vessel of water placed inside the box, so as to check 
any swinging motion of the weight. In the cover of the 
box is a small hole through which the wire passes, and by 
turning the screws in the baseboard the apparatus may be 
readily leveled, so that the wire shall swing freely in the 
center of the hole without touching the cover of the box. 


Guy wires, shown in the figure, are applied so as to stiffen 
the whole apparatus. A board with a screw eye at each 
end may be pivoted to the upright, as in Fig. 6, for measur- 
ing altitudes ; or to the box, as in Fig. 7, for observing the 
time at which a star in its diurnal motion passes through 
the plane determined by the plumb line and the center of 
the screw eye through which the observer looks. 

The whole apparatus may be constructed by any person 
of ordinary mechanical skill at a very small cost, and it or 
something equivalent should be provided for every class be- 
ginning observational astronomy. To use the apparatus for 
the experiment of 10, it should be leveled, and the board 
with the screw eyes, attached as in Fig. 7, should be turned 
until the observer, looking through the screw eye, sees 
Polaris exactly behind the wire. Use a bicycle lamp to 
illumine the wire by night. The apparatus is now adjusted, 
and the observer has only to wait for the stars which he 
desires to observe, and to note by his watch the time at 
which they pass behind the wire. It will be seen that the 
wire takes the place of the vertical edge of the building, 
and that the board with the screw eyes is introduced solely 
to keep the observer in the right place relative to the 

12. A sidereal clock. Clocks are sometimes so made and 
regulated that they show always the same hour and minute 
when the stars come back to the same place, and such a 
timepiece is called a sidereal clock i. e., a star-time clock. 
Would such a clock gain or lose in comparison with an ordi- 
nary watch ? Could an ordinary watch be turned into a 
sidereal watch by moving the regulator ? 

13. Photographing the stars. EXERCISE 7. For any stu- 
dent who uses a camera. Upon some clear and moonless 
night point the camera, properly focused, at Polaris, and 
expose a plate for three or four hours. Upon developing 
the plate you should find a series of circular trails such as 
are shown in Fig. 8, only longer. Each one of these is pro- 


duced by a star moving slowly over the plate, in conse- 
quence of its changing position in the sky. The center 
indicated by these curved trails is called the pole of the 
heavens. It is that part of the sky toward which is pointed 
the axis about which the earth rotates, and the motion of 
the stars around the center is only an apparent motion due 
to the rotation of the earth which daily carries the observer 
and his camera around this axis while the stars stand still, 
just as trees and fences and telegraph poles stand still, 

FIG. 8. Photographing the circumpolar star?. BARNARD. 

although to the passenger upon a railway train they appear 
to be in rapid motion. So far as simple observations are 
concerned, there is no method by which the pupil can tell 
for himself that the motion of the stars is an apparent 
rather than a real one, and, following the custom of astron- 
omers, we shall habitually speak as if it were a real move- 
ment of the stars. How long was the plate exposed in 
photographing Fig. 8 ? 


14. Finding the stars, On Plate I, opposite page 124, 
the pole of the heavens is at the center of the map, near 
Polaris, and the heavy trail near the center of Fig. 8 is 
made by Polaris. See if you can identify from the map 
any of the stars whose trails show in the photograph. The 
brighter the star the bolder and heavier its trail. 

Find from the map and locate in the sky the two bright 
stars Capella and Vega, which are on opposite sides of 
Polaris and nearly equidistant from it. Do these stars 
share in the motion around the pole ? Are they visible on 
every clear night, and all night ? 

Observe other bright stars farther from Polaris than 
are Vega and Capella and note their movement. Do they 
move like the sun and moon ? Do they rise and set ? 

In what part of the sky do the stars move most rapidly, 
near the pole or far from it ? 

How long does it take the fastest moving stars to make 
the circuit of the sky and come back to the same place ? 
How long does it take the slow stars ? 

15. Rising and setting of the stars. A study of the sky 
along the lines indicated in these questions will show that 
there is a considerable part of it surrounding the pole 
whose stars are visible on every clear night. The same 
star is sometimes high in the sky, sometimes low, some- 
times to the east of the pole and at other times west of it, 
but is always above the horizon. Such stars are said to 
be circumpolar. A little farther from the pole each star, 
when at the .lowest point of its circular path, dips for a 
time below the horizon and is lost to view, and the farther 
it is away from the pole the longer does it remain invisible, 
until, in the case of stars 90 away from the pole, we find 
them hidden below the horizon for twelve hours out of 
every twenty-four (see Fig. 9). The sun is such a star, 
and in its rising and setting acts precisely as does every 
other star at a similar distance from the pole only, as we 
shall find later, each star keeps always at (nearly) the same 


distance from the pole, while the sun in the course of a 
year changes its distance from the pole very greatly, and 
thus changes the amount of time it spends above and be- 

FIG. 9. -Diurnal motion of the northern constellations. 

low the horizon, producing in this way the long days of 
summer and the short ones of winter. 

How much time do stars which are more than 90 from 
the pole spend above the horizon ? 

We say in common speech that the sun rises in the 
east, but this is strictly true only at the time when it is 90 
distant from the pole i. e., in March and September. At 
other seasons it rises north or south of east according as 
its distance from the pole is less or greater than 90, and 
the same is true for the stars. 


16. The geography of the sky, Find from a map the 
latitude and longitude of your schoolhouse. Find on the 
map the place whose latitude is 39 and longitude 77 west 
of the meridian of Greenwich. Is there any other place in 
the world which has the same latitude and longitude as 
your schoolhouse ? 

The places of the stars in the sky are located in exactly 
the manner which is illustrated by these geographical 
questions, only different names are used. Instead of lati- 
tude the astronomer says declination, in place of longitude 
he says right ascension, in place of meridian he says hour 
circle, but he means by these new names the same ideas 
that the geographer expresses by the old ones. 

Imagine the earth swollen up until it fills the whole 
sky ; the earth's equator would meet the sky along a line 
(a great circle) everywhere 90 distant from the pole, and 
this line is called the celestial equator. Trace its posi- 
tion along the middle of the map opposite page 190 and 
notice near what stars it runs. Every meridian of the 
swollen earth would touch the sky along an hour circle 
i. e., a great circle passing through the pole and therefore 
perpendicular to the equator. Xote that in the map one of 
these hour circles is marked 0. It plays the same part in 
measuring right ascensions as does the meridian of Green- 
wich in measuring longitudes ; it is the beginning, from 
which they are reckoned. Xote also, at the extreme left 
end of the map, the four bright stars in the form of a 
square, one side of which is parallel and close to the hour 
circle, which is marked 0. This is familiarly called the 
Great Square in Pegasus, and may be found high up in the 
southern sky whenever the Big Dipper lies below the pole. 
Why can it not be seen when Ursa Major is above the 

Astronomers use the right ascensions of the stars not 
only to tell in what part of the sky the star is placed, but 
also in time reckonings, to regulate their sidereal clocks, and 


with regard to this use they find it convenient to express 
right ascension not in degrees but in hours, 24 of which 
fill up the circuit of the sky and each of which is equal to 
15 of arc, 24 X 15 = 360. The right ascension of Capella 
is 5h. 9m. = 77.2, but the student should accustom him- 
self to using it in hours and minutes as given and not to 
change it into degrees. He should also note that some 

FIG. 10. From a photograph of the Pleiades. 

stars lie on the side of the celestial equator toward Polaris, 
and others are on the opposite side, so that the astronomer 
has to distinguish between north declinations and south 
declinations, just as the geographer distinguishes between 
north latitudes and south latitudes. This is done by the 
use of the + and signs, a 4- denoting that the star lies 
north of the celestial equator i. e., toward Polaris. 

Find on Plate II, opposite page 190, the Pleiades 


(Pleades), E. A. = 3h. 42m., Dec. = + 23.8. Why do 
they not show on Plate I, opposite page 124? In what 
direction are they from Polaris ? This is one of the 
finest star clusters in the sky, but it needs a telescope to 
bring out its richness. See how many stars you can count 
in it with the naked eye, and afterward examine it with 
an opera glass. Compare what you see with Fig. 10. Find 
Antares, E. A. = 16h. 23m. Dec. = 26.2. How far is 
it, in degrees, from the pole ? Is it visible in your sky ? 
If so, what is its color ? 

Find the E. A. and Dec. of a Ursse Majoris ; of j3 Ursae 
Majoris ; of Polaris. Find the Northern Crown, Corona 
Borealis, E. A. = 15h. 30m., Dec. = -f 27.0 ; the Beehive, 
Prmepe, E. A. = 8h. 33m., Dec. = + 20.4. 

These should be looked up, not only on the map, but 
also in the sky. 

17. Reference lines and circles. As the stars move across 
the sky in their diurnal motion, they carry the framework 
of hour circles and equator with them, so that the right 
ascension and declination of each star remain unchanged 
by this motion, just as longitudes and latitudes remain un- 
changed by the earth's rotation. They are the same when 
a star is rising and when it is setting ; when it is above the 
pole and when it is below it. During each day the hour 
circle of every star in the heavens passes overhead, and at 
the moment when any particular hour circle is exactly 
overhead all the stars which lie upon it are said to be " on 
the meridian " i. e., at that particular moment they stand 
directly over the observer's geographical meridian and upon 
the corresponding celestial meridian. 

An eye placed at the center of the earth and capable of 
looking through its solid substance would see your geograph- 
ical meridian against the background of the sky exactly cov- 
ering your celestial meridian and passing from one pole 
through your zenith to the other pole. In Fig. 11 the inner 
circle represents the terrestrial meridian of a certain place, 



0, as seen from the center of the earth, (7, and the outer 
circle represents the celestial meridian of as seen from 
C, only we must imagine, what can not be shown on the 
figure, that the outer circle is so large that the inner one 
shrinks to a mere point in 
comparison with it. i$s#P z 

represents the direction IB. 
which the earth's axis passes 
through the center, then C E 
at right angles to it must 
be the direction of the equa- 
tor which we suppose to be 
turned edgewise toward us ; 
and if C is the direction of 
some particular point on the 
earth's surface, then Z di- 
rectly overhead is called the 
zenith of that point, upon 

the celestial sphere. The line C H represents a direction 
parallel to the horizon plane at 0, and HOP is the angle 
which the axis of the earth makes with this horizon plane. 
The arc E measures the latitude of 0, and the arc Z E 
measures the declination of Z, and since by elementary 
geometry each of these arcs contains the same number of 
degrees as the angle E O Z, we have the 

Theorem. The latitude of any place is equal to the~~\ 
declination of its zenith. 

Corollary. Any star whose declination is equal to your 
latitude will once in each day pass through your zenith. 

18. Latitude. From the construction of the figure 


FIG. 11. Reference lines and circles. 

from which we find by subtraction and transposition 

and this gives the further 


Theorem. The latitude of any place is equal to the 
elevation of the pole above its horizon plane. 

"" An observer who travels north or south over the earth 
changes his latitude, and therefore changes the angle be- 
tween 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 ? 

EXEKCISE 8. Determine your 
latitude by taking the altitude of 
Polaris when it is at some one of the 
four points of its diurnal path, shown 

FIG. 12.-Diurnal path of j F j ^ ^ ifc j t 1 j t j 

said to be at upper culmination, and 

the star Ursae Minoris in the handle of the Big Dipper 
will be directly below it. When at 2 it is at western elon- 
gation, and the star Castor is near the meridian. When it 
is at S 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 altitude ob- 
served at either 2 or 4 may be considered equal to the lati- 
tude of the place, but the altitude observed when Polaris 
is at the positions marked 1 and 8 must be corrected for 
the star's distance from the pole, which may be assumed 
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 altitudes 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 artifi- 
cial 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 altitude of the 

After you have determined your latitude from Polaris, 
compare the result with your position as shown upon the 
best map available. With a little practice and considerable 
care the latitude 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 culmina- 
tion drive into the ground two stakes in line with the star 
and the plumb line. Such a meridian line is of great con* 
venience in observing the stars and should be laid out and 
permanently marked in some convenient open space 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 passing through Sirius 
coincides with the meridian, the sidereal time is 6h. 40m., 
since that is the right ascension of Sirius, and in astronom- 
ical 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 in- 
dicate 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 reg- 
ulated for this purpose will gain about four minutes per 
day in comparison with ordinary clocks, and when so reg- 
ulated 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 nut- 
meg clock or a watch of the cheapest kind is quite suffi- 

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 ob- 


served 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 ad- 
justed, 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 dis- 
appears behind the wire as seen through the center of the 
screw eye. If the star is too high up in the sky for con- 
venient observation, place a mirror, face up, just north of 
the screw eye and observe star, wire and screw eye by re- 
flection 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 preces- 
sion (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 second star of the table will be 
Oh. 38.6m. + i#m. Oh. 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 

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 -j- sign in the equa- 
tion 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. Any- 
thing 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 fel- 
low-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, com- 
mit 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 

The Meridian is that hour circle which passes through 
the zenith. 

A Vertical Circle is any great circle which 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 be- 
tween 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 meas- 
ured either at the pole where the two hour circles inter- 
sect, as is done in the star map opposite page 124, or 
along the equator, as is done in the map opposite page 
190. Eight ascension is always measured from the ver- 
nal 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 

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 mo- 
tion 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 sun- 
set ? 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 ? 



23. Star maps, Select from the map some conspicuous 
constellation that will be conveniently placed for observa- 
tion 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 addi- 
tions made to it by night should be carefully done, and foi 
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 s 
or a square with three others, etc. 

A series of maps of the more prominent constellations, 
such as Ursa Major, Cassiopea, Pegasus, Taurus, Orion, 
Gemini, Canis Major, Leo, Corvus, Bootes, Virgo, Hercules, 
Lyra, Aquila, Scorpius, should be constructed in this man- 
ner upon a uniform scale and preserved as a part of the 
student's work. Let the magnitude of the stars be repre- 
sented 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., Alde- 
baran 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 

FIG. 13. Star map of the region about Orion. 

star itself. Algol is one of the most conspicuous of these 
variable stars, as they are called. 

24. The moon's motion among the stars. Whenever the 
moon is visible note its position among the stars by allinea- 
tions, 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 re- 
quire 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 centime- 
ters 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 glass will prove of 
great assistance in this work. 

Use your drawings and the positions of the moon plot- 
ted 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 ? 

Each of these questions can be correctly answered from 
the student's own observations without recourse to any 

25. The sun and its motion. Examine the face of the 
sun through a smoked glass to see if there is anything 
there which you can sketch. 

By day as well as by night the sky is studded with stars, 
only they can not be seen by day on account of the over- 
whelming glare of sunlight, but the position of the sun 


among the stars may be found quite as accurately as was 
that of the moon, by observing from day to day its right 
ascension and declination, and this should be practiced at 
noon on clear days by different members of the class. 

EXERCISE 10. The right ascension of the sun may be 
found by observing with the sidereal clock the time of its 
transit over the meridian. Use the equation in 20, and 
substitute in place of U the value of the clock correction 
found from observations of stars on a preceding or fol- 
lowing night. If the clock gains or loses with respect to 
sidereal time, take this into account in the value of U. 

EXEECISE 11. To determine the sun's decimation, 
measure its altitude at the time it crosses the meridian. 
Use either the method of Exercise 4, or that used with 
Polaris in Exercise 8. The student should be able to show 
from Fig. 11 that the declination is equal to the sum of 
the altitude and the latitude of the place diminished by 
90, or in an equation 

Declination = Altitude -j- Latitude 90. 

If the declination as found from this equation is a negative 
number it indicates that the sun is on the south side of the 

The right ascension and declination of the sun as ob- 
served on each day should be plotted on the map and the 
date, written opposite it. If the work has been correctly 
done, the plotted points should fall upon the curved line 
(ecliptic) which runs lengthwise of the map. This line, in 
fact, represents the sun's path among the stars. 

Note that the hours of right ascension increase from 
up to 24, while the numbers on the clock dial go only from 
to 12, and then repeat to 12 again during the same 
day. When the sidereal time is 13 hours, 14 hours, etc., 
the clock will indicate 1 hour, 2 hours, etc., and 12 hours 
must then be added to the time shown on the dial. 

If observations of the sun's right ascension and declina- 


tion are made in the latter part of either March or Septem- 
ber the student will find that the sun crosses the equator 
at these times, and he should determine from his observa- 
tions, as accurately as possible, the date and hour of this 
crossing and the point on the equator at which the sun 
crosses it. These points are called the equinoxes, Vernal 
Equinox and Autumnal Equinox for the spring and autumn 
crossings respectively, and the student will recall that the 
vernal equinox is the point from which right ascensions 
are measured. Its position among the stars is found by 
astronomers from observations like those above described, 
only made with much more elaborate apparatus. 

Similar observations made in June and December show 
that the sun's midday altitude is about 47 greater in sum- 
mer than in winter. They show also that the sun is as far 
north of the equator in June as he is south of it in Decem- 
ber, from which it is easily inferred that his path, the 
ecliptic, is inclined to the equator at an angle of 23. 5, one 
half of 47. This angle is called the obliquity of the eclip- 
tic. The student may recall that in the geographies the 
torrid zone is said to extend 23. 5 on either side of the 
earth's equator. Is there any connection between these 
limits and the obliquity of the ecliptic ? Would it be cor- 
rect to define the torrid zone as that part of the earth's 
surface within which the sun may at some season of the 
year pass through the zenith ? 

EXERCISE 12. After a half dozen observations of the 
sun have been plotted upon the map, find by measurement 
the rate, in degrees per day, at which the sun moves along 
the ecliptic. How many days will be required for it to 
move completely around the ecliptic from vernal equinox 
back to vernal equinox again ? Accurate observations with 
the elaborate apparatus used by professional astronomers 
show that this period, which is called a tropical year, is 365 
days 5 hours 48 minutes 46 seconds. Is this the same as 
the ordinary year of our calendars ? 


26. The planets. Any one who has watched the sky and 
who has made the drawings prescribed in this chapter can 
hardly fail to have fonnd in the course of his observations 
some bright stars not set down on the printed star maps, 
and to have fonnd also that these stars do not remain fixed 
in position among their fellows, bnt wander about from 
one constellation to another. Observe the motion of one 
of these planets from night to night and plot its posi- 
tions on the star map, precisely as was done for the moon. 
What kind of path does it follow ? 

Both the ancient Greeks and the modern Germans have 
called these bodies wandering stars, and in English we name 
them planets, which is simply the Greek word for wanderer, 
bent to our use. Besides the sun and moon there are in 
the heavens five planets easily visible to the naked eye and, 
as we shall see later, a great number of smaller ones visible 
only in the telescope. More than 2,000 years ago astron- 
omers began observing the motion of sun, moon, and 
planets among the stars, and endeavored to account for 
these motions by the theory that each wandering star 
moved in an orbit about the earth. Classical and mediaeval 
literature are permeated with this idea, which was displaced 
only after a long struggle begun by Copernicus (1543 A. D.), 
who taught that the moon alone of these bodies revolves 
about the earth, while the earth and the other planets re- 
volve around the sun. The ecliptic is the intersection of 
the plane of the earth's orbit with the sky, and the sun ap- 
pears to move along the ecliptic because, as the earth moves 
around its orbit, the sun is always seen projected against 
the opposite side of it. The moon and planets all appear 
to move near the ecliptic because the planes of their orbits 
nearly coincide with the plane of the earth's orbit, and a 
narrow strip on either side of the ecliptic, following its 
course completely around the sky, is called the zodiac, n 
word which may be regarded as the name of a narrow street 
(16 wide) within which all the wanderings of the visible 


planets are confined and outside of which they never ven- 
ture. Indeed, Mars is the only planet which ever approaches 
the edge of the street, the others traveling near the middle 
of the road. 

27. A typical case of planetary motion. The Copernican 
theory, enormously extended and developed through the 

*/3 Ariet is 

*7 Arietis 

+ 1] Piscium 
* * 

I Arietis 

% TT Piscium 
Dec. 31 , 




Arietis ^.^-"Oct.2 ___________ <D 

* f <- ----- -O ------ O ---------- Z~ Aug. 3 

Sept. 12 Sept. 2 Aug. 23 

V Piscium 

% Piscium 

if- a Piscium 
FIG. 14. The apparent motion of a planet. 

Newtonian law of gravitation (see Chapter IV), has com- 
pletely supplanted the older Ptolemaic doctrine, and an 
illustration of the simple manner in which it accounts for 
the apparently complicated motions of a planet among the 
stars is found in Figs. 14 and 15, the first of which repre- 
sents the apparent motion of the planet Mars through the 
constellations Aries and Pisces during the latter part of the 


year 1894, while the second shows the true motions of Mars 
and the earth in their orbits about the sun during the same 
period. The straight line in Fig. 14, with cross ruling upon 
it, is a part of the ecliptic, and the numbers placed opposite 
it represent the distance, in degrees, from the vernal equi- 
nox. In Fig. 15 the straight line represents the direction 
from the sun toward the vernal equinox, and the angle 
which this line makes with the line joining earth and sun is 
called the earth's longitude. The imaginary line joining 
the earth and sun is called the earth's radius vector, and 
the pupil should note that the longitude and length of the 
radius vector taken together show the direction and dis- 
tance of the earth from the sun i. e., they fix the relative 
positions of the two bodies. The same is nearly true for 
Mars and would be wholly true if the orbit of Mars lay in 
the same plane with that of the earth. How does Fig. 14 
show that the orbit of Mars does not lie exactly in the same 
plane with the orbit of the earth ? 

EXERCISE 13. Find from Fig. 15 what ought to have 
been the apparent course of Mars among the stars during 
the period shown in the two figures, and compare what you 
find with Fig. 14. The apparent position of Mars among 
the stars is merely its direction from the earth, and this 
direction is represented in Fig. 14 by the distance of the 
planet from the ecliptic and by its longitude. 

The longitude of Mars for each date can be found from 
Fig. 15 by measuring the angle between the straight line 
S V and the line drawn from the earth to Mars. Thus for 
October 12th we may find with the protractor that the angle 
between the line S V and the line joining the earth to Mars 
is a 4ittle more than 30, and in Fig. 14 the position of 
Mars for this date is shown nearly opposite the cross line 
corresponding to 30 on the ecliptic. Just how far below 
the ecliptic this position of Mars should fall can not be 
told from Fig. 15, which from necessity is constructed as if 
the orbits of Mars and the earth lay in the same plane, and 


Mars in this case would always appear to stand exactly on 
the ecliptic and to oscillate back and forth as shown in Fig. 
14, but without the up-and-down motion there shown. In 
this way plot in Fig. 14 the longitudes of Mars as seen from 


^-'' ^ 

if,* -^ 

*- CP 

*4 ^ '< 

** ^ ^ 


FIG. 15. The real motion of a planet. 

the earth for other dates and observe how the forward mo- 
tion of the two planets in their orbits accounts for the appar- 
ently capricious motion of Mars to and fro among the stars. 



28. The orbits of the planets. Each planet, great or 
small, moves in its own appropriate orbit about the sun, 
and the exact determination of these orbits, their sizes, 
shapes, positions, etc., has been one of the great problems 

FIG. 16. The orbits of Jupiter and Saturn. 

of astronomy for more than 2,000 years, in which succes- 
sive generations of astronomers have striven to push to a 
still higher degree of accuracy the knowledge attained by 
their predecessors. Without attempting to enter into the 
details of this problem we may say, generally, that every 


planet moves in a plane passing through the sun, and for 
the six planets visible to the naked eye these planes nearly 
coincide, so that the six orbits may all be shown without 
much error as lying in the flat surface of one map. It is, 
however, more convenient to use two maps, such as Figs. 16 
and 17, one of which shows the group of planets, Mercury, 
Venus, the earth, and Mars, which are near the sun, and 
on this account are sometimes called the inner planets, 
while the other shows the more distant planets, Jupiter and 
Saturn, together with the earth, whose orbit is thus made 
to serve as a connecting link between the two diagrams. 
These diagrams are accurately drawn to scale, and are in- 
tended to be used by the student for accurate measure- 
ment in connection with the exercises and problems which 

In addition to the six planets shown in the figures the 
solar system contains two large planets and several hundred 
small ones, for the most part invisible to the naked eye, 
which are omitted in order to avoid confusing the dia- 

29. Jupiter and Saturn. In Fig. 16 the sun at the center 
is encircled by the orbits of the three planets, and inclosing 
all of these is a circular border showing the directions from 
the sun of the constellations which lie along the zodiac. 
The student must note carefully that it is only the direc- 
tions of these constellations which are correctly shown, and 
that in order to show them at all they have been placed 
very much too close to the sun. The cross lines extending 
from the orbit of the earth toward the sun with Eoman 
numerals opposite them show the positions of the earth in 
its orbit on the first day of January (7), first day of Feb- 
ruary (//), etc., and the similar lines attached to the orbits 
of Jupiter and Saturn with Arabic numerals show the posi- 
tions of those planets on the first day of January of each 
year indicated, so that the figure serves to show not only 
the orbits of the planets, but their actual positions in their 



orbits for something more than the first decade of the twen- 
tieth century. 

The line drawn from the sun toward the right of the 
figure shows the direction to the vernal equinox. It forms 
one side of the angle which measures a planet's longitude. 

FIG. 17. The orbits of the inner planets. 

EXERCISE 14. Measure with your protractor the longi- 
tude of the earth on January 1st. Is this longitude the 
same in all years ? Measure the longitude of Jupiter on 
January 1, 1900; on July 1, 1900; on September 25, 1906. 


Draw neatly on the map a pencil line connecting the 
position of the earth for January 1, 1900, with the position 
of Jupiter for the same date, and produce the line beyond 
Jupiter until it meets the circle of the constellations. This 
line represents the direction of Jupiter from the earth, and 
points toward the constellation in which the planet appears 
at that date. But this representation of the place of Jupi- 
ter in the sky is not a very accurate one, since on the scale 
of the diagram the stars are in fact more than 100,000 times 
as far off as they are shown in the figure, and the pencil 
mark does not meet the line of constellations at the same 
intersection it would have if this line were pushed back 
to its true position. To remedy this defect we must draw 
another line from the sun parallel to the one first drawn, 
and its intersection with the constellations will give very 
approximately the true position of Jupiter in the sky. 

EXERCISE 15. Find the present positions of Jupiter 
and Saturn, and look them up in the sky by means of your 
star maps. The planets will appear in the indicated con- 
stellations as very bright stars not shown on the map. 

Which of the planets, Jupiter and Saturn, changes its 
direction from the sun more rapidly ? Which travels the 
greater number of miles per day ? When will Jupiter and 
Saturn be in the same constellation ? Does the earth move 
faster or slower than Jupiter ? 

The distance of Jupiter or Saturn from the earth at any 
time may be readily obtained from the figure. Thus, by 
direct measurement with the millimeter scale we find for 
January 1, 1900, the distance of Jupiter from the earth is 6.1 
times the distance of the sun from the earth, and this may 
be turned into miles by multiplying it by 93,000,000, which 
is approximately the distance of the sun from the earth. 
For most purposes it is quite as well to dispense with this 
multiplication and call the distance 6.1 astronomical units, 
remembering that the astronomical unit is the distance of 
the sun from the earth. 


EXEKCISE 16. What is Jupiter's distance from the earth 
at its nearest approach ? What is the greatest distance it 
ever attains? Is Jupiter's least distance from the earth 
greater or less than its least distance from Saturn ? 

On what day in the year 1906 will the earth be on 
line between Jupiter and the sun? On this day Jupiter 
is said to be in opposition -i. e., the planet and the sun 
are on opposite sides of the earth, and Jupiter then comes 
to the meridian of any and every place at midnight. When 
the sun is between the earth and Jupiter (at what date in 
1906?) the planet is said to be in conjunction with the 
sun, and of course passes the meridian with the sun at 
noon. Can you determine from the figure the time at 
which Jupiter comes to the meridian at other dates than 
opposition and conjunction? Can you determine when it 
is visible in the evening hours ? Tell from the figure what 
constellation is on the meridian at midnight on January 
1st. Will it be the same constellation in every year ? 

30. Mercury, Venus, and Mars. Fig. 17, which repre- 
sents the orbits of the inner planets, differs from Fig. 16 
only in the method of fixing the positions of the planets 
in their orbits at any given date. The motion of these plan- 
ets is so rapid, on account of their proximity to the sun, that 
it would not do to mark their positions as was done for 
Jupiter and Saturn, and with the exception of the earth they 
do not always return to the same place on the same day in 
each year. It is therefore necessary to adopt a slightly dif- 
ferent method, as follows : The straight line extending from 
the sun toward the vernal equinox, F, is called the prime 
radius, and we know from past observations that the earth 
in its motion around the sun crosses this line on September 
23d in each year, and to fix the earth's position for Septem- 
ber 23d in the diagram we have only to take the point at 
which the prime radius intersects the earth's orbit. A 
month later, on October 23d, the earth will no longer be at 
this point, but will have moved on along its orbit to the 


point marked 30 (thirty days after September 23d). Sixty 
days after September 23d it will be at the point marked 60, 
etc., and for any date we have only to find the number of 
days intervening between it and the preceding September 
23d, and this number will show at once the position of the 
earth in its orbit. Thus for the date July 4, 1900, we find 

1900, July 4 1899, September 23 = 284 days, 
and the little circle marked upon the earth's orbit between 
the numbers 270 and 300 shows the position of the earth on 
that date. 

In what constellation was the sun on July 4, 1900? 
What zodiacal constellation came to the meridian at mid- 
night on that date? What other constellations came to 
the meridian at the same time ? 

The positions of the other planets in their orbits are 
found in the same manner, save that they do not cross the 
prime radius- on the same date in each year, and the times 
at which they do cross it must be taken from the following 
table : 


A. D. 





Period . . . 

88.0 days. 
Feb. 18th. 
Feb 5th 

224. 7 days. 
Jan. llth. 
\pril 5th 

365.25 days. 
Sept. 23d. 
Sept 23d 

687.1 days. 
April 28th. 


Jan. 23d. 
April 8th 

June 29th. 
Feb. 8th. 

Sept, 23d. 
Sept 23d 

March 16th. 


March 25th 

May 3d. 

Sept. 23d. 

Feb. 1st. 


March 12th. 
Feb 27th 

July 26th. 
March 8th 

Sept. 23d. 
Sept 23d 

Dec. 19th. 


Feb 14th 

May 31st. 

Sept 23d 

Nov. 6th. 


Feb. 1st 

Jan. llth. 

Sept. 23d. 


Jan. 18th. 
Jan 5th 

April 4th. 
June 28th. 

Sept. 23d. 
Sept 23d 

Sept, 23d. 

The first line of figures in this table shows the num- 
ber of days that each of these planets requires to make 
a complete revolution about the sun, and it appears from 
these numbers that Mercury makes about four revolutions 


in its orbit per year, and therefore crosses the prime radius 
four times in each year, while the other planets are decid- 
edly slower in their movements. The following lines of 
the table show for each year the date at which each planet 
first crossed the prime radius in that year; the dates of 
subsequent crossings in any year can be found by adding 
once, twice, or three times the period to the given date, 
and the table may be extended to later years, if need be, by 
continuously adding multiples of the period. In the case 
of Mars it appears that there is only about one year out of 
two in which this planet crosses the prime radius. 

After the date at which the planet crosses the prime 
radius has been determined its position for any required 
date is found exactly as in the case of the earth, and the 
constellation in which the planet will appear from the 
earth is found as explained above in connection with Jupi- 
ter and Saturn. 

The broken lines in the figure represent the construc- 
tion for finding the places in the sky occupied by Mercury, 
Venus, and Mars on July 4, 1900. Let the student make a 
similar construction and find the positions of these planets 
at the present time. Look them up in the sky and see if 
they are where your work puts them. 

31. Exercises. The "evening star" is a term loosely 
applied to any planet which is visible in the western sky 
soon after sunset. It is easy to see that such a planet must 
be farther toward the east in the sky than is the sun, and 
in either Fig. 16 or Fig. 17 any planet which viewed from 
the position of the earth lies to the left of the sun and 
not more than 50 away from it will be an evening star. 
If to the right of the sun it is a morning star, and may be 
seen in the eastern sky shortly before sunrise. 

What planet is the evening star now 9 Is there more 
than one evening star at a time? What is the morning 
star now ? 

Do Mercury, Venus, or Mars ever appear in opposition ? 


What is the maximum angular distance from the sun at 
which \ 7 enus can ever be seen ? Why is Mercury a more 
difficult planet to see than Venus? In what month of the 
year does Mars come nearest to the earth? Will it always 
be brighter in this month than in any other ? Which of 
all the planets comes nearest to the earth ? 

The earth always comes to the same longitude on the 
same day of each year. Why is not this true of the other 
planets ? 

The student should remember that in one respect Figs. 
16 and 17 are not altogether correct representations, since 
they show the orbits as all lying in the same plane. If this 
were strictly true, every planet would move, like the sun, 
always along the ecliptic ; but in fact all of the orbits are 
tilted a little out of the plane of the ecliptic and every 
planet in its motion deviates a little from the ecliptic, first 
to one side then to the other ; but not even Mars, which is 
the most erratic in this respect, ever gets more than eight 
degrees away from the ecliptic, and for the most part all 
of them are much closer to the ecliptic than this limit. 

A . >->^ 




32. The beginnings of celestial mechanics. From the ear- 
liest dawn of civilization, long before the beginnings of 
written history, the motions of sun and moon and planets 
among the stars from constellation to constellation had 
commanded the attention of thinking men, particularly of 
the class of priests. The religions of which they were the 
guardians and teachers stood in closest relations with the 
movements of the stars, and their own power and influence 
were increased by a knowledge of them. 

Out of these professional needs, as well as from a spirit 
of scientific research, there grew up and flourished for 
many centuries a study of the motions of the planets, sim- 
ple and crude at first, because the observations that could 
then be made were at best but rough ones, but growing 
more accurate and more complex as the development of the 
mechanic arts put better and more precise instruments into 
the hands of astronomers and enabled them to observe with 
increasing accuracy the movements of these bodies. It was 
early seen that while for the most part the planets, includ- 
ing the sun and moon, traveled through the constellations 
from west to east, some of them sometimes reversed their 
motion and for a time traveled in the opposite way. This 
clearly can not be explained by the simple theory which 
had early been adopted that a planet moves always in the 
same direction around a circular orbit having the earth at 
its center, and so it was said to move around in a small 
circular orbit, called an epicycle, whose center was situated 

ISAAC NEWTON ( 1643-1727 ). 


upon and moved along a circular orbit, called the deferent, 
within which the earth was placed, as is shown in Fig. 18, 
where the small circle is the epicycle, the large circle is the 
deferent, P is the planet, and E the earth. When this 
proved inadequate to account for the really complicated 
movements of the planets, another epicycle was put on top 
of the first one, and then another and another, until the 
supposed system became so complicated that Copernicus, a 
Polish astronomer, repudiated 
its fundamental theorem and 
taught that the motions of 
the planets take place in cir- 
cles around the sun instead 
of about the earth, and that 
the earth itself is only one of 
the planets moving around 
the sun in its- own appropri- 
ate orbit and itself largely re- 
sponsible for the seemingly 

& J FIG. 18. Epicycle and deferent. 

erratic movements of the 

other planets, since from day to day we see them and ob- 
serve their positions from different points of view. 

33. Kepler's laws. Two generations later came Kepler 
with his three famous laws of planetary motion : 

I. Every planet moves in an ellipse which has the sun 
at one of its foci. 

II. The radius vector of each planet moves over equal 
areas in equal times. 

III. The squares of the periodic times of the planets 
are proportional to the cubes of their mean distances from 
the sun. 

These laws are the crowning glory, not only of Kepler's 
career, but of all astronomical discovery from the begin- 
ning up to his time, and they well deserve careful study 
and explanation, although more modern progress has shown 
that they are only approximately true. 


EXERCISE 17. Drive two pins into a smooth board an 
inch apart and fasten to them the ends of a string a foot 
long. Take up the slack of the string with the point of a 
lead pencil and, keeping the string drawn taut, move the 
pencil point over the board into every possible position. 
The curve thus traced will be an ellipse having the pins at 
the two points which are called its foci. 

In the case of the planetary orbits one focus of the 
ellipse is vacant, and, in accordance with the first law, the 
center of the sun is at the other focus. In Fig. 17 the dot, 
inside the orbit of Mercury, which is marked , shows the 
position of the vacant focus of the orbit of Mars, and the 
dot b is the vacant focus of Mercury's orbit. The orbits of 
Venus and the earth are so nearly circular that their vacant 
foci lie very close to the sun and are not marked in the 
figure. The line drawn from the sun to any point of the 
orbit (the string from pin to pencil point) is a radius vector. 
The point midway between the pins is the center of the 
ellipse, and the distance of either pin from the center meas- 
ures the eccentricity of the ellipse. 

Draw several ellipses with the same length of string, 
but with the pins at different distances apart, and note that 
the greater the eccentricity the flatter is the ellipse, but 
that all of them have the same length.- 

If both pins were driven into the same hole, what kind 
of an ellipse would you get ? 

The Second Law was worked out by Kepler as his answer 
to a problem suggested by the first law. In Fig. 17 it is 
apparent from a mere inspection of the orbit of Mercury 
that this planet travels much faster on one side of its orbit 
than on the other, the distance covered in ten days between 
the numbers 10 and 20 being more than fifty per cent greater 
than that between 50 and 60. The same difference is found, 
though usually in less degree, for every other planet, and 
Kepler's problem was to discover a means by which to 
mark upon the orbit the figures showing the positions of 


the planet at the end of equal intervals of time. His solu- 
tion of this problem, contained in the second law, asserts 
that if we draw radii vectores from the sun to each of the 
marked points taken at equal time intervals around the 
orbit, then the area of the sector formed by two adjacent 
radii vectores and the arc included between them is equal 
to the area of each and every other such sector, the short 
radii vectores being spread apart so as to include a long 
arc between them while the long radii vectores have a short 
arc. In Kepler's form of stating the law the radius vector 
is supposed to travel with the planet and in each day to 
sweep over the same fractional part of the total area of the 
orbit. The spacing of the numbers in Fig. 17 was done by 
means of this law. 

For the proper understanding of Kepler's Third Law we 
must note that the " mean distance " which appears in it is 
one half of the long diameter of the orbit and that the 
"periodic time" means the number of days or years re- 
quired by the planet to make a complete circuit in its orbit. 
Representing the first of these by a and the second by T, 
we have, as the mathematical equivalent of the law, 

where the quotient, (7, is a number which, as Kepler found, 
is the same for every planet of the solar system. If we take 
the mean distance of the earth from the sun as the unit of 
distance, and the year as the unit of time, we shall find by 
applying the equation to the earth's motion, C = 1. Ap- 
plying this value to any other planet we shall find in the 
same units, a = T , by means of which we may determine 
the distance of any planet from the sun when its periodic 
time, I 7 , has been learned from observation. 

EXERCISE 18. Uranus requires 84 years to make a 
revolution in its orbit. What is its mean distance from the 
sun ? What are the mean distances of Mercury, Venus, and 
Mars ? (See Chapter III for their periodic times.) Would 


it be possible for two planets at different distances from 
the sun to move around their orbits in the same time ? 

A circle is an ellipse in which the two foci have been 
brought together. Would Kepler's laws hold true for such 
an orbit ? 

34. Newton's laws of motion, Kepler studied and de- 
scribed the motion of the planets. Newton, three genera- 
tions later (1727 A. D.), studied and described the mechan- 
ism which controls that motion. To Kepler and his age the 
heavens were supernatural, while to Newton and his suc- 
cessors they are a part of Nature, governed by the same 
laws which obtain upon the earth, and we turn to the ordi- 
nary things of everyday life as the foundation of celestial 

Every one who has ridden a bicycle knows that he can 
coast farther upon a level road if it is smooth than if it is 
rough ; but however smooth and hard the road may be and 
however fast the wheel may have been started, it is sooner 
or later stopped by the resistance which the road and the 
air offer to its motion, and when once stopped or checked 
it can be started again only by applying fresh power. We 
have here a familiar illustration of what is called 

The first law of motion." Every body continues in its 
state of rest or of uniform motion in a straight line except 
in so far as it may be compelled by force to change that 
state." A gust of wind, a stone, a careless movement of 
the rider may turn the bicycle to the right or the left, but 
unless some disturbing force is applied it will go straight 
ahead, and if all resistance to its motion could be removed 
it would go always at the speed given it by the last power 
applied, swerving neither to the one hand nor the other. 

When a slow rider increases his speed we recognize at 
once that he has applied additional power to the wheel, and 
when this speed is slackened it equally shows that force has 
been applied against the motion. It is force alone which 
can produce a change in either velocity or direction of 


motion ; but simple as this law now appears it required the 
genius of Galileo to discover it and of Newton to give it the 
form in which it is stated above. 

35. The second law of motion, which is also due to Gali- 
leo and Newton, is : 

" Change of motion is proportional to force applied and 
takes place in the direction of the straight line in which 
the force acts." Suppose a man to fall from a balloon at 
some great elevation in the air ; his own weight is the force 
which pulls him down, and that force operating at every 
instant is sufficient to give him at the end of the first sec- 
ond of his fall a downward velocity of 32 feet per second 
i. e., it has changed his state from rest, to motion at this 
rate, and the motion is toward the earth because the force 
acts in that direction. During the next second the cease- 
less operation of this force will have the same effect as in 
the first second and will add another 32 feet to his ve- 
locity, so that two seconds from the time he commenced to 
fall he will be moving at the rate of 64 feet per second, etc. 
The column of figures marked v in the table below shows 
what his velocity will be at the end of subsequent seconds. 
The changing velocity here shown is the change of motion 
to which the law refers, and the velocity is proportional to 
the time shown in the first column of the table, because the 
amount of force exerted in this case is proportional to the 
time during which it operated. The distance through 
which the man will fall in each second is shown in the col- 
umn marked d, and is found by taking the average of his 
velocity at the beginning and end of this second, and the 
total distance through which he has fallen at the end of 
each second, marked s in the table, is found by taking the 
sum of all the preceding values of d. The velocity, 32 feet 
per second, which measures the change of motion in each 
second, also measures the accelerating force which produces 
this motion, and it is usually represented in formulae by 
the letter g. Let the student show from the numbers in 


the table that the accelerating force, the time, ^, during 
which it operates, and the space, s, fallen through, satisfy 
the relation 

s = | g t 2 , 

which is usually called the law of falling bodies. How does 
the table show that g is equal to 32 ? 


























etc. etc. etc. etc. 

If the balloon were half a mile high how long would it 
take to fall to the ground ? What would be the velocity 
just before reaching the ground ? 

Fig. 19 shows the path through the air of a ball which 
has been struck by a bat at the point A, and started off in 
the direction A B with a velocity of 200 feet per second. 
In accordance with the first law of motion, if it were acted 
upon by no other force than the impulse given by the bat, 
it should travel along the straight line A S at the uniform 
rate of 200 feet per second, and at the end of the fourth 
second it should be 800 feet from A, at the point marked 4, 
but during these four seconds its weight has caused it to 
fall 256 feet, and its actual position, 4', is 256 feet below 
the point 4. In this way we find its position at the end of 
each second, 1', 2', 3', 4', etc., and drawing a line through 
these points we shall find the actual path of the ball under 
the influence of the two forces to be the curved line A C. 
No matter how far the ball may go before striking the 
ground, it can not get back to the point A, and the curve 

GALILEO GALILEI (1564-1642). 



A C therefore can not be a part of a circle, since that curve 
returns into itself. It is, in fact, a part of a parabola, 
which, as we shall see later, is a kind of orbit in which 
comets and some other heavenly bodies move. A skyrocket 

FIG. 19. The path of a ball. 

moves in the same kind of a path, and so does a stone, a 
bullet, or any other object hurled through the air. 

36. The third law of motion. " To every action there is 
always an equal and contrary reaction ; or the mutual ac- 
tions of any two bodies are always equal and oppositely 
directed." This is well illustrated in the case of a man 
climbing a rope hand over hand. The direct force or action 
which he exerts is a downward pull upon the rope, and it is 
the reaction of the rope to this pull which lifts him along 
it. We shall find in a later chapter a curious application 
of this law to the history of the earth and moon. 


It is the great glory of Sir Isaac Newton that he first of 
all men recognized that these simple laws of motion hold 
true in the heavens as well as upon the earth ; that the 
complicated motion of a planet, a comet, or a star is de- 
termined in accordance with these laws by the forces 
which act upon the bodies, and that these forces are 
essentially the same as that which we call weight. The 
formal statement of the principle last named is in- 
cluded in 

37. Newton's law of gravitation, " Every particle of 
matter in the universe attracts every other particle with a 
force whose direction is that of a line joining the two, and 
whose magnitude is directly as the product of their masses, 
and inversely as the square of their distance from each 
other." We know that we ourselves and the things about 
us are pulled toward the earth by a force (weight) which is 
called, in the Latin that Newton wrote, gravitas, and the 
word marks well the true significance of the law of gravita- 
tion. Newton did not discover a new force in the heavens, 
but he extended an old and familiar one from a limited 
terrestrial sphere of action to an unlimited and celestial 
one, and furnished a precise statement of the way in which 
the force operates. Whether a body be hot or cold, wet or 
dry, solid, liquid, or gaseous, is of no account in deter- 
mining the force which it exerts, since this depends solely 
upon mass and distance. 

The student should perhaps be warned against straining 
too far the language which it is customary to employ in 
this connection. The law of gravitation is certainly a far- 
reaching one, and it may operate in every remotest corner 
of the universe precisely as stated above, but additional 
information about those corners would be welcome to sup- 
plement our rather scanty stock of knowledge concerning 
what happens there. We may not controvert the words of_J>- 
a popular preacher who says, " When I lift my hand I move 
the stars in Ursa Major," but we should not wish to stand 


sponsor for them, even though they are justified by a rigor- 
ous interpretation of the Newtonian law. 

The word mass, in the statement of the law of gravita- 
tion, means the quantity of matter contained in the body, 
and if we represent by the letters m' and m" the respective 
quantities of matter contained in the two bodies whose dis- 
tance from each other is r, we shall have, in accordance 
with the law of gravitation, the following mathematical 
expression for the force, F, which acts between them : 

This equation, which is the general mathematical ex- 
pression for the law of gravitation, may be made to yield 
some curious results. Thus, if we select two bullets, each 
having a mass of 1 gram, and place them so that their qen- 
ters are 1 centimeter apart, the above expression for the 
force exerted between them becomes 

from which it appears that the coefficient Ic is the force 
exerted between these bodies. This is called the gravita- 
tion constant, and it evidently furnishes a measure of the 
specific intensity with which one particle of matter attracts 
another. Elaborate experiments which have been made to 
determine the amount of this force show that it is sur- 
prisingly small, for in the case of the two bullets whose 
mass of 1 gram each is supposed to be concentrated into 
an indefinitely small space, gravity would have to operate 
between them continuously for more than forty minutes in 
order to pull them together, although they were separated 
by only 1 centimeter to start with, and nothing save their 
own inertia opposed their movements. It is only when one 
or both of the masses m\ m" are very great that the force 
of gravity becomes large, and the weight of bodies at the 


surface of the earth is considerable because of the great 
quantity of matter which goes to make up the earth. 
Many of th'e heavenly bodies are much more massive than 
the earth, as the mathematical astronomers have found by 
applying the law of gravitation to determine numerically 
their masses, or, in more popular language, to " weigh " 

The student should observe that the two terms mass 
and weight are not synonymous ; mass is defined above as 
the quantity of matter contained in a body, while weight 
is the force with which the earth attracts that body, and 
in accordance with the law of gravitation its weight de- 
pends upon its distance from the center of the earth, while 
its mass is quite independent of its position with respect 
to the earth. 

By the third law of motion the earth is pulled toward a 
falling body just as strongly as the body is pulled toward 
the earth i. e., by a force equal to the weight of the body. 
How much does the earth rise toward the body ? 

38. The motion of a planet. In Fig. 20 /S represents the 
sun and P a planet or other celestial body, which for the 
moment is moving along the straight line P 1. In accord- 
ance with the first law of motion it would continue to move 
along this line with uniform velocity if no external force 
acted upon it; but such a force, the sun's attraction, is 
acting, and by virtue of this attraction the body is pulled 
aside from the line P 1. 

Knowing the velocity and direction of the body's motion 
and the force with which the sun attracts it, the mathema- 
tician is able to apply Newton's laws of motion so as to 
determine the path of the body, and a few of the possible 
orbits are shown in the figure where the short cross stroke 
marks the point of each orbit which is nearest to the sun. 
This point is called the perihelion. 

Without any formal application of mathematics we may 
readily see that the swifter the motion of the body at P 


the shorter will he the time during which it is subjected to 
the sun's attraction at close range, and therefore the force 
exerted by the sun, and the resulting change of motion, will 
be small, as in the orbits P 1 and P 2. 

On the other hand, P 5 and P 6 represent orbits in which 
the velocity at P was comparatively small, and the resulting 
change of motion greater 
than would be possible for 
a more swiftly moving body. 

What would be the or_ 
bit if the velocity at P were 
reduced to nothing at all ? 

What would be the effect 
if the body starting at P 
moved directly away from 1? 

The student should not 
fail to observe that the sun's 
attraction tends to pull the 
body at P forward along its 
path, and therefore increas- 
es its velocity, and that this 
influence continues until 

the planet reaches perihelion, at which point it attains its 
greatest velocity, and the force of the sun's attraction is 
wholly expended in changing the direction of its motion. 
After the planet has passed perihelion the sun begins to 
pull backward and to retard the motion in just the same 
measure that before perihelion passage it increased it, so 
that the two halves of the orbit on opposite sides of a line 
drawn from the perihelion through the sun are exactly 
alike. We may here note the explanation of Kepler's sec- 
ond law : when the planet is near the sun it moves faster, 
and the radius vector changes its direction more rapidly 
than when the planet is remote from the sun on account 
of the greater force with which it is attracted, and the ex- 
act relation between the rates at which the radius vector 

FIG. 20. Different kinds of orbits. 


turns in different parts of the orbit, as given by the second 
law, depends upon the changes in this force. 

When the velocity is not too great, the sun's backward 
pull, after a planet has passed perihelion, finally overcomes 
it and turns the planet toward the sun again, in such a way 
that it comes back to the point P, moving in the same di- 
rection and with the same speed as before i. e., it has gone 
around the sun in an orbit like P 6 or P 4, an ellipse, along 
which it will continue to move ever after. But we must 
not fail to note that this return into the same orbit is a 
consequence of the last line in the statement of the law of 
gravitation (p. 54), and that, if the magnitude of this force 
were inversely as the cube of the distance or any other pro- 
portion than the square, the orbit would be something very 
different. If the velocity is too great for the sun's attrac- 
tion to overcome, the orbit will be a hyperbola, like P 2, 
along which the body will move away never to return, while 
a velocity just at the limit of what the sun can control gives 
an orbit like P 3, a parabola, along which the body moves 
with parabolic velocity, which is ever diminishing as the 
body gets farther from the sun, but is always just sufficient 
to keep it from returning. If the earth's velocity could be 
increased 41 per cent, from 19 up to 27 miles per second, it 
would have parabolic velocity, and would quit the sun's 

The summation of the whole matter is that the orbit in 
which a body moves around the sun, or past the sun, de- 
pends upon its velocity and if this velocity and the direc- 
tion of the motion at any one point in the orbit are known 
the whole orbit is determined by them, and the position of 
the planet in its orbit for past as well as future times can 
be determined through the application of Newton's laws ; 
and the same is true for any other heavenly body moon, 
comet, meteor, etc. It is in this way that astronomers are 
able to predict, years in advance, in what particular part of 
the sky a given planet will appear at a given time. 


It is sometimes a source of wonder that the planets 
move in ellipses instead of circles, but it is easily seen from 
Fig. 20 that the planet, P, could not by any possibility 
move in a circle, since the direction of its motion at P is 
not at right angles with the line joining it to the sun as it 
must be in a circular orbit, and even if it were perpen- 
dicular to the radius vector the planet must needs have 
exactly the right velocity given to it at this point, since 
either more or less speed would change the circle into an 
ellipse. In order to produce circular motion there must be 
a balancing of conditions as nice as is required to make a 
pin stand upon its point, and the really surprising thing is 
that the orbits of the planets should be so nearly circular 
as they are. If the orbit of the earth were drawn accu- 
rately to scale, the untrained eye would not detect the 
slightest deviation from a true circle, and even the orbit of 
Mercury (Fig. 17), which is much more 
eccentric than that of the earth, might al- 
most pass for a circle. 

The orbit P 2, which lies between the 
parabola and the straight line, is called in 
geometry a hyperbola, and Newton suc- 
ceeded in proving from the law of gravita- 
tion that a body might move under the 
sun's attraction in a hyperbola as well as 
in a parabola or ellipse ; but it must move 
in some one of these curves ; no other or- 
bit is possible.* Thus it would not be An orbit . 
possible for a body moving under the law 
of gravitation to describe about the sun any such orbit 
as is shown in Fig. 21. If the body passes a second time 
through any point of its orbit, such as P in the figure, then 
it must retrace, time after time, the whole path that it first 

* The circle and straight line are considered to be special cases of 
these curves, which, taken collectively, are called the conic sections. 


traversed in getting from P around to P again i. e., the 
orbit must be an ellipse. 

Newton also proved that Kepler's three laws are mere 
corollaries from the law of gravitation, and that to be 
strictly correct the third law must be slightly altered so as 
to take into account the masses of the planets. These are, 
however, so small in comparison with that of the sun, that 
the correction is of comparatively little moment. 

39. Perturbations. In what precedes we have considered 
the motion of a planet under the influence of no other 
force than the sun's attraction, while in fact, as the law of 
gravitation asserts, every other body in the universe is in 
some measure attracting it and changing its motion. The 
resulting disturbances in the motion of the attracted ,body 
are called perturbations, but for the most part these are 
insignificant, because the bodies by whose disturbing attrac- 
tions they are caused are either very small or very remote, 
and it is only when our moving planet, P, comes under the 
influence of some great disturbing power like Jupiter or 
one of the other planfets that the perturbations caused by 
their influence need to be taken into account. 

The problem of the motion of three bodies sun, Jupiter, 
planet which must then be dealt with is vastly more com- 
plicated than that which we have considered, and the ablest 
mathematicians and astronomers have not been able to fur- 
nish a complete solution for it, although they have worked 
upon the problem for two centuries, and have developed an 
immense amount of detailed information concerning it. 

In general each planet works ceaselessly upon the orbit 
of every other, changing its size and shape and position, 
backward and forward in accordance with the law of gravi- 
tation, and it is a question of serious moment how far this 
process may extend. If the diameter of the earth's orbit 
were very much increased or diminished by the perturbing 
action of the other planets, the amount of heat received 
from the sun would be correspondingly changed, and the 


earth, perhaps, be rendered unfit for the support of life. 
The tipping of the plane of the earth's orbit into a new 
position might also produce serious consequences ; but the 
great French mathematician of a century ago, Laplace, 
succeeded in proving from the law of gravitation that al- 
though both of these changes are actually in progress they 
can not, at least for millions of years, go far enough to 
prove of serious consequence, and the same is true for all 
the other planets, unless here and there an asteroid may 
prove an exception to the rule. 

The precession (Chapter V) is a striking illustration 
of a perturbation of slightly different character from the 
above, and another is found in connection with the plane 
of the moon's orbit. It will be remembered that the moon 
in its motion among the stars never goes far from the 
ecliptic, but in a complete circuit of the heavens crosses it 
twice, once -in going from south to north and once in the 
opposite direction. The points at which it crosses the 
ecliptic are called the nodes, and under the perturbing in- 
fluence of the sun these nodes move westward along the 
ecliptic about twenty degrees per year, an extraordinarily 
rapid perturbation, and one of great consequence in the 
theory of eclipses. 

40. Weighing the planets. Although these perturbations 
can not be considered dangerous, they are interesting since 
they furnish a method for weighing the planets which pro- 
duce them. From the law of gravitation we learn that the 
ability of a planet to produce perturbations depends di- 
rectly upon its mass, since the force F which it exerts con- 
tains this mass, m', as a factor. So, too, the divisor r 2 in 
the expression for the force shows that the distance be- 
tween the disturbing and disturbed bodies is a matter of 
great consequence, for the smaller the distance the greater 
the force. When, therefore, the mass of a planet such as 
Jupiter is to be determined from the perturbations it pro- 
duces, it is customary to select some such opportunity as 



FIG. 22. A planet subject to great per- 
turbations by Jupiter. 

is presented in Fig. 22, where one of the small planets, 
called asteroids, is represented as moving in a very eccen- 
tric orbit, which at one point approaches close to the orbit 
of Jupiter, and at another place comes near to the orbit of 

the earth. For the most part 
Jupiter will not exert any 
very great disturbing influ- 
ence upon a planet moving in 
such an orbit as this, since it 
is only at rare intervals that 
the asteroid and Jupiter ap- 
proach so close to each other, 
as is shown in the figure. 
The time during which the 
asteroid is little aifected by 
the attraction of Jupiter is 
used to study the motion giv- 
en to it by the sun's attrac- 
tion that is, to determine carefully the undisturbed orbit 
in which it moves ; but there comes a time at which the 
asteroid passes close to Jupiter, as shown in the figure, and 
the orbital motion which the sun imparts to it will then be 
greatly disturbed, and when the planet next comes round 
to the part of its orbit near the earth the effect of these 
disturbances upon its apparent position in the sky will be 
exaggerated by its close proximity to the earth. If now 
the astronomer observes the actual position of the asteroid 
in the sky, its right ascension and declination, and com- 
pares these with the position assigned to the planet by the 
law of gravitation when the attraction of Jupiter is ignored, 
the differences between the observed right ascensions and 
declinations and those computed upon the theory of undis- 
turbed motion will measure the influence that Jupiter has 
had upon the asteroid, and the amount by which Jupiter has 
shifted it, compared with the amount by which the sun has 
moved it that is, with the motion in its orbit furnishes 


the mass of Jupiter expressed as a fractional part of the 
mass of the sun. 

There has been determined in this manner the mass of 
every planet in the solar system which is large enough to 
produce any appreciable perturbation, and all these masses 
prove to be exceedingly small fractions of the mass of the 
sun, as may be seen from the following table, in which is 
given opposite the name of each planet the number by 
which the mass of the sun must be divided in order to 
get the mass of the planet : 

Mercury 7,000,000 (?) 

Venus 408,000 

Earth 329,000 

Mars 3,093,500 

Jupiter 1,047.4 

Saturn 3,502 

Uranus 22,800 

Neptune 19,700 

It is to be especially noted that the mass given for each 
planet includes the mass of all the satellites which attend 
it, since their influence was felt in the perturbations from 
which the mass was derived. Thus the mass assigned to 
the earth is the combined mass of earth and moon. 

41. Discovery of Neptune. The most famous example of 
perturbations is found in connection with the discovery, 
in the year 1846, of Neptune, the outermost planet of the 
solar system. For many years the motion of Uranus, his 
next neighbor, had proved a puzzle to astronomers. In 
accordance with Kepler's first law this planet should move 
in an ellipse having the sun at one of its foci, but no ellipse 
could be found which exactly fitted its observed path among 
the stars, although, to be sure, the misfit was not very pro- 
nounced. Astronomers surmised that the small deviations 
of Uranus from the best path which theory combined with 
observation could assign, were due to perturbations in its 


motion caused by an unknown planet more remote from 
the sun a thing easy to conjecture but hard to prove, and 
harder still to find the unknown disturber. But almost 
simultaneously two young men, Adams in England and 
Le Verrier in France, attacked the problem quite inde- 
pendently of each other, and carried it to a successful so- 
lution, showing that if the irregularities in the motion of 
Uranus were indeed caused by an unknown planet, then 
that planet must, in September, 1846, be in the direction 
of the constellation Aquarius ; and there it was found on 
September 23d by the astronomers of the Berlin Observatory 
whom Le Verrier had invited to search for it, and found 
within a degree of the exact point which the law of gravi- 
tation in his hands had assigned to it. 

This working backward from the perturbations experi- 
enced by Uranus to the cause which produced them is justly 
regarded as one of the greatest scientific achievements of 
the human intellect, and it is worthy of note that we are 
approaching the time at which it may be repeated, for Nep- 
tune now behaves much as did Uranus three quarters of a 
century ago, and the most plausible explanation which can 
be offered for these anomalies in its path is that the bounds 
of the solar system must be again enlarged to include an- 
other disturbing planet. 

42. The shape of a planet, There is an effect of gravita- 
tion not yet touched upon, which is of considerable interest 
and wide application in astronomy viz., its influence in de- 
termining the shape of the heavenly bodies. The earth is 
a globe because every part of it is drawn toward the center 
by the attraction of the other parts, and if this attraction 
on its surface were everywhere of equal force the material 
of the earth would be crushed by it into a truly spherical 
form, no matter what may have been the shape in which it 
was originally made. But such is not the real condition of 
the earth, for its diurnal rotation develops in every particle 
of its body a force which is sometimes called centrifugal, 


but which is really nothing more than the inertia of its 
particles, which tend at every moment to keep unchanged 
the direction of their motion and which thus resist the at- 
traction that pulls them into a circular path marked out 
by the earth's rotation, just as a stone tied at the end of 
a string and swung swiftly in a circle pulls upon the 
string and opposes the constraint which keeps it moving 
in a circle. A few experiments with such a stone will 
show that the faster it goes the harder does it pull upon 
the string, and the same is true of each particle of the 
earth, the swiftly moving ones near the equator having 
a greater centrifugal force than the slow ones near the 
poles. . At the equator the centrifugal force is directly 
opposed to the force of gravity, and in effect diminishes it, 
so that, comparatively, there is an excess of gravity at the 
poles which compresses the earth along its axis and causes 
it to bulge out at the equator until a balance is thus re- 
stored. As we have learned from the study of geography, 
in the case of the earth, this compression amounts to about 
27 miles, but in the larger planets, Jupiter and Saturn, it 
is much greater, amounting to several thousand miles. 

But rotation is not the only influence that tends to 
pull a planet out of shape. The attraction which the earth 
exerts upon the moon is stronger on the near side and 
weaker on the far side of our satellite than at its center, 
and this difference of attraction tends to warp the moon, as 
is illustrated in Fig. 23 where ./, #, and 8 represent pieces 
of iron of equal mass placed in line on a table near a horse- 
shoe magnet, H. Each piece of iron is attracted by the 
magnet and is held back by a weight to which it is 
fastened by means of a cord running over a pulley, P, 
at the edge of the table. These weights are all to be 
supposed equally heavy and each of them pulls upon its 
piece of iron with a force just sufficient to balance the 
attraction of the magnet for the middle piece, No. 2. 
It is clear that under this arrangement No. 2 will move 



neither to the right nor to the left, since the forces exerted 
upon it by the magnet and the weight just balance each 
other. Upon No. 1, however, the magnet pulls harder 
than upon No. #, because it is nearer and its pull there- 

FIG. 23. Tide-raising forces. 

fore more than balances the force exerted by the weight, 
so that No. 1 will be pulled away, from No. 2 and will 
stretch the elastic cords, which are represented by the 
lines joining 1 and #, until their tension, together with the 
force exerted by the weight, just balances the attraction 
of the magnet. For No. 8, the force exerted by the magnet 
is less than that of the weight, and it will also be pulled 
away from No. 2 until its elastic cords are stretched to the 
proper tension. The net result is that the three blocks 
which, without the magnet's influence, would be held close 
together by the elastic cords, are pulled apart by this out- 
side force as far as the resistance of the cords will permit. 
An entirely analogous set of forces produces a similar 
effect upon the shape of the moon. The elastic cords of 
Fig. 23 stand for the attraction of gravitation by which all 
the parts of the moon are bound together. The magnet 
represents the earth pulling with unequal force upon differ- 
ent parts of the moon. The weights are the inertia of the 
moon in its orbital motion which, as we have seen in a 



previous section, upon the whole just balances the earth's 
attraction and keeps the moon from falling into it. The 
effect of these forces is to stretch out the moon along a line 
pointing toward the earth, just as the blocks were stretched 
out along the line of the magnet, and to make this diam- 
eter of the moon slightly but permanently longer than 
the others. 

The tides. Similarly the moon and the sun attract op- 
posite sides of the earth with different forces and feebly 
tend to pull it out of shape. But here 
a new element comes into play : the 
earth turns so rapidly upon its axis 
that its solid parts have no time in 
which to yield sensibly to the strains, 
which shift rapidly from one diameter 
to another as different parts of the 
earth are turned toward the moon, and 
it is chiefly the waters of the sea which 
respond to the distorting effect of the 
sun's and moon's attraction. These are 
heaped up on opposite sides of the 
earth so as to produce a slight elonga- 
tion of its diameter, and Fig. 24 shows 
how by the earth's rotation this swell- 
ing of the waters is swept out from 
under the moon and is pulled back by 
the moon until it finally takes up some 
such position as that shown in the fig- 
ure where the effect of the earth's rota- 
tion in carrying it one way is just bal- 
anced by the moon's attraction urging 
it back on line with the moon. This heaping up of the 
waters is called a tide. If /in the figure represents a little 
island in the sea the waters which surround it will of 
course accompany it in its diurnal rotation about the 
earth's axis, but whenever the island comes back to the 

FIG. 24. The tides. 


position /, the waters will swell up as a part of the tidal 
wave and will encroach upon the land in what is called 
high tide or flood tide. So too when they reach 7", half a 
day later, they will again rise in flood tide, and midway 
between these points, at /', the waters must subside, giv- 
ing low or ebb tide. 

The height of the tide raised by the moon in the open 
sea is only a very few feet, and the tide raised by the sun is 
even less, but along the coast of a continent, in bays and 
angles of the shore, it often happens that a broad but low 
tidal wave is forced into a narrow corner, and then the rise 
of the water may be many feet, especially when the solar 
tide and the lunar tide come in together, as they do twice 
in every month, at new and full moon. Why do they come 
together at these times instead of some other ? 

Small as are these tidal effects, it is worth noting that 
they may in certain cases be very much greater e. g., if 
the moon were as massive as is the sun its tidal effect 
would be some millions of times greater than it now is and 
would suffice to grind the earth into fragments. Although 
the earth escapes this fate, some other bodies are not so 
fortunate, and we shall see in later chapters some evidence 
of their disintegration. 

43. The scope of the law of gravitation. In all the do- 
main of physical science there is no other law so famous as 
the Newtonian law of gravitation ; none other that has been 
so dwelt upon, studied, and elaborated by astronomers and 
mathematicians, and perhaps none that can be considered 
so indisputably proved. Over and over again mathemat- 
ical analysis, based upon this law, has pointed out conclu- 
sions which, though hitherto unsuspected, have afterward 
been found true, as when Newton himself derived as a corol- 
lary from this law that the earth ought to be flattened at 
the poles a thing not known at that time, and not proved 
by actual measurement until long afterward. It is, in fact, 
this capacity for predicting the unknown and for explain- 


ing in minutest detail the complicated phenomena of the 
heavens and the earth that constitutes the real proof of the 
law of gravitation, and it is therefore worth while to note 
that at the present time there are a very few points at 
which the law fails to furnish a satisfactory account of 
things observed. Chief among these is the case of the planet 
Mercury, the long diameter of whose orbit is slowly turning 
around in a way for which the law of gravitation as yet fur- 
nishes no explanation. Whether this is because the law itself 
is inaccurate or incomplete, or whether it only marks a case 
in which astronomers have not yet properly applied the 
law and traced out its consequences, we do not know ; but 
whether it be the one or the other, this and other simila-r 
cases show that even here, in its most perfect chapter, 
astronomy still remains an incomplete science. 



44. The size of the earth, The student is presumed to 
have learned, in his study of geography, that the earth is a 
globe about 8,000 miles in diameter and, without dwelling 
upon the " proofs " which are commonly given for these 
statements, we proceed to consider the principles upon 

which the measurement of 
the earth's size and shape 
are based. 

In Fig. 25 the circle rep- 
resents a meridian section 
of the earth ; P P' is the 
axis about which it rotates, 
and the dotted lines repre- 
sent a beam of light com- 
ing from a star in the plane 
of the meridian, and so dis- 
tant that the dotted lines 
are all practically parallel 

Pio. 25,-Measuring the size of the earth. ^ ^ ^^ ^ ^^ 

radii drawn through the points -/, #, #, represent the direc- 
tion of the vertical at these points, and the angles which 
these radii produced, make with the rays of starlight are 
each equal to the angular distance of the star from the 
zenith of the place at the moment the star crosses the me- 
ridian. We have already seen, in Chapter II, how these 
angles may be measured, and it is apparent from the figure 
that the difference between any two of these angles e. g., 


the angles at 1 and 2 is equal to the angle at the center, 
0, between the points 1 and 2. By measuring these angu- 
lar distances of the star from the zenith, the astronomer 
finds the angles at the center of the earth between the sta- 
tions 1, 2, 3, etc., at which his observations are made. If 
the meridian were a perfect circle the change of zenith dis- 
tance of the star, as one traveled along a meridian from the 
equator to the pole, would be perfectly uniform the same 
number of degrees for each hundred miles traveled and 
observations made in many parts of the earth show that 
this is very nearly true, but that, on the whole, as we ap- 
proach the pole it is necessary to travel a little greater dis- 
tance than is required for a given change in the angle at 
the equator. The earth is, in fact, flattened at the poles to 
the amount of about 27 miles in the length of its diameter, 
and by this -amount, as well as by smaller variations due to 
mountains and valleys, the shape of the earth differs from 
a perfect sphere. These astronomical measurements of the 
curvature of the earth's surface furnish by far the most sat- 
isfactory proof that it is very approximately a sphere, and 
furnish as its equatorial diameter 7,926 miles. 

Neglecting ths compression, as it is called, i. e., the 27 
miles by which the equatorial diameter exceeds the polar, 
the size of the earth may easily be found by measuring the 
distance 1 2 along the surface and by combining with this 
the angle 102 obtained through measuring the meridian 
altitudes of any star as seen from 1 and 2. Draw on paper 
an angle equal to the measured difference of altitude and 
find how far you must go from its vertex in order to have 
the distance between the sides, measured along an arc of 
a circle, equal to the measured distance between 1 and 2. 
This distance from the vertex will be the earth's radius. 

EXERCISE 19. Measure the diameter of the earth by 
the method given above. In order that this may be done 
satisfactorily, the two stations at which observations are 
made must be separated by a considerable distance i. e., 


200 miles. They need not be on the same meridian, but if 
they are on different meridians in place of the actual dis- 
tance between them, there must be used the projection of 
that distance upon the meridian i. e., the north and south 
part of the distance. 

By co-operation between schools in the Northern and 
Southern States, using a good map to obtain the required 
distances, the diameter of the earth 
may be measured with the plumb- 
line apparatus described in Chapter 
II and determined within a small 
percentage of its true value. 

45. The mass of the earth. We 
have seen in Chapter IV the possi- 
bility of determining the masses of 
the planets as fractional parts of 
the sun's mass, but nothing was 
there shown, or could be shown, 
about measuring these masses after 
the common fashion in kilogrammes 
or tons. To do this we must first 
get the mass of the earth in tons or 
kilogrammes, and while the princi- 
ples involved in this determination 
are simple enough, their actual ap- 
. 26. -illustrating the prin- plication is delicate and difficult. 

In Fig. 26 we suppose a long 
plumb line to be suspended above 
the surface of the earth and to be attracted toward the 
center of the earth, (7, by a force whose intensity is (Chap- 
ter IV) 


ciples involved in weighing 
the earth. 

where E denotes the mass of the earth, which is to be de- 
termined by experiment, and R is the radius of the earth, 
3,963 miles. If there is no disturbing influence present, 


the plumb line will point directly downward, but if a mas- 
sive ball of lead or other heavy substance is placed at one 
side, ^, it will attract the plumb line with a force equal to 

/ = k m ^ , 

where r is the distance of its center from the plumb bob 
and B is its mass which we may suppose, for illustration, 
to be a ton. In consequence of this attraction the plumb 
line will be pulled a little to one side, as shown by the dot- 
ted line, and if we represent by I the length of the plumb 
line and by d the distance between the original and the 
disturbed positions of the plumb bob we may write the pro- 

and introducing the values of F and / given above, and 
solving for J^the proportion thus transformed, we find 

T7T ~D v / -iV 

J]j =T } . . 

d \ T 

In this equation the mass of the ball, B, the length of the 
plumb line, I, the distance between the center of the ball 
and the center of the plumb bob, r, and the radius of the 
earth, R, can all be measured directly, and d, the amount 
by which the plumb bob is pulled to one side by the ball, is 
readily found by shifting the ball over to the other side, at 
2) and measuring with a microscope how far the plumb 
bob moves. This distance will, of course, be equal to 2 d. 

By methods involving these principles, but applied in a 
manner more complicated as well as more precise, the mass 
of the earth is found to be, in tons, 6,642 X 10 18 i. e., 6,642 
followed by 18 ciphers, or in kilogrammes 60,258 X 10 20 . 
The earth's atmosphere makes up about a millionth part 
of this mass. 

If the length of the plumb line were 100 feet, the 
weight of the ball a ton, and the distance between the two 


positions of the ball, 1 and #, six feet, how many inches, d, 
would the plumb bob be pulled out of place ? 

Find from the mass of the earth and the data of 40 
the mass of the sun in tons. Find also the mass of Mars. 
The computation can be very greatly abridged by the use 
of logarithms. 

46. Precession, That the earth is isolated in space and 
has no support upon which to rest, is sufficiently shown by 
the fact that the stars are visible upon every side of it, and 
no support can be seen stretching out toward them. We 
must then consider the earth to be a globe traveling freely 
about the sun in a circuit which it completes once every 
year, and rotating once in every twenty-four hours about 
an axis which remains at all seasons directed very nearly 
toward the star Polaris. The student should be able to 
show from his own observations of the sun that, with refer- 
ence to the stars, the direction of the sun from the earth 
changes about a degree a day. Does this prove that the 
earth revolves about the sun ? 

But it is only in appearance that the pole maintains its 
fixed position among the stars. If photographs are taken 
year after year, after the manner of Exercise 7, it will be 
found that slowly the pole is moving (nearly) toward Po- 
laris, and making this star describe a smaller and smaller 
circle in its diurnal path, while stars on the other side of 
the pole (in right ascension 12h.) become more distant 
from it and describe larger circles in their diurnal motion ; 
but the process takes place so slowly that the space of a 
lifetime is required for the motion of the pole to equal the 
angular diameter of the full moon. 

Spin a top and note how its rapid whirl about its axis 
corresponds to the earth's diurnal rotation. When the axis 
about which the top spins is truly vertical the top " sleeps " ; 
but if the axis is tipped ever so little away from the verti- 
cal it begins to wabble, so that if we imagine the axis pro- 
longed out to the sky and provided with a pencil point as 


a marker, this would trace a circle around the zenith, along 
which the pole of the top would move, and a little observa- 
tion will show that the more the top is tipped from the 
vertical the larger does this circle become and the more 
rapidly does the wabbling take place. Were it not for the 
spinning of the top about its axis, it would promptly fall 
over when tipped from the vertical position, but the spin 
combines with the force which pulls the top over and pro- 
duces the wabbling motion. Spin the top in opposite 
directions, with the hands of a watch and contrary to the 
hands of a watch, and note the effect which is produced 
upon the wabbling. 

The earth presents many points of resemblance to the 
top. Its diurnal rotation is the spin about the axis. This 
axis is tipped 23.5 away frojn the perpendicular to its 
orbit (obliquity of the ecliptic) just as the axis of the top 
is tipped away from the vertical line. In consequence of 
its rapid spin, the body of the earth bulges out at the equa- 
tor (27 miles), and the sun and moon, by virtue of their at- 
traction (see Chapter IV), lay hold of this protuberance and 
pull it down toward the plane of the earth's orbit, so that if 
it were not for the spin this force would straighten the axis 
up and set it perpendicular to the orbit plane. But here, as 
in the case of the top, the spin and the tipping force com- 
bine to produce a wabble which is called precession, and 
whose effect we recognize in the shifting position of the 
pole among the stars. The motion of precession is very 
much slower than the wabbling of the top, since the tip- 
ping force for the earth is relatively very small, and a pe- 
riod of nearly 26,000 years is required for a complete cir- 
cuit of the pole about its center of motion. Friction ulti- 
mately stops both the spin and the wabble of the top, but 
this influence seems wholly absent in the case of the earth, 
and both rotation and precession go on unchanged from 
century to century, save for certain minor forces which for 
a time change the direction or rate of the precessional 


motion, first in one way and then in another, without in 
the long run producing any results of consequence. 

The center of motion, about which the pole travels in a 
small circle having an angular radius of 23.5, is at that 
point of the heavens toward which a perpendicular to the 
plane of the earth's orbit points, and may be found on the 
star map in right ascension 18h. Om. and declination 66.5. 

EXERCISE 20. Find this point on the map, and draw 
as well as you can the path of the pole about it. The mo- 
tion of the pole along its path is toward the constellation 
Cepheus. Mark the position of the pole along this path 
at intervals of 1,000 years, and refer to these positions in 
dealing with some of the following questions : 

Does the wabbling of the top occur in the same direc- 
tion as the motion of precession ? Do the tipping forces 
applied to the earth and top act in the same direction ? 
What will be the polar star 12,000 years hence? The 
Great Pyramid of Egypt is thought to have been used 
as an observatory when Alpha Draconis was the bright star 
nearest the pole. How long ago was that ? 

The motion of the pole of course carries the equator 
and the equinoxes with it, and thus slowly changes the 
right ascensions and declinations of all the stars. On this 
account it is frequently called the precession of the equi- 
noxes, and this motion of the equinox, slow though it is, 
is a matter of some consequence in connection with chro- 
nology and the length of the year. 

Will the precession ever bring back the right ascen- 
sions and declinations to be again what they now are ? 

In what direction is the pole moving with respect to 
the Big Dipper ? Will its motion ever bring it exactly to 
Polaris ? How far away from Polaris will the precession 
carry the pole ? What other bright stars will be brought 
near the pole by the precession ? 

47. The warming of the earth. Winter and summer alike 
the day is on the average warmer than the night, and it is 


easy to see that this surplus of heat comes from the sun by 
day and is lost by night through radiation into the void 
which surrounds the earth ; just as the heat contained in a 
mass of molten iron is radiated away and the iron cooled 
when it is taken out from the furnace and placed amid 
colder surroundings. The earth's loss of heat by radiation 
goes on ceaselessly day and night, and were it not for the 
influx of solar heat this radiation would steadily diminish 
the temperature toward what is called the " absolute zero " 
i. e., a state in which all heat has been taken away and 
beyond which there can be no greater degree of cold. This 
must not be confounded with the zero temperatures shown 
by our thermometers, since it lies nearly 500 below the zero 
of the Fahrenheit scale (273 Centigrade), a temperature 
which by comparison makes the coldest winter weather 
seem warm, although the ordinary thermometer may regis- 
ter many degrees below its zero. The heat radiated by the 
sun into the surrounding space on every side of it is another 
example of the same cooling process, a hot body giving up 
its hea.t to the colder space about it, and it is the minute 
fraction of this heat poured out by the sun, and in small 
part intercepted by the earth, which warms the latter and 
produces what we call weather, climate, the seasons, etc. 

Observe the fluctuations, the ebb and flow, which are 
inherent in this process. From sunset to sunrise there is 
nothing to compensate the steady outflow of heat, and 
air and ground grow steadily colder, but with the sunrise 
there comes an influx of solar heat, feeble at first' because 
it strikes the earth's surface very obliquely, but becoming 
more and more efficient as the sun rises higher in the sky. 
But as the air and the ground grow warm during the morn- 
ing hours they part more and more readily and rapidly with 
their store of heat, just as a steam pipe or a cup of coffee 
radiates heat more rapidly when very hot. The warmest 
hour of the day is reached when these opposing tendencies 
of income and expenditure of heat are just balanced ; and 


barring such disturbing factors as wind and clouds, the gain 
in temperature usually extends to the time an hour or two 
beyond noon at which the diminishing altitude of the sun 
renders his rays less efficient, when radiation gains the 
upper hand and the temperature becomes for a short time 
stationary, and then commences to fall steadily until the 
next sunrise. 

We have here an example of what is called a periodic 
change i. e., one which, within a definite and uniform 
period (24 hours), oscillates from a minimum up to a 
maximum temperature and then back again to a minimum, 
repeating substantially the same variation day after day. 
But it must be understood that minor causes not taken 
into account above, such as winds, water, etc., produce 
other fluctuations from day to day which sometimes ob- 
scure or even obliterate the diurnal variation of tempera- 
ture caused by the sun. 

Expose the back of your hand to the sun, holding the 
hand in such a position that the sunlight strikes perpen- 
dicularly upon it; then turn the hand so that the light 
falls quite obliquely upon it and note how much more vig- 
orous is the warming effect of the sun in the first position 
than in the second. It is chiefly this difference of angle 
that makes the sun's warmth more effective when he is 
high up in the sky than when he is near the horizon, and 
more effective in summer than in winter. 

We have seen in Chapter III that the sun's motion 
among the stars takes place along a path which carries it 
alternately north and south of the equator to a distance 
of 23.5, and the stars show by their earlier risings and 
later settings, as we pass from the equator toward the 
north pole of the heavens, that as the sun moves north- 
ward from the equator, each day in the northern hemi- 
sphere will become a little longer, each night a little shorter, 
and every day the sun will rise higher toward the zenith 
until this process culminates toward the end of June, when 


the sun begins to move southward, bringing shorter days 
and smaller altitudes until the Christmas season, when 
again it is reversed and the sun moves northward. "We 
have here another periodic variation, which runs its com- 
plete course in a period of a year, and it is easy to see that 
this variation must have a marked effect on the warming 
of the earth, the long days and great altitudes of summer 
producing the greater warmth of that season, while the 
shorter days and lower altitudes of December, by diminish- 
ing the daily supply of solar heat, bring on the winter's 
cold. The succession of the seasons, winter following sum- 
mer and summer winter, is caused by the varying altitude 
of the sun, and this in turn is due to the obliquity of the 
ecliptic, or, what is the same thing, the amount by which 
the axis of the earth is tipped from being perpendicular to 
the plane of its orbit, and the seasons are simply a periodic 
change in the warming of the earth, quite comparable with 
the diurnal change but of longer period. 

It is evident that the period within which the succession 
of winter and summer is completed, the year, as we com- 
monly call it, must equal the time required by the sun to 
go from the vernal equinox around to the vernal equinox 
again, since this furnishes a complete cycle of the sun's 
motions north and south from the equator. On account 
of the westward motion of the equinox (precession) this 
is not quite the same as the time required for a com- 
plete revolution of the earth in its orbit, but is a little 
shorter (20m. 23s.), since the equinox moves back to meet 
the sun. 

48. Relation of the sun to climate, It is clear that both 
the northern and southern hemispheres of the earth must 
have substantially the same kind of seasons, since the mo- 
tion of the sun north and south affects both alike ; but 
when the sun is north of the equator and warming our 
hemisphere most effectively, his light falls more obliquely 
upon the other hemisphere, the days there are short and 


winter reigns at the time we are enjoying summer, while 
six months later the conditions are reversed. 

In those parts of the earth near the equator the torrid 
zone there is no such marked change from cold to warm 
as we experience, because, as the sun never gets more than 
23.5 away from the celestial equator, on every day of the 
year he mounts high in the tropic skies, always coming 
within 23.5 of the zenith, and usually closer than this, so 
that there is no such periodic change in the heat supply as 
is experienced in higher latitudes, and within the tropics 
the temperature is therefore both higher and more uniform 
than in our latitude. 

In the frigid zones, on the contrary, the sun never rises 
high in the sky ; at the poles his greatest altitude is only 
23.5, and during the winter season he does not rise at all, 
so that the temperature is here low the whole year round, 
and during the winter season, when for weeks or months at 
a time the supply of solar light is entirely cut off, the tem- 
perature falls to a degree unknown in more favored climes. 

If the obliquity of the ecliptic were made 10 greater, 
what would be the effect upon the seasons in the temperate 
zones ? What if it were made 10 less ? 

Does the precession of the equinoxes have any effect 
upon the seasons or upon the climate of different parts of 
the earth ? 

If the axis of the earth pointed toward Arcturus instead 
of Polaris, would the seasons be any different from what 
they are now ? 

49. The atmosphere. Although we live upon its surface, 
we are not outside the earth, but at the bottom of a sea of 
air which forms the earth's outermost layer and extends 
above our heads to a height of many miles. The study of 
most of the phenomena of the atmosphere belongs to that 
branch of physics called meteorology, but there are a few 
matters which fairly come within oar consideration of the 
earth as a planet. 


We can not see the stars save as we look through this 
atmosphere, and the light which comes through it is bent 
and oftentimes distorted so as to present serious obstacles 
to any accurate telescopic study of the heavenly bodies. 
Frequently this disturbance is visible to the naked eye, and 
the stars are said to twinkle i. e., to quiver and change 
color many times per second, solely in consequence of a dis- 
turbed condition of the air and not from anything which 
goes on in the star. This effect is more marked low down 
in the sky than near the zenith, and it is worth noting that 
the planets show very little of it because the light they 
send to the earth comes from a disk of sensible area, while 
a star, being much smaller and farther from the earth, has 
its disk reduced practically to a mere point whose light is 
more easily affected by local disturbances in the atmosphere 
than is the broader beam which comes from the planets' 

50. Refraction. At all times, whether the stars twinkle 
or not, their light is bent in its passage through the atmos- 
phere, so that the stars appear to stand higher up in the 
sky than their true positions. This effect, which the as- 
tronomer calls refraction, must be allowed for in observa- 
tions of the more precise class, although save at low alti- 
tudes its amount is a very small fraction of a degree, but 
near the horizon it is much exaggerated in amount and 
becomes easily visible to the naked eye by distorting the 
disks of the sun and moon from circles into ovals with 
their long diameters horizontal. The refraction lifts both 
upper and lower edge of the sun, but lifts the lower edge 
more than the upper, thus shortening the vertical diameter. 
See Fig. 27, which shows not only this effect, but also the 
reflection of the sun from the curved surface of the sea, 
still further flattening the image. If the surface of the 
water were flat, the reflected image would have the same 
shape as the sun's disk, and its altered appearance is some- 
times cited as a proof that the earth's surface is curved. 



The total amount of the refraction at the horizon is a 
little more than half a degree, and since the diameters of 
the sun and moon subtend an angle of about half a degree, 
we have the remarkable result that in reality the whole 


FIG. 2?. Flattening of the sun's disk by refraction and by reflection from the 
surface of the sea. 

disk of either sun or moon is below the horizon at the 
instant that the lower edge appears to touch the horizon 
and sunset or moonset begins. The same effect exists at 
sunrise, and as a consequence the duration of sunshine or 
of moonshine is on the average about six minutes longer 
each day than it would be if there were no atmosphere and 
no refraction. A partial offset to this benefit is found in 
the fact that the atmosphere absorbs the light of the heav- 
enly bodies, so that stars appear much less bright when 
near the horizon than when they are higher up in the sky, 
and by reason of this absorption the setting sun can be 
looked at with the naked eye without the discomfort which 
its dazzling luster causes at noon. 

51. The twilight. Another effect of the atmosphere, 
even more marked than the preceding, is the twilight. As 


at sunrise the mountain top catches the rays of the coming 
sun before they reach the lowland, and at sunset it keeps 
them after they have faded from the regions below, so the 
particles of dust and vapor, which always float in the atmos- 
phere, catch the sunlight and reflect it to the surface of the 
earth while the sun is still below the horizon, giving at the 
beginning and end of day that vague and diffuse light which 
we call twilight. 

Fig. 28 shows a part of the earth surrounded by such a 
dust-laden atmosphere, which is illuminated on the left by 
the rays of the sun, but which, on the right of the figure, 
lies in the shadow cast 
by the earth. To an 
observer placed at 1 the 
sun is just setting, and 
all the atmosphere 
above 'him is illumined 
with its rays, which 

furnish a bright twi- FIG. 28.-Twilight phenomena. 

light. When, by the earth's rotation, this observer has been 
carried to #, all the region to the east of his zenith lies in 
the shadow, while to the west there is a part of the atmos- 
phere from which there still comes a twilight, but now com- 
paratively faint, because the lower part of the atmosphere 
about our observer lies in the shadow, and it is mainly 
its upper regions from which the light comes, and here the 
dust and moisture are much less abundant than in the lower 
strata. Still later, when the observer has been carried by the 
earth's rotation to the point 3, every vestige of twilight will 
have vanished from his sky, because all of the illuminated 
part of the atmosphere is now below his horizon, which is 
represented by the line 8 L. In the figure the sun is rep- 
resented to be 78 below this horizon line at the end of twi- 
light, but this is a gross exaggeration, made for the sake of 
clearness in the drawing in fact, twilight is usually said 
to end when the sun is 18 below the horizon. 


Let the student redraw Fig. 28 on a large scale, so that 
the points 1 and 2 shall be only 18 apart, as seen from the 
earth's center. He will find that the point L is brought 
down much closer to the surface of the earth, and measur- 
ing the length of the line 2 L, he should find for the " height 
of the atmosphere " about one-eightieth part of the radius 
of the earth i. e., a little less than 50 miles. This, how- 
ever, is not the true height of the atmosphere. The air 
extends far beyond this, but the particles of dust and vapor 
which are capable of sending sunlight down to the earth 
seem all to lie below this limit. 

The student should not fail to watch the eastern sky 
after sunset, and see the shadow of the earth rise up and 
fill it while the twilight arch retreats steadily toward the 

Duration of tivilight. Since twilight ends when the sun 
is 18 below the horizon, any circumstance which makes 

FIG. 29. The cause of long and short twilights. 

the sun go down rapidly will shorten the duration of twi- 
light, and anything which retards the downward motion 
of the sun will correspondingly prolong it. Chief among 
influences of this kind is the angle which the sun's course 
makes with the horizon. If it goes straight down, as at 
a, Fig. 29, a much shorter time will suffice to carry it to 
a depression of 18 than is needed in the case shown at 
I in the same figure, where the motion is very oblique to 
the horizon. If we consider different latitudes and differ- 
ent seasons of the year, we shall find every possible variety 


of circumstance from a to #, and corresponding to these, 
the duration of twilight varies from an all-night duration 
in the summers of Scotland and more northern lands to a 
half hour or less in the mountains of Peru. 

Coleridge does not much exaggerate the shortness of 
tropical twilight in the lines, 

" The sun's rim dips ; the stars rush out : 
At one stride comes the dark." 

The, Ancient Mariner. 

In the United States the longest twilights come at the 
end of June, and last for a little more than two hours, 
while the shortest ones are in March and September, 
amounting to a little more than an hour and a half ; but 
at all times the last half hour of twilight is hardly to be 
distinguished from night, so small is the quantity of re- 
flecting matter in the upper regions of the atmosphere. 
For practical convenience it is customary to assume in 
the courts of law that twilight ends an hour after sunset. 

How long does twilight last at the north pole ? 

The Aurora. One other phenomenon of the atmos- 
phere may be mentioned, only to point out that it is not 
of an astronomical character. The Aurora, or northern 
lights, is as purely an affair of the earth as is a thunder- 
storm, and its explanation belongs to the subject of ter- 
restrial magnetism. 



52. Solar time. To measure any quantity we need a unit 
in terms of which it must be expressed. Angles are meas- 
ured in degrees, and the degree is the unit for angular meas- 
urement. For most scientific purposes the centimeter is 
adopted as the unit with which to measure distances, and 
similarly a day is the fundamental unit for the measure- 
ment of time. Hours, minutes, and seconds are aliquot 
parts of this unit convenient for use in dealing with shorter 
periods than a day, and the week, month, and year which 
we use in our calendars are multiples of the day. 

Strictly speaking, a day is not the time required by the 
earth to make one revolution upon its axis, but it is best 
defined as the amount of time required for a particular part 
of the sky to make the complete circuit from the meridian 
of a particular place through west and east back to the 
meridian again. The day begins at the moment when this 
specified part of the sky is on the meridian, and " the time " 
at any moment is the hour angle of this particular part of 
the sky i. e., the number of hours, minutes, etc., tha have 
elapsed since it was on the meridian. 

The student has already become familiar with the kind 
of day which is based upon the motion of the vernal equi- 
nox, and which furnishes sidereal time, and he has seen 
that sidereal time, while very convenient in dealing with 
the motions of the stars, is decidedly inconvenient for the 
ordinary affairs of life since in the reckoning of the hours 
it takes no account of daylight and darkness. One can not 


tell off-hand whether 10 hours, sidereal time, falls in the day 
or in the night. We must in some way obtain a day and a 
system of time reckoning based upon the apparent diurnal 
motion of the sun, and we may, if we choose, take the sun 
itself as the point in the heavens whose transit over the 
meridian shall mark the beginning and the end of the day. 
In this system " the time " is the number of hours, minutes, 
etc., which have elapsed since the sun was on the meridian, 
and this is the kind of time which is shown by a sun dial, 
and which was in general use, years ago, before clocks and 
watches became common. Since the sun moves among the 
stars about a degree per day, it is easily seen that the rotat- 
ing earth will have to turn farther in order to carry any 
particular meridian from the sun around to the sun again, 
than to carry it from a star around to the same star, or 
from the vernal equinox around to the vernal equinox 
again; just as the minute hand of a clock turns farther 
in going from the hour hand round to the hour hand again 
than it turns in going from XII to XII. These solar days 
and hours and minutes are therefore a little longer than 
the corresponding sidereal ones, and this furnishes the ex- 
planation why the stars come to the meridian a little ear- 
lier, by solar time, every night than on the night before, and 
why sidereal time gains steadily upon solar time, this gain 
amounting to approximately 3m. 56.5s. per day, or exactly 
one day per year, since the sun makes the complete circuit 
of the constellations once in a year. 

With the general introduction of clocks and watches 
into use about a century ago this kind of solar time went 
out of common use, since no well-regulated clock could 
keep the time correctly. The earth in its orbital motion 
around the sun goes faster in some parts of its orbit than 
in others, and in consequence the sun appears to move 
more rapidly among the stars in winter than in summer ; 
moreover, on account of the convergence of hour circles 
as we go away from the equator, the same amount of mo- 


tion along the ecliptic produces more effect in winter and 
summer when the sun is north or south, than it does in the 
spring and autumn when the sun is near the equator, and 
as a combined result of these causes and other minor ones 
true solar time, as it is called, is itself not uniform, but 
falls behind the uniform lapse of sidereal time at a variable 
rate, sometimes quicker, sometimes slower. A true solar 
day, from noon to noon, is 51 seconds linger in September 
than in December. 

53. Mean solar time. To remedy these inconveniences 
there has been invented and brought into common use 



















* X 











n.f Fcb.i Ma 

r.t Apr.fMa 

V 1 Jin 

e 1 Jv 

y 1 Ji, 

g.ffept.f Oc 

t.1 Nor.f DC 

c.i Jaw./ 

FIG. 30. The equation of time. 

what is called mean solar time, which is perfectly uniform 
in its lapse and which, by comparison with sidereal time, 
loses exactly one day per year. " The time " in this system 
never differs much from true solar time, and the difference 
between the two for any particular day may be found in 
any good almanac, or may be read from the curve in Fig. 
30, in which the part of the curve above the line marked 
Om shows how many minutes mean solar time is faster than 
true solar time. The correct name for this difference be- 
tween the two kinds of solar time is the equation of time, but 
in the almanacs it is frequently marked " sun fast " or " sun 
slow." In sidereal time and true solar time the distinction 


between A. M. hours (ante meridiem = before the sun reaches 
the meridian) and p. M. hours (post meridiem = after the 
sun has passed the meridian) is not observed, " the time " 
being counted from hours to 24 hours, commencing when 
the sun or vernal equinox is on the meridian. Occasion- 
ally the attempt is made to introduce into common use 
this mode of reckoning the hours, beginning the day 
(date) at midnight and counting the hours consecutively 
up to 24, when the next date is reached and a new start 
made. Such a system would simplify railway time tables 
and similar publications ; but the American public is slow 
to adopt it, although the system has come into practical 
use in Canada and Spain. 

54. To find (approximately) the sidereal time at any mo- 
ment. RULE I. When the mean solar time is known. Let 
W represent the time shown by an ordinary watch, and 
represent by S the corresponding sidereal time and by D 
the number of days that have elapsed from March 23d to 
the date in question. Then 

S= W+ftxDX*. 

The last term is expressed in minutes, and should be re- 
duced to hours and minutes. Thus at 4 p. M. on July 4th 

D = 103 days. 
f J X D X 4 = 406m. 

= 6h. 46m. 
W=4h. Om. 


The daily gain of sidereal upon mean solar time is f- of 4 
minutes, and March 23d is the date on which sidereal and 
mean solar time are together, taking the average of one year 
with another, but it varies a little from year to year on 
account of the extra day introduced in leap years. 

RULE II. When the stars in the northern sky can be 
seen. Find (3 Cassiopeiae, and imagine a line drawn from it 


to Polaris, and another line from Polaris to the zenith. 
The sidereal time is equal to the angle between these lines, 
provided that that angle must be measured from the zenith 
toward the west Turn the angle from degrees into hours 
by dividing by 15. 

55. The earth's rotation. We are familiar with the fact 
that a watch may run faster at one time than at another, 
and it is worth while to inquire if the same is not true of 
our chief timepiece the earth. It is assumed in the sec- 
tions upon the measurement of time that the earth turns 
about its axis with absolute uniformity, so that mean solar 
time never gains or loses even the smallest fraction of a 
second. Whether this be absolutely true or not, no one has 
ever succeeded in finding convincing proof of a variation 
large enough to be measured, although it has recently been 
shown that the axis about which it rotates is not perfectly 
fixed within the body of the earth. The solid body of the 
earth wriggles about this axis like a fish upon a hook, so 
that the position of the north pole upon the earth's sur- 
face changes within a year to the extent of 40 or 50 feet 
(15 meters) without ever getting more than this distance 
away from its average position. This is probably caused 
by the periodical shifting of masses of air and water from 
one part of the earth to another as the seasons change, 
and it seems probable that these changes will produce 
some small effect upon the rotation of the earth. But in 
spite of these, for any such moderate interval of time as a 
year or a century, so far as present knowledge goes, we may 
regard the earth's rotation as uniform and undisturbed. 
For longer intervals e. g., 1,000,000 or 10,000,000 years 
the question is a very different one, and we shall have to 
meet it again in another connection. 

56. Longitude and time. In what precedes there has 
been constant reference to the meridian. The day begins 
when the sun is on the meridian. Solar time is the angu- 
lar distance of the sun past the meridian. Sidereal time 



FIG. 31. Longitude and time. 

was determined by observing transits of stars over a me- 
ridian line actually laid out upon the ground, etc. But 
every place upon the earth has its own meridian from 
which " the time " may be reckoned, and in Fig. 31, where 
the rays of sunlight 
are represented as 
falling upon a part 
of the earth's equa- 
tor through which 
the meridians o1 
New York, Chicago, 
and San Francisco 
pass, it is evident 
that these rays make 
different angles with 
the meridians, and 
that the sun is farther from the meridian of New York; 
than from that of San Francisco by an amount just equal 
to the angle at between these meridians. This angle is 
called by geographers the difference of longitude between 
the two places, and the student should note that the word 
longitude is here used in a different sense from that on 
page 36. From Fig. 31 we obtain the 

Theorem. The difference between " the times " at any 
two meridians is equal to their difference of longitude, and 
the time at the eastern meridian is greater than at the 
western meridian. Astronomers usually express differences 
of longitude in hours instead of degrees. Ih. = 15. 

The name given to any kind of time should distinguish 
all the elements which enter into it e. g., New York 
sidereal time means the hour angle of the vernal equinox 
measured from the meridian of New York, Chicago true 
solar time is the hour angle of the sun reckoned from the 
meridian of Chicago, etc. 

57. Standard time. The requirements of railroad traffic 
have led to the use throughout the United States and 


Canada of four " standard times," each of which is a mean 
solar time some integral number of hours slower than the 
time of the meridian passing through the Royal Observa- 
tory at Greenwich, England. 

Eastern time is 5 hours slower than that of Greenwich. 
Central " 6 " 
Mountain " 7 " 
Pacific " 8 " 

In Fig. 32 the broken lines indicate roughly the parts of 
the United States and Canada in which these several kinds 
of time are used, and illustrate how irregular are the bound- 
aries of these parts. 

Standard time is sent daily into all of the more impor- 
tant telegraph offices of the United States, and serves to 
regulate watches and clocks, to the almost complete exclu- 
sion of local time. 

58. To determine the longitude. With an ordinary watch 
observe the time of the sun's transit over your local me- 
ridian, and correct the observed time for the equation of 
time by means of the curve in Fig. 30. The difference 
between the corrected time and 12 o'clock will be the cor- 
rection of your watch referred to local mean solar time. 
Compare your watch with the time signals in the nearest 
telegraph office and find its correction referred to standard 
time. The difference between the two corrections is the 
difference between your longitude and that of the standard 

X. B. Don't tamper with the watch by trying to " set it 
right." No harm will be done if it is wrong, provided you 
take due account of the correction as indicated above. 

If the correction of the watch changed between your 
observation and the comparison in the telegraph office, 
what effect would it have upon the longitude determina- 
tion ? How can you avoid this effect ? 

59. Chronology, The Century Dictionary defines chro- 
nology as " the science of time " that is, " the method of 


measuring or computing time by regular divisions or pe- 
riods according to the revolutions of the sun or moon." 

We have already seen that for the measurement of short 
intervals of time the day and its subdivisions hours, 
minutes, seconds furnish a very complete and convenient 
system. But for longer periods, extending to hundreds and 
thousands of days, a larger unit of time is required, and for 
the most part these longer units have in all ages and among 
all peoples been based upon astronomical considerations. 
But to this there is one marked exception. The week is a 
simple multiple of the day, as the dime is a multiple of the 
cent, and while it may have had its origin in the changing 
phases of the moon this is at best doubtful, since it does 
not follow these with any considerable accuracy. If the 
still longer units of time the month and the year had 
equally been made to consist of an integral number of days 
much confusion and misunderstanding might have been 
avoided, and the annals of ancient times would have pre- 
sented fewer pitfalls to the historian than is now the case. 
The month is plainly connected with the motion of the 
moon among the stars. The year is, of course, based upon 
the motion of the sun through the heavens and the change 
of seasons which is thus produced ; although, as commonly 
employed, it is not quite the same as the time required by 
the earth to make one complete revolution in its orbit. 
This time of one revolution is called a sidereal year, while, 
as we have already seen in Chapter V, the year which 
measures the course of the seasons is shorter than this on 
account of the precession of the equinoxes. It is called a 
tropical year with reference to the circuit which the sun 
makes from one tropic to the other and back again. 

We can readily understand why primitive peoples should 
adopt as units of time these natural periods, but in so 
doing they incurred much the same kind of difficulty that 
we should experience in trying to use both English and 
American money in the ordinary transactions of life. How 


many dollars make a pound sterling ? How shall we make 
change with English shillings and American dimes, etc. ? 
How much is one unit worth in terms of the other ? 

One of the Greek poets * has left us a quaint account of 
the confusion which existed in his time with regard to the* 
place of months and moons in the calendar : 

" The moon by us to you her greeting sends, 
But bids us say that she's an ill-used moon 
And takes it much amiss that you will still 
Shuffle her days and turn them topsy-turvy, 
So that when gods, who know their feast days well, 
By your false count are sent home supperless, 
They scold and storm at her for your neglect." 

60. Day, month, and year. If the day, the month, and 
the year are to be used concurrently, it is necessary to 
determine how many days are contained in the month and 
year, and when this has been done by the astronomer the 
numbers are found to be very awkward and inconvenient 
for daily use ; and much of the history of chronology 
consists in an account of the various devices by which in- 
genious men have sought to use integral numbers to replace 
the cumbrous decimal fractions which follow. 

According to Professor Harkness, for the epoch 1900 
A. D. 

One tropical year = 365.242197 mean solar days. 

" = 365d. 5h. 48m. 45.8s. 
One lunation = 29.530588 mean solar days. 
= 29d. 12h. 44m. 2.8s. 

The word lunation means the average interval from one 
new moon to the next one i. e., the time required by the 
moon to go from conjunction with the sun round to con- 
junction again. 

A very ancient device was to call a year equal to 365 

* Aristophanes, The Clouds, WhewelPs translation. 


days, and to have months alternately of 29 and 30 days in 
length, but this was unsatisfactory in more than, one way. 
At the end of four years this artificial calendar would be 
about one day ahead of the true one, at the end of forty 
years ten days in error, and within a single lifetime the 
seasons would have appreciably changed their position in 
the year, April weather being due in March, according to 
the calendar. So, too, the year under this arrangement 
did not consist of any integral number of months, 12 
months of the average length of 29.5 days being 354 days, 
and 13 months 383.5 days, thus making any particular 
month change its position from the beginning to the mid- 
dle and the end of the year within a comparatively short 
time. Some peoples gave up the astronomical year as an 
independent unit and adopted a conventional year of 12 
lunar months, 354 days, which is now in use in certain 
Mohammedan countries, where it is known as the wander- 
ing year, with reference to the changing positions of the 
seasons in such a year. Others held to the astronomical 
year and adopted a system of conventional months, such 
that twelve of them would just make up a year, as is done 
to this day in our own calendar, whose months of arbitrary 
length we are compelled to remember by some such jingle 
as the following : 

" Thirty days hath September, 
April, June, and November ; 
All the rest have thirty-one 
Save February, 

Which alone hath twenty-eight, 
Till leap year gives it twenty-nine." 

61. The calendar. The foundations of our calendar may 
fairly be ascribed to Julius Caesar, who, under the advice 
of the Egyptian astronomer Sosigines, adopted the old 
Egyptian device of a leap year, whereby every fourth year 
was to consist of 366 days, while ordinary years were only 
365 days long. He also placed the beginning of the year 


at the first of January, instead of in March, where it had 
formerly been, and gave his own name, Julius, to the month 
which we now call July. August was afterward named in 
honor of his successor^ Augustus. The names of the earlier 
months of the year are drawn from Eoman mythology; 
those of the later months, September, October, etc., mean- 
ing seventh month, eighth month, represent the places of 
these months in the year, before Caesar's reformation, and 
also their places in some of the subsequent calendars, for 
the widest diversity of practice existed during mediaeval 
times with regard to the day on which -the new year should 
begin, Christmas, Easter, March 25th, and others having been 
employed at different times and places. 

The system of leap years introduced by Caesar makes 
the average length of a year 365.25 days, which differs by 
about eleven minutes from the true length of the tropical 
year, a difference so small that for ordinary purposes no 
better approximation to the true length of the year need 
be desired. But any deviation from the true length, how- 
ever small, must in the course of time shift the seasons, the 
vernal and autumnal equinox, to another part of the year, 
and the ecclesiastical authorities of mediaeval Europe found 
here ground for objection to Caesar's calendar, since the 
great Church festival of Easter has its date determined 
with reference to the vernal equinox, and with the lapse of 
centuries Easter became more and more displaced in the 
calendar, until Pope Gregory XIII, late in the sixteenth 
century, decreed another reformation, whereby ten days 
were dropped from the calendar, the day after March llth 
being called March 21st, to bring back the vernal equinox 
to the date on which it fell in A. D. 325, the time of the 
Council of Nicaea, which Gregory adopted as the funda- 
mental epoch of his calendar. 

The calendar having thus been brought back into agree- 
ment with that of old time, Gregory purposed to keep it in 
such agreement for the future by modifying Caesar's leap- 


year rule so that it should run : Every year whose number 
is divisible by 4 shall be a leap year except those years 
whose numbers are divisible by 100 but not divisible by 
400. These latter years e. g., 1900 are counted as com- 
mon years. The calendar thus altered is called Gregorian 
to distinguish it from the older, Julian calendar, and it 
found speedy acceptance in those civilized countries whose 
Church adhered to Rome ; but the Protestant powers were 
slow to adopt it, and it was introduced into England and 
her American colonies by act of Parliament in the year 
1752, nearly two centuries after Gregory's time. In Rus- 
sia the Julian calendar has remained in common use to 
our own day, but in commercial affairs it is there cus- 
tomary to write the date according to both calendars 
e. g., July T \, and at the present time strenuous exertions 
are making in that country for the adoption of the Gre- 
gorian calendar to the complete exclusion of the Julian 

The Julian and Gregorian calendars are frequently rep- 
resented by the abbreviations 0. S. and N". S., old style, 
new style, and as the older historical dates are usually ex- 
pressed in 0. S., it is sometimes convenient to transform a 
date from the one calendar to the other. This is readily 
done by the formula 

= ./+(.- 2) -J 

where G and J are the respective dates, N is the number 
of the century, and the remainder is to be neglected in the 
division by 4. For September 3, 1752, 0. S., we have 

,7= Sept. 3 

N-2 = +15 

G = Sept. 14 


and September 14 is the date fixed by act of Parliament to 
correspond to September 3, 1752, 0. S. Columbus discovered 
America on October 12, 1492, 0. S. What is the corre- 
sponding date in the Gregorian calendar ? 

62. The day of the week, A problem similar to the 
above but more complicated consists in finding the day of 
the week on which any given date of the Gregorian cal- 
endar falls e. g., October 21, 1492. 

The formula for this case is 

Y-l Y-l Y-l 

where Y denotes the given year, D the number of the day 
(date) in that year, and q and r are respectively the quo- 
tient and the remainder obtained by dividing the second 
member of the equation by 7. If r 1 the date falls on 
Sunday, etc., and if r = the day is Saturday. For the 
example suggested above we have 

Jan. 31 Y = 1492 

Feb. 29 -\-D +295 

Mch. 31 +(;r_i)_- 4= + 373 

April 30 - ( r - 1) -^ 100 = 14 

May 31 + (Y 1) -f- 400 = + 3 

June 30 ~*j~^L48 

July 31 

Aug. 31 0= 306 

Sept. 30 r = 6 = Friday. 

Oct. 21 

Find from some history the day of the week on which 
Columbus first saw America, and compare this with the 

On what day of the week did last Christmas fall ? On 
what day of the week were you born ? In the formula for 
the day of the week why does q have the coefficient 7 ? 


What principles in the calendar give rise to the divisors 4, 

For much curious and interesting information about 
methods of reckoning the lapse of time the student may 
consult the articles Calendar and Chronology in any good 



63. The nature of eclipses. Every planet has a shadow 
which travels with the planet along its orbit, always point- 
ing directly away from the sun, and cutting off from a cer- 
tain region of space the sunlight which otherwise would fill 
it. For the most part these shadows are invisible, but occa- 
sionally one of them falls upon a planet or some other body 
which shines by reflected sunlight, and, cutting off its sup- 
ply of light, produces the striking phenomenon which we 
call an eclipse. The satellites of Jupiter, Saturn, and Mars 
are eclipsed whenever they plunge into the shadows cast by 
their respective planets, and Jupiter himself is partially 
eclipsed when one of his own satellites passes between him 
and the sun, and casts upon his broad surface a shadow too 
small to cover more than a fraction of it. 

But the eclipses of most interest to us are those of the 
sun and moon, called respectively solar and lunar eclipses. 
In Fig. 33 the full moon, M' , is shown immersed in the 
shadow cast by the earth, and therefore eclipsed, and in the 
same figure the new moon, Jf, is shown as casting its shadow 
upon the earth and producing an eclipse of the sun. From 
a mere inspection of the figure we may learn that an eclipse 
of the sun can occur only at new moon i. e., when the 
moon is on line between the earth and sun and an eclipse 
of the moon can occur only at full moon. Why ? Also, the 
eclipsed moon, M' , will present substantially the same ap- 
pearance from every part of the earth where it is at all vis- 
ible the same from North America as from South Amer- 



, ica but the eclipsed sun will present very 
.different aspects from different parts of 
the earth. Thus, at L, within the moon's 
shadow, the sunlight will be entirely cut 
off, producing what is called a total eclipse. 
At points of the earth's surface near J and 
K there will be no interference whatever 
with the sunlight, and no eclipse, since the 
moon is quite off the line joining these re- 
gions to any part of the sun. At places be- 
tween J and L or K and L the moon will 
cut off a part of the sun's light, but not all 
of it, and will produce what is called a par- 
\ tial eclipse, which, as seen from the north- 
i ern parts of the earth, will be an eclipse of 
the lower (southern) part of the sun, and 
as seen from the southern hemisphere will 
be an eclipse of the northern part of the 


The moon revolves around the earth in 
a plane, which, in the figure, we suppose to 
be perpendicular to the surface of the pa- 
per, and to pass through the sun along the 
line M' M produced. But it frequently 
happens that this plane is turned to one 
side of the sun, along some such line as 
P Q, and in this case the full moon would 
cut through the edge of the earth's shadow 
without being at any time wholly immersed 
in it, giving a partial eclipse of the moon, 
as is shown in the figure. 

In what parts of the earth would this 
eclipse be visible? What kinds of solar 
eclipse would be produced by the new moon 
at Q? In what parts of the earth would 
they be visible ? 


64. The shadow cone. The shape and position of the 
earth's shadow are indicated in Fig. 33 by the lines drawn 
tangent to the circles which represent the sun and earth, 
since it is only between these lines that the earth interferes 
with the free radiation of sunlight, and since both sun and 
earth are spheres, and the earth is much the smaller of the 
two, it is evident that the earth's shadow must be, in geo- 
metrical language, a cone whose base is at the earth, and 
whose vertex lies far to the right of the figure in other 
words, the earth's shadow, although very long, tapers off 
finally to a point and ends. So, too, the shadow of the 
moon is a cone, having its base at the moon and its vertex 
turned away from the sun, and, as shown in the figure, just 
about long enough to reach the earth. 

It is easily shown, by the theorem of similar triangles in 
connection with the known size of the earth and sun, that 
the distance from the center of the earth to the vertex of 
its shadow is always equal to the distance of the earth from 
the sun divided by 108, and, similarly, that the length of 
the moon's shadow is equal to the distance of the moon 
from the sun divided by 400, the moon's shadow being the 
smaller and shorter of the two, because the moon is smallei 
than the earth. The radius of the moon's orbit is just about 
T th part of the radius of the earth's orbit i. e., the dis- 
tance of the moon from the earth is i^th part of the dis- 
tance of the earth from the sun, and it is this " chance " 
agreement between the length of the moon's shadow and 
the distance of the moon from the earth which makes the 
tip of the moon's shadow fall very near the earth at the 
time of solar eclipses. Indeed, the elliptical shape of the 
moon's orbit produces considerable variations in the dis- 
tance of the moon from the earth, and in consequence of 
these variations the vertex of the shadow sometimes falls 
short of reaching the earth, and sometimes even projects 
considerably beyond its farther side. When the moon's 
distance is too great for the shadow to bridge the space be- 


tween earth and moon there can be no total eclipse of the 
sun, for there is no shadow which can fall upon the earth, 
even though the moon does come directly between earth 
and sun. But there is then produced a peculiar kind of 
partial eclipse called annular, or ring-shaped, because the 
moon, although eclipsing the central parts of the sun, is 
not large enough to cover the whole of it, but leaves the 
sun's edge visible as a ring of light, which completely sur- 
rounds the moon. Although, strictly speaking, this is only 
a partial eclipse, it is customary to put total and annular 
eclipses together in one class, which is called central eclipses, 
since in these eclipses the line of centers of sun and moon 
strikes the earth, while in ordinary partial eclipses it passes 
to one side of the earth without striking it. In this latter 
case we have to consider another cone called the penumbra 
i. e., partial shadow which is shown in Fig. 33 by the 
broken lines tangent to the sun and moon, and crossing at 
the point F, which is the vertex of this cone. This penum- 
bral cone includes within its surface all that region of space 
within which the moon cuts off any of the sunlight, and 
of course it includes the shadow cone which produces total 
eclipses. Wherever the penumbra falls there will be a solar 
eclipse of some kind, and the nearer the place is to the axis 
of the penumbra, the more nearly total will be the eclipse. 
Since the moon stands about midway between the earth and 
the vertex of the penumbra, the diameter of the penumbra 
where it strikes the earth will be about twice as great as 
the diameter of the moon, and the student should be able 
to show from this that the region of the earth's surface 
within which a partial solar eclipse is visible extends in a 
straight line about 2,100 miles on either side of the region 
where the eclipse is total. Measured along the curved 
surface of the earth, this distance is frequently much 

Is it true that if at any time the axis of the shadow cone 
comes within 2,100 miles of the earth's surface a partial 


eclipse will be visible in those parts of the earth nearest the 
axis of the shadow ? 

65. Different characteristics of lunar and solar eclipses. 
One marked difference between lunar and solar eclipses 
which has been already suggested, may be learned from Fig. 
33. The full moon, M' , will be seen eclipsed from every 
part of the earth where it is visible at all at the time of the 
eclipse that is, from the whole night side of the earth ; 
while the eclipsed sun will be seen eclipsed only from those 
parts of the day side of the earth upon which the moon's 
shadow or penumbra falls. Since the point of the shadow 
at best but little more than reaches to the earth, the 
amount of space upon the earth which it can cover at any 
one moment is very small, seldom more than 100 to 200 
miles in length, and it is only within the space thus ac- 
tually covered by the shadow that the sun is at any given 
moment totally eclipsed, but within this region the sun 
disappears, absolutely, behind the solid body of the moon, 
leaving to view only such outlying parts and appendages as 
are too large for the moon to cover. At a lunar eclipse, on 
the other hand, the earth coming between sun and moon 
cuts off the light from the latter, but, curiously enough, 
does not cut it off so completely that the moon disappears 
altogether from sight even in mid-eclipse. The explana- 
tion of this continued visibility is furnished by the broken 
lines extending, in Fig. 33, from the earth through the 
moon. These represent sunlight, which, entering the 
earth's atmosphere near the edge of the earth (edge as seen 
from sun and moon), passes through it and emerges in a 
changed direction, refracted, into the shadow cone and 
feebly illumines the moon's surface with a ruddy light like 
that often shown in our red sunsets. Eclipse and sunset 
alike show that when the sun's light shines through dense 
layers of air it is the red rays which come through most 
freely, and the attentive observer may often see at a clear 
sunset something which corresponds exactly to the bending 


of the sunlight into the shadow cone ; just before the sun 
reaches the horizon its disk is distorted from a circle into 
an oval whose horizontal diameter is longer than the verti- 
cal one (see 49). 

QUERY. At a total lunar eclipse what would be the 
effect upon the appearance of the moon if the atmosphere 
around the edge of the earth were heavily laden with 
clouds ? 

66. The track of the shadow. We may regard the moon's 
shadow cone as a huge pencil attached to the moon, mov- 
ing with it along its orbit in the direction of the arrow- 
head (Fig. 34), and as it moves drawing a black line across 
the face of the earth at the time of total eclipse. This black 
line is the path of the shadow and marks out those regions 
within which the eclipse will be total at some stage of its 
progress. If the point of the shadow just reaches the 
earth its trace will have no sensible width, while, if the 
moon is nearer, the point of the cone will be broken off, 
and, like a blunt pencil, it will draw a broad streak across 
the earth, and this under the most favorable circumstances 
may have a breadth of a little more than 160 miles and a 
length of 10,000 or 12,000 miles. The student should 
be able to show from the known distance of the moon 
(240,000 miles) and the known interval between consecutive 
new moons (29.5 days) that on the average the moon's 
shadow sweeps past the earth at the rate of 2,100 miles per 
hour, and that in a general way this motion is from west 
to east, since that is the direction of the moon's motion in 
its orbit. The actual velocity with which the moon's shadow 
moves past a given station may, however, be considerably 
greater or less than this, since on the one hand when the 
shadow falls very obliquely, as when the eclipse occurs near 
sunrise or sunset, the shifting of the shadow will be very 
much greater than the actual motion of the moon which 
produces it, and on the other hand the earth in revolving 
upon its axis carries the spectator and the ground upon 


which he stands along the same direction in which the 
shadow is moving. At the equator, with the sun and moon 
overhead, this motion of the earth subtracts about 1,000 
miles per hour from the velocity with which the shadow 
passes by. It is chiefly on this account, the diminished 
velocity with which the shadow passes by, that total solar 
eclipses last longer in the tropics than in higher latitudes, 
but even under the most favorable circumstances the dura- 
tion of totality does not reach eight minutes at any one 
place, although it may take the shadow several hours to 
sweep the entire length of its path across the earth. 

According to Whitmell the greatest possible duration of 
a total solar eclipse is 7m. 40s., and it can attain this limit 
only when the eclipse occurs near the beginning of July 
and is visible at a place 5 north of the equator. 

The duration of a lunar eclipse depends mainly upon 
the position of the moon with respect to the earth's shadow. 
If it strikes the shadow centrally, as at Jf' , Fig. 33, a total 
eclipse may last for about two hours, with an additional 
hour at the beginning and end, during which the moon is 
entering and leaving the earth's shadow. If the moon 
meets the shadow at one side of the axis, as at P, the total 
phase of the eclipse may fail altogether, and between these 
extremes the duration of totality may be anything from 
two hours downward. 

67. Relation of the lunar nodes to eclipses. To show why 
the moon sometimes encounters the earth's shadow cen- 
trally and more frequently at full moon passes by without 
touching it at all, we resort to Fig. 34, which represents a 
part of the orbit of the earth about the sun, with dates 
showing the time in each year at which the earth passes 
the part of its orbit thus marked. The orbit of the moon 
about the earth, M M', is also shown, with the new moon, 
Jf, casting its shadow toward the earth and the full moon, 
Jfaf', apparently immersed in the earth's shadow. But here 
appearances are deceptive, and the student who has made 


the observations set forth in Chapter III has learned for 
himself a fact of which careful account must now be taken. 
The apparent paths of the moon and sun among the stars 
are great circles which lie near each other, but are not 
exactly the same ; and since these great circles are only the 
intersections of the sky with the planes of the earth's orbit 

FIG. 34. Relation of the lunar nodes to eclipses. 

and the moon's orbit, we see that these planes are slightly 
inclined to each other and must therefore intersect along 
some line passing through the center of the earth. This 
line, N' N" ', is shown in the figure, and if we suppose the 
surface of the paper to represent the plane of the earth's 
orbit, we shall have to suppose the moon's orbit to be tipped 
around this line, so that the left side of the orbit lies above 
and the right side below the surface of the paper. But 
since the earth's shadow lies in the plane of its orbit i. e., 
in the surface of the paper the full moon of March, Jf' , 
must have passed below the shadow, and the new moon, J/, 
must have cast its shadow above the earth, so that neither 
a lunar nor a solar eclipse could occur in that month. But 
toward the end of May the earth and moon have reached 
a position where the line N' N" points almost directly 
toward the sun, in line with the shadow cones which hide 
it. Note that the line N' N" remains very nearly parallel 
to its original position, while the earth is moving along 


its orbit. The full moon will now be very near this line 
and therefore very close to the plane of the earth's orbit, if 
not actually in it, and must pass through the shadow of the 
earth and be eclipsed. So also the new moon will cast its 
shadow in the plane of the ecliptic, and this shadow, falling 
upon the earth, produced the total solar eclipse of May 28, ' 

N 1 N" is called the line of nodes of the moon's orbit ( 39), 
and the two positions of the earth in its orbit, diametrically 
opposite each other, at which N' N" points exactly toward 
the sun, we shall call the nodes of the lunar orbit. Strictly 
speaking, the nodes are those points of the sky against 
which the moon's center is projected at the moment when 
in its orbital motion it cuts through the plane of the earth's 
orbit. Bearing in mind these definitions, we may condense 
much of what precedes into the proposition : Eclipses of 
either sun or moon can occur only when the earth is at or 
near one of the nodes of the moon's orbit. Corresponding 
to these positions of the earth there are in each year two 
seasons, about six months apart, at which times, and at 
these only, eclipses can occur. Thus in the year 1900 the 
earth passed these two points on June 2d and November 
24th respectively, and the following list of eclipses which 
occurred in that year shows that all of them were within a 
few days of one or the other of these dates : 

Eclipses of the Year 1900 

Total solar eclipse May 28th. 

Partial lunar eclipse June 12th. 

Annular (solar) eclipse November 21st. 

68. Eclipse limits. If the earth is exactly at the node at 
the time of new moon, the moon's shadow will fall cen- 
trally upon it and will produce an eclipse visible within the 
torrid zone, since this is that part of the earth's surface 
nearest the plane of its orbit. If the earth is near but not 
at the node, the new moon will stand a little north or south 


of the plane of the earth's orbit, and its shadow will strike 
the earth farther north or south than before, producing an 
eclipse in the temperate or frigid zones ; or the shadow may 
even pass entirely above or below the earth, producing no 
eclipse whatever, or at most a partial eclipse visible near 
the north or south pole. Just how many days' motion the 
earth may be away from the node and still permit an eclipse 
is shown in the following brief table of eclipse limits, as 
they are called : 

Solar Eclipse Limits 
If at any new moon the earth is 

Less than 10 days away from a node, a central eclipse is certain. 

Between 10 and 16 days " " " some kind of eclipse is certain. 

Between 16 and 19 days " " " a partial eclipse is possible. 

More than 19 days " " " no eclipse is possible. 

Lunar Eclipse Limits 
If at any full moon the earth is 

Less than 4 days away from a node, a total eclipse is certain. 
Between 4 and 10 days " " " some kind of eclipse is certain. 
Between 10 and 14 days " " " a partial eclipse is possible. 
More than 14 days " " " no eclipse is possible. 

From this table of eclipse limits we may draw some 
interesting conclusions about the frequency with which 
eclipses occur. 

69. Number of eclipses in a year. Whenever the earth 
passes a node of the moon's orbit a new moon must occur at 
some time during the 2 X 16 days that the earth remains 
inside the limits where some kind of eclipse is certain, and 
there must therefore be an eclipse of the sun every time the 
earth passes a node of the moon's orbit. But, since there 
are two nodes past which the earth moves at least once in 
each year, there must be at least two solar eclipses every 
year. Can there be more than two ? On the average, will 
central or partial eclipses be the more numerous ? 

A similar line of reasoning will not hold true for 
eclipses of the moon, since it is quite possible that no full 


moon should occur during the 20 days required by the 
earth to move past the node from the western to the east- 
ern limit. This omission of a full moon while the earth is 
within the eclipse limits sometimes happens at both nodes 
in the same year, and then we have a year with no eclipse 
of the moon. The student may note in the list of eclipses 
for 1900 that the partial lunar eclipse of June 12th oc- 
curred 10 days after the earth passed the node, and was 
therefore within the doubtful zone where eclipses may 
occur and may fail, and corresponding to this position the 
eclipse was a very small one, only a thousandth part of the 
moon's diameter dipping into the shadow of the earth. 
By so much the year 1900 escaped being an illustration of 
a year in which no lunar eclipse occurred. 

A partial eclipse of the moon will usually occur about a 
fortnight before or after a total eclipse of the sun, since 
the full moon will then be within the eclipse limit at the 
opposite node. A partial eclipse of the sun will always 
occur about a fortnight before or after a total eclipse of the 

70. Eclipse maps. It is the custom of astronomers to 
prepare, in advance of the more important eclipses, maps 
showing the trace of the moon's shadow across the earth, 
and indicating the times of beginning and ending of the 
eclipses, as is shown in Fig. 35. While the actual construc- 
tion of such a map requires much technical knowledge, the 
principles involved are simple enough : the straight line 
passed through the center of sun and moon is the axis of 
the shadow cone, and the map contains little more than a 
graphical representation of when and where this cone meets 
the surface of the earth. Thus in the map, the " Path of 
Total Eclipse " is the trace of the shadow cone across the 
face of the earth, and the width of this path shows that the 
earth encountered the shadow considerably inside the ver- 
tex of the cone. The general direction of the path is from 
west to east, and the slight sinuosities which it presents 


are for the most part due to unavoidable distortion of the 
map caused by the attempt to represent the curved surface 
of the earth upon the flat surface of the paper. On either 
side of the Path of Total Eclipse is the region within which 
the eclipse was only partial, and the broken lines marked Be- 
gins at 3h., Ends at 3h., show the intersection of the penum- 
bral cone with the surface of the earth at 3 P. M., Green*- 
wich time. These two lines inclose every part of the earth's 
surface from which at that time any eclipse whatever could 
be seen, and at this moment the partial eclipse was just be- 
ginning at every point on the eastern edge of the penumbra 
and just ending at every point on the western edge, while 
at the center of the penumbra, on the Path of Total Eclipse, 
lay the shadow of the moon, an oval patch whose greatest 
diameter was but little more than 60 miles in length, and 
within which lay every part of the earth where the eclipse 
was total at that moment. 

The position of the penumbra at other hours is also 
shown on the map, although with more distortion, because 
it then meets the surface of the earth more obliquely, and 
from these lines it is easy to obtain the time of beginning 
and end of the eclipse at any desired place, and to estimate 
by the distance of the place from the Path of Total Eclipse 
how much of the sun's face was obscured. 

Let the student make these " predictions " for Washing- 
ton, Chicago, London, and Algiers. 

The points in the map marked First Contact, Last Con- 
tact, show the places at which the penumbral cone first 
touched the earth and finally left it. According to compu- 
tations made as a basis for the construction of the map the 
Greenwich time of First Contact was Oh. 12.5m. and of Last 
Contact 5h. 35.6m., and the difference between these two 
times gives the total duration of the eclipse upon the earth 
i. e., 5 hours 23.1 minutes. 

71. Future eclipses. An eclipse map of a different kind 
is shown in Fig. 36, which represents the shadow paths of 



all the central eclipses of the sun, visible during the period 
1900-1918 A. D., in those parts of the earth north of the 
south temperate zone. Each continuous black line shows 
the path of the shadow in a total eclipse, from its begin- 

FIG. 36. Central eclipses for the first two decades of the twentieth century. 

ning, at sunrise, at the western end of the line to its end, 
sunset, at the eastern end, the little circle near the mid- 
dle of the line showing the place at which the eclipse 
was total at noon. The broken lines represent similar 
data for the annular eclipses. This map is one of a se- 
ries prepared by the Austrian astronomer, Oppolzer, show- 
ing the path of every such eclipse from the year 1200 


B. c. to 2160 A. D., a period of more than three thousand 

If we examine the dates of the eclipses shown in this 
map we shall find that they are not limited to the particu- 
lar seasons, May and N ovember, in which those of the year 
1900 occurred, but are scattered through all the months of 
the year, from January to December. This shows at once 
that the line of nodes, N' N", of Fig. 34, does not remain 
in a fixed position, but turns round in the plane of the 
earth's orbit so that in different years the earth reaches the 
node in different months. The precession has already fur- 
nished us an illustration of a similar change, the slow rota- 
tion of the earth's axis, producing a corresponding shifting 
of the line in which the planes of the equator and ecliptic 
intersect ; and in much the same way, through the disturb- 
ing influence of the sun's attraction, the line N' N" is made 
to revolve westward, opposite to the arrowheads in Fig. 
34, at the rate of nearly 20 per year, so that the earth 
comes to each node about 19 days earlier in each year than 
in the year preceding, and the eclipse season in each year 
comes on the average about 19 days earlier than in the year 
before, although there is a good deal of irregularity in the 
amount of change in particular years. 

72. Recurrence of eclipses. Before the beginning of the 
Christian era astronomers had found out a rough-and-ready 
method of predicting eclipses, which is still of interest and 
value. The substance of the method is that if we start 
with any eclipse whatever e. g., the eclipse of May 28, 1900 
and reckon forward or backward from that date a period of 
18 years and 10 or 11 days, we shall find another eclipse quite 
similar in its general characteristics to the one with Avhich 
we started. Thus, from the map of eclipses (Fig. 36), we 
find that a total solar eclipse will occur on June 8, 1918, 
18 years and 11 days after the one illustrated in Fig. 35. 
This period of 18 years and 11 days is called saros, an 
ancient word which means cycle or repetition, and since 


every eclipse is repeated after the lapse of a saros, we may 
find the dates of all the eclipses of 1918 by adding 11 
days to the dates given in the table of eclipses for 1900 
( 67), and it is to be especially noted that each eclipse of 
1918 will be like its predecessor of 1900 in character 
lunar, solar, partial, total, etc. The eclipses of any year 
may be predicted by a similar reference to those which 
occurred eighteen years earlier. Consult a file of old 

The exact length of a saros is 223 lunar months, each of 
which is a little more than 29.5 days long, and. if we multi- 
ply the exact value of this last number (see 60) by 223, 
we shall find for the product 6,585.32 days, which is equal 
to 18 years 11.32 days when there are four leap years in- 
cluded in the 18, or 18 years 10.32 days when the num- 
ber of leap years is five ; and in applying the saros to the 
prediction of eclipses, due heed must be paid to the number 
of intervening leap years. To explain why eclipses are 
repeated at the end of the saros, we note that the occurrence 
of an eclipse depends solely upon the relative positions of 
the earth, moon, and node of the moon's orbit, and the 
eclipse will be repeated as often as these three come back 
to the position which first produced it. This happens at 
the end of every saros, since the saros is, approximately, the 
least common multiple of the length of the year, the length 
of the lunar month, and the length of time required by the 
line of nodes to make a complete revolution around the 
ecliptic. If the saros were exactly a multiple of these 
three periods, every eclipse would be repeated over and 
over again for thousands of years ; but such is not the 
case, the saros is not an exact multiple of a year, nor 
is it an exact multiple of the time required for a revo- 
lution of the line of nodes, and in consequence the 
restitution which comes at the end of the saros is not a 
perfect one. The earth at the 223d new moon is in fact 
about half a day's motion farther west, relative to the node, 



than it was at the beginning, and the re- 
sulting eclipse, while very similar, is not 
precisely the same as before. After another 
18 years, at the second repetition, the earth 
is a day farther from the node than at first, 
and the eclipse differs still more in charac- 
ter, etc. This is shown in Fig. 37, which 
represents the apparent positions of the 
disks of the sun and moon as seen from the 
center of the earth at the end of each sixth 
saros, 108 years, where the upper row of 
figures represents the number of repetitions 
of the eclipse from the beginning, marked 
0, to the end, 72. The solar eclipse limits, 
10, 16, 19 days, are also shown, and all those 
eclipses which fall between the 10-day lim- 
its will be central as seen from some part of 
the earth, those between 16 and 19 partial 
wherever seen, while between 10 and 16 
they may be either total or partial. Com- 
pare the figure with the following descrip- 
tion given by Professor Newcomb : " A se- 
ries of such eclipses commences with a very 
small eclipse near one pole of the earth. 
Gradually increasing for about eleven recur- 
rences, it will become central near the same 
pole. Forty or more central eclipses will 
then recur, the central line moving slowly 
toward the other pole. The series will then 
become partial, and finally cease. The en- 
tire duration of the series will be more than 
a thousand years. A new series commences, 
on the average, at intervals of thirty years." 
A similar figure may be constructed to 
represent the recurrence of lunar eclipses ; 
but here, in consequence of the smaller 


eclipse limits, we shall find that a series is of shorter dura- 
tion, a little over eight centuries as compared with twelve 
centuries, which is the average duration of a series of solar 

One further matter connected with the saros deserves 
attention. During the period of 6,585.32 days the earth 
has 6,585 times turned toward the sun the same face upon 
which the moon's shadow fell at the beginning of the saros, 
but at the end of the saros the odd 0.32 of a day gives the 
earth time to make about a third of a revolution more 
before the eclipse is repeated, and in consequence the 
eclipse is seen in a different region of the earth, on the 
average about 116 farther west in longitude. Compare in 
Fig. 36 the regions in which the eclipses of 1900 and 1918 
are visible. 

Is this change in the region where the repeated eclipse 
is visible, true of lunar eclipses as well as solar ? 

73. Use of eclipses. At all times and among all peoples 
eclipses, and particularly total eclipses of the sun, have 
been reckoned among the most impressive phenomena of 
Nature. In early times and among uncultivated people 
they were usually regarded with apprehension, often amount- 
ing to a terror and frenzy, which civilized travelers have 
not scrupled to use for their own purposes with the aid of 
the eclipse predictions contained in their almanacs, threat- 
ening at the proper time to destroy the sun or moon, and 
pointing to the advancing eclipse as proof that their 
threats were not vain. In our own day and our own land 
these feelings of awe have not quite disappeared, but for 
the most part eclipses are now awaited with an interest and 
pleasure which, contrasted with the. former feelings of man- 
kind, furnish one of the most striking illustrations of the 
effect of scientific knowledge in transforming human fear 
and misery into a sense of security and enjoyment. 

But to the astronomer an eclipse is more than a beau- 
tiful illustration of the working of natural laws ; it is in 


varying degree an opportunity of adding to his store of 
knowledge respecting the heavenly bodies. The region 
immediately surrounding the sun is at most times closed to 
research by the blinding glare of the sun's own light, so 
that a planet as large as the moon might exist here unseen 
were it not for the occasional opportunity presented by a 
total eclipse which shuts off the excessive light and permits 
not only a search for unknown planets but for anything 
and everything which may exist around the sun. More 
than one astronomer has reported the discovery of such 
planets, and at least one of these has found a name and a 
description in some of the books, but at the present time 
most astronomers are very skeptical about the existence of 
any such object of considerable size, although there is 
some reason to believe that an enormous number of little 
bodies, ranging in size from grains of sand upward, do 
move in this region, as yet unseen and offering to the 
future problems for investigation. 

But in other directions the study of this region at the 
times of total eclipse has yielded far larger returns, and in 
the chapter on the sun we shall have to consider the mar- 
velous appearances presented by the solar prominences and 
by the corona, an appendage of the sun which reaches out 
from his surface for millions of miles but is never seen 
save at an eclipse. Photographs of the corona are taken 
by astronomers at every opportunity, and reproductions of 
some of these may be found in Chapter X. 

Annular eclipses and lunar eclipses are of comparatively 
little consequence, but any recorded eclipse may become of 
value in connection with chronology. We date our letters 
in a particular year of the twentieth century, and commonly 
suppose that the years are reckoned from the birth of 
Christ ; but this is an error, for the eclipses which were ob- 
served of old and by the chroniclers have been associated 
with events of his life, when examined by the astronomers 
are found quite inconsistent with astronomic theory. 


They are, however, reconciled with it if we assume that our 
system of dates has its origin four years after the birth of 
Christ, or, in other words, that Christ was born in the 
year 4 B. c. A mistake was doubtless made at he time 
the Christian era was introduced into chronology. At 
many other points the chance record of an eclipse in 
the early annals of civilization furnishes a similar means of 
controlling and correcting the dates assigned by the histo- 
rian to events long past. 



74. Two familiar instruments. In previous chapters we 
have seen that a clock and a divided circle (protractor) are 
needed for the observations which an astronomer makes, 
and it is worth while to note here that the geography of 
the sky and the science of celestial motions depend funda- 
mentally upon these two instruments. The protractor is a 
simple instrument, a humble member of the family of 
divided circles, but untold labor and ingenuity have been 
expended on this family to make possible the construction 
of a circle so accurately divided that with it angles may be 
measured to the tenth of a second instead of to the tenth 
of a degree i. e., 3,600 times as accurate as the protractor 

The building of a good clock is equally important and 
has cost a like amount of labor and pains, so that it is a far 
cry from Galileo and his discovery that a pendulum " keeps 
time " to the modern clock with its accurate construction 
and elaborate provision against disturbing influences of 
every kind. Every such timepiece, whether it be of the 
nutmeg variety which sells for a dollar, or whether it be the 
standard clock of a great national observatory, is made up 
of the same essential parts which fall naturally into four 
classes, which we may compare with the departments of a 
well-ordered factory : I. A timekeeping department, the 
pendulum or balance spring, whose oscillations must all be 
of equal duration. II. A power department, the weights or 
9 121 


mainspring, which, when wound, store up the power applied 
from outside and give it out piecemeal as required to keep 
the first department running. III. A publication depart- 
ment, the dial and hands, which give out the time furnish- 
ed by Department I. IV. A transportation department, 
the wheels, which connect the other three and serve as a 
means of transmitting power and time from one to the 
other. The case of either clock or watch is merely the 
roof which shelters it and forms no department of its in- 
dustry. Of these departments the first is by far the most 
important, and its good or bad performance makes or mars 
the credit of the clock. Beware of meddling with the 
balance wheel of your watch. 

75. Radiant energy, But we have now to consider other 
instruments which in practice supplement or displace the 
simple apparatus hitherto employed. Among the most im- 
portant of these modern instruments are the telescope, the 
spectroscope, and the photographic camera ; and since all 
these instruments deal with the light which comes from 
the stars to the earth, we must for their proper understand- 
ing take account of the nature of that light, or, more strictly 
speaking, we must take account of the radiant energy emit- 
ted by the sun and stars, which energy, coming from the 
sun, is translated by our nerves into the two different sen- 
sations of light and heat. The radiant energy which comes 
from the stars is not fundamentally different from that of 
the sun, but the amount of energy furnished by any star is 
so small that it is unable to produce through our nerves 
any sensible perception of heat, and for the same reason 
the vast majority of stars are invisible to the unaided eye ; 
they do not furnish a sufficient amount of energy to affect 
the optic nerves. A hot brick taken into the hand reveals 
its presence by the two different sensations of heat and 
pressure (weight) ; but as there is only one brick to produce 
the two sensations, so there is only one energy to produce 
through its action upon different nerves the two sensations 


of light and heat, and this energy is called radiant because 
it appears to stream forth radially from everything which 
has the capacity of emitting it. For the detailed study 
of radiant energy the student is referred to that branch 
of science called physics ; but some of its elementary prin- 
ciples may be learned through the following simple experi- 
ment, which the student should not fail to perform for 
himself : 

Drop a bullet or other similar object into a bucket 
of water and observe the circular waves which spread 
from the place where it enters the water. These waves 
are a form of radiant energy, but differing from light or 
heat in that they are visibly confined to a single plane, 
the surface of the water, instead of filling the entire sur- 
rounding space. By varying the size of the bucket, the 
depth of the water, the weight of the bullet, etc., differ- 
ent kinds of waves, big and little, may be produced ; but 
every such set of waves may be described and defined in 
all its principal characteristics by means of three num- 
bers viz., the vertical height of the waves from hollow 
to crest ; the distance of one wave from the next ; and 
the velocity with which the waves travel across the water. 
The last of these quantities is called the velocity of propa- 
gation ; the second is called the wave length ; one half 
of the first is called the amplitude ; and all these terms 
find important applications in the theory of light and 

The energy of the falling bullet, the disturbance which 
it produced on entering the water, was carried by the 
waves from the center to the edge of the bucket but not 
beyond, for the wave can go only so far as the water 
extends. The transfer of energy in this way requires a 
perfectly continuous medium through which the waves 
may travel, and the whole visible universe is supposed to 
be filled with something called ether, which serves every- 
where as a medium for the transmission of radiant energy 


just as the water in the experiment served as a medium 
for transmitting in waves the energy furnished to it by the 
falling bullet. The student may think of this energy as be- 
ing transmitted in spherical waves through the ether, every 
glowing body, such as a star, a candle flame, an arc lamp, a 
hot coal, etc., being the origin and center of such systems 
of waves, and determining by its own physical and chem- 
ical properties the wave length and amplitude of the wave 
systems given off. 

The intensity of any light depends upon the amplitude 
of the corresponding vibration, and its color depends upon 
the wave length. By ingenious devices which need not be 
here described it has been found possible to measure the 
wave length corresponding to different colors e. g., all of 
the colors of the rainbow, and some of these wave lengths 
expressed in tenth meters are as follows : A tenth meter is 
the length obtained by dividing a meter into 10 10 equal 
parts. 10 10 = 10,000,000,000. 

Color. Wave length. 

Extreme limit of visible violet 3.900 

Middle of the violet : 4,060 

blue 4,730 

green 5,270 

yellow 5,810 

orange 5,970 

red 7,000 

Extreme limit of visible red 7,600 

The phrase " extreme limit of visible violet " or red 
used above must be understood to mean that in general the 
eye is not able to detect radiant energy having a wave 
length less than 3,900 or greater than 7,600 tenth meters. 
Radiant energy, however, exists in waves of both greater 
and shorter length than the above, and may be readily 
detected by apparatus not subject to the limitations of the 
human eye e. g., a common thermometer will show a rise 
of temperature when its bulb is exposed to radiant energy 
of wave length much greater than 7,600 tenth meters, and 






a photographic plate will be strongly affected by energy of 
shorter wave length than 3,900 tenth meters. 

76. Reflection and condensation of waves. When the 
waves produced by dropping a bullet into a bucket of 
water meet the sides of the bucket, they appear to rebound 
and are reflected back toward the center, and if the bullet is 
dropped very near the center of the bucket the reflected 
waves will meet simultaneously at this point and produce 
there by their combined action a wave higher than that 
which was reflected at the walls of the bucket. There has 
been a condensation of energy produced by the reflection, 
and this increased energy is shown by the greater amplitude 
of the wave. The student should not fail to notice that 
each portion of the wave has traveled out and back over 
the radius of the bucket, and that they meet simultaneously 
at the center because of this equality of the paths over which 
they travel, and the resulting equality of time required to 
go out and back. If the bullet were dropped at one side of 
the center, would the reflected waves produce at any point 
a condensation of energy ? 

If the bucket were of elliptical instead of circular cross 
section and the bullet were dropped at one focus of the 
ellipse there would be produced a condensation of reflected 
energy at the other focus, since the sum of the paths trav- 
ersed by each portion of the wave before and after reflec- 
tion is equal to the sum of the paths traversed by every 
other portion, and all parts of the wave reach the second 
focus at the same time. Upon what geometrical principle 
does this depend ? 

The condensation of wave energy in the circular and 
elliptical buckets are special cases under the general prin- 
ciple that such a condensation will be produced at any 
point which is so placed that different parts of the wave 
front reach it simultaneously, whether by reflection or by 
some other means, as shown below. 

The student will note that for the sake of greater pre- 


cision we here say wave front instead of wave. If in any 
wave we imagine a line drawn along the crest, so as to touch 
every drop which at that moment is exactly at the crest, we 
shall have what is called a wave front, and similarly a line 
drawn through the trough between two waves, or through 
any set of drops similarly placed on a wave, constitutes a 
wave front. 

77. Mirrors and lenses. That form of radiant energy 
which we recognize as light and heat may be reflected and 
condensed precisely as are the waves of water in the exer- 
cise considered above, but owing to the extreme shortness 
of the wave length in this case the reflecting surface should 
be very smooth and highly polished. A piece of glass hol- 
lowed out in the center by grinding, and with a light film 
of silver chemically deposited upon the hollow surface and 
carefully polished, is often used by astronomers for this pur- 
pose, and is called a concave mirror. 

The radiant energy coming from a star or other distant 
object and falling upon the silvered face of such a mirror 
is reflected and condensed at a point a little in front of the 
mirror, and there forms an image of the star, which may be 
seen with the unaided eye, if it is held in the right place, or 
may be examined through a magnifying glass. Similarly, 
an image of the sun, a planet, or a distant terrestrial object 
is formed by the mirror, which condenses at its appropriate 
place the radiant energy proceeding from each and every 
point in the surface of the object, and this, in common 
phrase, produces an image of the object. 

Another device more frequently used by astronomers 
for the production of images (condensation of energy) is a 
lens which in its simplest form is a round piece of glass, 
thick in the center and thin at the edge, with a cross sec- 
tion, such as is shown at A B in Fig. 38. If we suppose 
E G D to represent a small part of a wave front coming from 
a very distant source of radiant energy, such as a star, this 
wave front will be practically a plane surface represented 


by the straight line ED, but in passing through the lens 
this surface will become warped, since light travels slower 
in glass than in air, and the central part of the beam, 0, 
in its onward motion will be retarded by the thick center 

FIG. 38. Illustrating the theory of lenses. 

of the lens, more than E or D will be retarded by the com- 
paratively thin outer edges of A B. On the right of the 
lens the wave front therefore will be transformed into a 
curved surface whose exact character depends upon the 
shape of the lens and the kind of glass of which it is made. 
By properly choosing these the new wave front may be 
made a part of a sphere having its center at the point F and 
the whole energy of the wave front, E G D, will then be con- 
densed at F, because this point is equally distant from all 
parts of the warped wave front, and therefore is in a posi- 
tion to receive them simultaneously. The distance of F 
from A B is called the focal length of the lens, and ^itself 
is called the focus. The significance of this last word 
(Latin, focus = fireplace) will become painfully apparent to 
the student if he will hold a common reading glass between 
his hand and the sun in such a way that the focus falls 
upon his hand. 

All the energy transmitted by the lens in the direc- 
tion GFis concentrated upon a very small area at F, and 
an image of the object e. g., a star, from which the light 
came is formed here. Other stars situated near the one in 
question will also send beams of light along slightly differ- 
ent directions to the lens, and these will be concentrated, 
each in its appropriate place, in the focal plane, F H, passed 
through the focus, F, perpendicular to the line, F G, and 



we shall find in this plane a picture of all the stars or other 
objects within the range of the lens. 

78. Telescopes. The simplest kind of telescope consists 
of a concave mirror to produce images, and a magnifying 
glass, called an eyepiece, through which to examine them ; 

but for convenience' 
sake, so that the observ- 
er may not stand in his 
own light, a small mir- 
ror is frequently added 
to this combination, as 
at H in Fig. 39, where 
the lines represent the 
directions along which 
the energy is propagated. 
By reflection from this mirror the focal plane and the 
images are shifted to F, where they may be examined from 
one side through the magnifying glass E. 

Such a combination of parts is called a reflecting tele- 
scope, while one in which the images are produced by a 
lens or combination of lenses is called a refracting tele- 
scope, the adjective having reference to the bending, re- 
fraction, produced by the glass upon the direction in which 
the energy is propagated. The customary arrangement of 
parts in such a telescope is shown in Fig. 40, where the 


). Essential parts of 


FIG. 40. A simple form of refracting telescope. 

part marked is called the objective and V E (the mag- 
nifying glass) is the eyepiece, or ocular, as it is sometimes 

Most objects with which we have to deal in using a 
telescope send to it not light of one color only, but a mix- 


ture of light of many colors, many different wave lengths, 
some of which are refracted more than others by the glass 
of which the lens is composed, and in consequence of these 
different amounts of refraction a single lens does not fur- 
nish a single image of a star, but gives a confused jumble of 
red and yellow and blue images much inferior in sharpness 
of outline (definition) to the images made by a good con- 
cave mirror. To remedy this defect it is customary to 
make the objective of two or more pieces of glass of differ- 
ent densities and ground to different shapes as is shown at 
in Fig. 40. The two pieces of glass thus mounted in one 
frame constitute a compound lens having its own focal 
plane, shown at F in the figure, and similarly the lenses 
composing the eyepiece have a focal plane between the 
eyepiece and the objective which must also fall at F, and 
in the use of a telescope the eyepiece must be pushed out 
or in until its focal plane coincides with that of the objec- 
tive. This process, which is called focusing, is what is 
accomplished in the ordinary opera glass by turning a screw 
placed between the two tubes, and it must be carefully 
done with every telescope in order to obtain distinct vision. 
79. Magnifying power. The amount by which a given 
telescope magnifies depends upon the focal length of the ob- 
jective (or mirror) and the focal length of the eyepiece, and 
is equal to the ratio of these two quantities. Thus in lig. 
40 the distance of the objective from the focal plane J^is 
about 16 times as great as the distance of the eyepiece 
from the same plane, and the magnifying power of this 
telescope is therefore 16 diameters. A magnifying power 
of 16 diameters means that the diameter of any object seen 
in the telescope looks 16 times as large as it appears with- 
out the telescope, and is nearly equivalent to saying that 
the object appears only one sixteenth as far off. Some- 
times the magnifying power is assumed to be the number 
of times that the area of an object seems increased ; and 
since areas are proportional to the squares of lines, the 


magnifying power of 16 diameters might be called a power 
of 256. Every large telescope is provided with several eye- 
pieces of different focal lengths, ranging from a quarter of 
an inch to two and a half inches, which are used to fur- 
nish different magnifying powers as may be required for 
the different kinds of work undertaken with the instru- 
ment. Higher powers can be used with large telescopes 
than with small ones, but it is seldom advantageous to 
use with any telescope an eyepiece giving a higher power 
than 60 diameters for each inch of diameter of the ob- 

The part played by the eyepiece in determining magni- 
fying power will be readily understood from the following 
experiment : 

Make a pin hole in a piece of cardboard. Bring a 
printed page so close to one eye that you can no longer see 
the letters distinctly, and then place the pin hole between 
the eye and the page. The letters which were before 
blurred may now be seen plainly through the pin hole, 
even when the page is brought nearer to the eye than be- 
fore. As it is brought nearer, notice how the letters seem 
to become larger, solely because they are nearer. A pin 
hole is the simplest kind of a magnifier, and the eyepiece 
in a telescope plays the same part as does the pin hole in 
the experiment ; it enables the eye to be brought nearer to 
the image, and the shorter the focal length of the eyepiece 
the nearer is the eye brought to the image and the higher 
is the magnifying power. 

80. The equatorial mounting, Telescopes are of all sizes, 
from the modest opera glass which may be carried in the 
pocket and which requires no other support than the hand, 
to the giant which must have a special roof to shelter it 
and elaborate machinery to support and direct it toward 
the sky. But for even the largest telescopes this machinery 
consists of the following parts, which are illustrated, with 
exception of the last one, in the small equatorial telescope 


shown in Fig. 41. It is not customary to place a driving 
clock on so small a telescope as this : 

(a) A supporting pier or tripod. 

(b) An axis placed parallel to the axis of the earth. 

(c) Another axis at 
right angles to b and 
capable of revolving 
upon b as an axle. 

(d) The telescope 
tube attached to c and ca- 
pable of revolving about c. 

(e) Graduated circles 
attached to c and d to 
measure the amount by 
which the telescope is 
turned on these axes. 

(/) A driving clock so 
connected with b as to 
make c (and d) revolve 
about b with an angular 
velocity equal and opposite 
to that with which the 
earth turns upon its axis. 

Such a support is called 
an equatorial mounting, 
and the student should 
note from the figure that 
the circles, e, measure the 
hour angle and declination 
of any star toward which FlG 41 _ A simp 7 e eqn ^ orial mounting . 
the telescope is directed, 

and conversely if the telescope be so set that these circles 
indicate the hour angle and declination of any given star, 
the telescope will then point toward that star. In this 
way it is easy to find with the telescope any moderately 
bright star, even in broad daylight, although it is then 


absolutely invisible to the naked eye. The rotation of the 
earth about its axis will speedily carry the telescope away 
from the star, but if the driving clock be started, its effect 
is to turn the telescope toward the west just as fast as the 
earth's rotation carries it toward the east, and by these 
compensating motions 
to keep it directed to- 
ward the star. In Fig. 
42, which represents 
the largest and one of 
the most perfect re- 
fracting telescopes 
ever built, let the stu- 
dent pick out and iden- 
tify the several parts 
of the mounting above 
described. A part of 
the driving clock may 
be seen within the head 
of the pier. In Fig. 
43 trace out the cor- 
responding parts in 
the mounting of a re- 
flecting telescope. 

A telescope is often 
only a subordinate part 
of some instrument or 
apparatus, and then its 
style of mounting is 
determined by the requirements of the special case ; but 
when the telescope is the chief thing, and the remainder 
of the apparatus is subordinate to it, the equatorial mount- 
ing is almost always adopted, although sometimes the ar- 
rangement of the parts is very different in appearance from 
any of those shown above. Beware of the popular error that 
an object held close in front of a telescope can be seen by an 

FIG. 43. The reflecting telescope of the 
Paris Observatory. 



observer at the eyepiece. The numerous stories of astrono- 
mers who saw spiders crawling over the objective of their 
telescope, and imagined they were beholding strange ob- 
jects in the sky, are all fictitious, since nothing on or near 
the objective could possibly be seen through the telescope. 
81. Photography. A photographic camera consists of a 
lens and a device for holding at its focus a specially pre- 
pared plate or film. This 
plate carries a chemical 
deposit which is very 
sensitive to the action 
of light, and which may 
be made to preserve the 
imprint of any picture 
which the lens forms 
upon it. If such a sen- 
sitive plate is placed at 
the focus of a reflecting 
telescope, the combina- 
tion becomes a camera 
available for astronom- 
ical photography, and at 
the present time the 
tendency is strong in 
nearly every branch of 
astronomical research to 
substitute the sensitive 
plate in place of the ob- 
server at a telescope. A 
refracting telescope may also be used for astronomical pho- 
tography, and is very much used, but some complications 
occur here on account of the resolution of the light into 
its constituent colors in passing through the objective. 
Fig. 44 shows such a telescope, or rather two telescopes, one 
photographic, the other visual, supported side by side upon 
the same equatorial mounting. 

FIG. 44. Photographic telescope of the Paris 


One of the great advantages of photography is found in 
connection with what is called 

82. Personal equation, It is a remarkable fact, first in- 
vestigated by the German astronomer Bessel, three quar- 
ters of a century ago, that where extreme accuracy is re- 
quired the human senses can not be implicitly relied upon. 
The most skillful observers will not agree exactly in their 
measurement of an angle or in estimating the exact instant 
at which a star crossed the meridian ; the most skillful 
artists can not draw identical pictures of the same ob- 
ject, etc. 

These minor deceptions of the senses are included in 
the term personal equation, which is a famous phrase in 
astronomy, denoting that the observations of any given 
person require to be corrected by means of some equation 
involving his personality. 

General health, digestion, nerves, fatigue, all influence 
the personal equation, and it was in reference to such mat- 
ters that one of the most eminent of living astronomers has 
given this description of his habits of observing : 

" In order to avoid every physiological disturbance, I 
"~Tiave adopted the rule to abstain for one or two hours be- 
fore commencing observations from every laborious occupa- 
tion ; never to go to the telescope with stomach loaded with 
food ; to abstain from everything which could affect the 
nervous system, from narcotics and alcohol, and especially 
from the abuse of coffee, which I have found to be exceed- 
ingly prejudicial to the accuracy of observation."* A 
regimen suggestive of preparation for an athletic contest 
thanj&rthe more quiet labors of an astronomer. 

83. Visual and photographic work. The photographic 
plate has no stomach and no nerves, and is thus free from 
many of the sources of error which inhere in visual observa- 
tions, and in special classes of work it possesses other 

* Schiaparelli, Osservazioni sulle Stelle Doppie. 


marked advantages, such as rapidity when many stars are 
to he dealt with simultaneously, permanence of record, and 
owing to the cumulative effect of long exposure of the plate 
it is possible to photograph with a given telescope stars far 
too faint to be seen through it. On the other hand, the 
eye has the advantage in some respects, such as studying 
the minute details of a fairly bright object e. g., the sur- 
face of a planet, or the sun's corona and, for the present at 
least, neither method of observing can exclude the other. 
For a remarkable case of discordance between the results 
of photographic and visual observations compare the pic- 
tures of the great nebula in the constellation Andromeda, 
which are given in Chapter XIV. A partial explanation 
of these discordances and other similar ones is that the 
eye is most strongly affected by greenish-yellow light, 
while the photographic plate responds most strongly to 
violet light ; the photograph, therefore, represents things 
which the eye has little capacity for seeing, and vice versa. 
84. The spectroscope. In some respects the spectroscope 
is the exact counterpart of the telescope. The latter con- 
denses radiant energy and the former disperses it. As a 
measuring instrument the telescope is mainly concerned 
with the direction from which light comes, and the differ- 
ent colors of which that light is composed affect it only as 
an obstacle to be overcome in its construction. On the 
other hand, with the spectroscope the direction from which 
the radiant energy comes is of minor consequence, and the 
all-important consideration is the intrinsic character of 
that radiation. What colors are present in the light and 
in what proportions ? What can these colors be made to 
tell about the nature and condition of the body from which 
they come, be it sun, or star, or some terrestrial source of 
light, such as an arc lamp, a candle flame, or a furnace in 
blast ? These are some of the characteristic questions of 
the spectrum analysis, and, as the name implies, they are 
solved by analyzing the radiant energy into its component 


parts, setting down the blue light in one place, the yellow 
in another, the red in still another, etc., and interpreting 
this array of colors by means of principles which we shall 
have to consider. Something of this process of color 
analysis may be seen in the brilliant hues shown by a soap 
bubble, or reflected from a piece of mother-of-pearl, and 
still more strikingly exhibited in the rainbow, produced by 

FIG. 45. Resolution of light into its component colors. 

raindrops which break up the sunlight into its component 
colors and arrange them each in its appropriate place. 
Any of these natural methods of decomposing light might 
be employed in the construction of a spectroscope, but in 
spectroscopes which are used for analyzing the light from 
feeble sources, such as a star, or a candle flame, a glass 
prism of triangular cross section is usually employed to re- 
solve the light into its component colors, which it does by 
refracting it as shown at the edges of the lens in Fig. 38. 

The course of a beam of light in passing through such 
a prism is shown in Fig. 45. Note that the bending of the 
light from its original course into a new one, which is here 
shown as produced by the prism, is quite similar to the 
bending shown at the edges of a lens and comes from the 


same cause, the slower velocity of light in glass than in 
air. It takes the light-waves as long to move over the 
path A B in glass as over the longer path 1, 2, 3, 4, of 
which only the middle section lies in the glass. 

'Not only does the prism bend the beam of light trans- 
mitted by it, but it bends in different degree light of differ- 
ent colors, as is shown in the figure, where the beam at the 
left of the prism is supposed to be made up of a mixture of 
blue and red light, while at the right of the prism the 
greater deviation imparted to the blue quite separates the 
colors, so that they fall at different places on the screen, 
S S. The compound light has been analyzed into its con- 
stituents, and in the same way every other color would be 
put down at its appropriate place on the screen, and a beam 
of white light falling upon the prism would be resolved by 
it into a sequence of colors, falling upon the screen in the 
order red, orange, yellow, green, blue, indigo, violet. The 
initial letters of these names make the word RoygMv, and 
by means of it their order is easily remembered. 

If the light which is to be examined comes from a star 
the analysis made by the prism is complete, and when 
viewed through a telescope the image of the star is seen to 
be drawn out into a band of light, which is called a spec- 
trum, and is red at one end and violet or blue at the other, 
with all the colors of the rainbow intervening in proper 
order between these extremes. Such a prism placed in 
front of the objective of a telescope is called an objec- 
tive prism, and has been used for stellar work with marked 
success at the Harvard College Observatory. But if the 
light to be analyzed comes from an object having an ap- 
preciable extent of surface, such as the sun or a planet, 
the objective prism can not be successfully employed, 
since each point of the surface will produce its own spec- 
trum, and these will appear in the view telescope super- 
posed and confused one with another in a very objection- 
able manner. To avoid this difficulty there is placed 


between the prism and the source of light an opaque 
screen, $, with a very narrow slit cut in it, through which all 
the light to be analyzed must pass and must also go through 
a lens, J, placed between the slit and the prism, as shown 
in Fig. 46. The slit and lens, together with the tube in 

FIG. 46. Principal parts of a spectroscope. 

which they are usually supported, are called a collimator, 
By this device a very limited amount of light is permitted 
to pass from the object through the slit and lens to the 
prism and is there resolved into a spectrum, which is in 
effect a series of images of the slit in light of different 
colors, placed side by side so close as to make practically a 
continuous ribbon of light whose width is the length of 
each individual picture of the slit. The length of the ribbon 
(dispersion) depends mainly upon the shape of the prism 
and the kind of glass of which it is made, and it may be 
very greatly increased and the efficiency of the spectro- 
scope enhanced by putting two, three, or more prisms in 
place of the single one above described. When the amount 
of light is very great, as in the case of the sun or an elec- 
tric arc lamp, it is advantageous to alter slightly the ar- 
rangement of the spectroscope ' and to substitute in place 
of the prism a grating i. e., a metallic mirror with a great 
number of fine parallel lines ruled upon its surface at equal 
intervals, one from another. It is by virtue of such a sys- 
tem of fine parallel grooves that mother-of-pearl displays 



its beautiful color effects, and a brilliant spectrum of great 
purity and high dispersion is furnished by a grating ruled 
with from 10,000 to 20,000 lines to the inch. Fig. 47 rep- 
resents, rather crudely, a part of the spec- 
trum of an arc light furnished by such a 
grating, or rather it shows three different 
spectra arranged side by side, and looking 
something like a rude ladder. The sides 
of the ladder are the spectra furnished by 
, the incandescent carbons of the lamp, and 
the cross pieces are the spectrum of the 
electric arc filling the space between the 
carbons. Fig. 48 shows a continuation of 
the same spectra into a region where the 
radiant energy is invisible to the eye, but 
is capable of being photographed. 

It is only when a lens is placed be- 
tween the lamp and the slit of the spec- 
troscope that the three spectra are shown 
distinct from each other as in the figure. 
The purpose of the lens is to make a pic- 
ture of the lamp upon the slit, so that 
all the radiant energy from any one point 
of the arc may be brought to one part of 
the slit, and thus appear in the resulting 
spectrum separated from the energy 
which comes from every other part of 
the arc. Such an instrument is called 
an analyzing spectroscope while one with- 
out the lens is called an integrating spec- 
troscope, since it furnishes to each point 
of the slit a sample of the radiant energy 
coming from every part of the source of 
light, and thus produces only an average 
spectrum of that source without distinction of its parts. 
When a spectroscope is attached to a telescope, as is often 


done (see Fig. 49), the eyepiece is removed to make way 
for it, and the telescope objective takes the part of the 
analyzing lens. A camera is frequently combined with 

FIG. 48. Violet and ultraviolet parts of spectrum of an arc lamp. 

such an apparatus to photograph the spectra it furnishes, 
and the whole instrument is then called a spectrograph. 

85. Spectrum analysis, Having seen the mechanism of 
the spectroscope by which the light incident upon it is 
resolved into its constituent parts and drawn out into a 
series of colors arranged in the order of their wave lengths, 
we have now to consider the interpretation which is to be 
placed upon the various kinds of spectra which may be 
seen, and here we rely upon the experience of physicists 
and chemists, from whom we learn as follows : 

The radiant energy which is analyzed by the spectro- 
scope has its source in the atoms and molecules which make 
up the luminous body from which the energy is radiated, 
and these atoms and molecules are able to impress upon 
the ether their own peculiarities in the shape of waves of 
different length and amplitude. We have seen that by 
varying the conditions of the experiment different kinds of 
waves may be produced in a bucket of water; and as a 
study of these waves might furnish an index to the condi- 
tions which produced them, so the study of the waves 
peculiar to the light which comes from any source may be 
made to give information about the molecules which make 
up that source. Thus the molecules of iron produce a 
system of waves peculiar to themselves and which can be 
duplicated by nothing else, and every other substance 
gives off its own peculiar type of energy, presenting a 



limited and definite number of wave lengths dependent 
upon the nature and condition of its molecules. If these 
molecules are free to behave in their own characteristic 
fashion without disturbance or crowding, they emit light of 
these wave lengths only, and we find in the spectrum a 
series of bright lines, pictures of the slit produced by light 
of these particular wave lengths, while between these bright 
lines lie dark spaces showing the absence from the radiant 
energy of light of intermediate wave lengths. Such a 
spectrum is shown in the central portion of Fig. 47, which, 

FIG. 49. A spectroscope attached to the Yerkes telescope. 

as we have already seen, is produced by the space between 
the carbons of the arc lamp. On the other hand, if the 
molecules are closely packed together under pressure they 
so interfere with each other as to give off a jumble of 
energy of all wave lengths, and this is translated by the 
spectroscope into a continuous ribbon of light with no dark 
spaces intervening, as in the upper and lower parts of Figs. 


47 and 48, produced by the incandescent solid carbons of 
the lamp. These two types are known as the continuous 
and discontinuous spectrum, and we may lay down the fol- 
lowing principle regarding them : 

A discontinuous spectrum, or bright-line spectrum as 
it is familiarly called, indicates that the molecules of the 
source of light are not crowded together, and therefore the 
light must come from an incandescent gas. A continuous 
spectrum shows only that the molecules are crowded to- 
gether, or are so numerous that the body to which they 
belong is not transparent and gives no further informa- 
tion. The body may be solid, liquid, or gaseous, but in 
the latter case the gas must be under considerable pres- 
sure or of great extent. 

A second principle is : The lines which appear in a spec- 
trum are characteristic of the source from which the light 
came e. g., the double line in the yellow part of the spec- 
trum at the extreme left in Fig. 47 is produced by sodium 
vapor in and around the electric arc and is never pro- 
duced by anything but sodium. When by laboratory ex- 
periments we have learned the particular set of lines 
corresponding to iron, we may treat the presence of these 
lines in another spectrum as proof that iron is present 
in the source from which the light came, whether that 
source be a white-hot poker in the next room or a star 
immeasurably distant. The evidence that iron is pres- 
ent lies in the nature of the light, and there is no reason 
to suppose that nature to be altered on the way from 
star to earth. It may, however, be altered by something 
happening to the source from which it comes e. g., chang- 
ing temperature or pressure may affect, and does affect, the 
spectrum which such a substance as iron emits, and we must 
be prepared to find the same substance presenting different 
spectra under different conditions, only these conditions 
must be greatly altered in order to produce radical changes 
in the spectrum. 



86. Wave lengths. To identi- 
fy a line as belonging to and pro- 
duced by iron or any other sub- 
stance, its position in the spec- 
trum i. e., its wave length must 
be very accurately determined, 
and for the identification of a sub- 
stance by means of its spectrum it 
is often necessary to determine ac- 
curately the wave lengths of many 
lines. A complicated spectrum 
may consist of hundreds or thou- 
sands of lines, due to the presence 
of many different substances in 
the source of light, and unless 
great care is taken in assigning 
the exact position of these lines 
in the spectrum, confusion and 
wrong identifications are sure to 
result. For the measurement of 
the required wave length a tenth 
meter ( 75) is the unit employed, 
and a scale of wave lengths ex- 
pressed in this unit is presented 
in Fig. 50. The accuracy with 
which some of these wave lengths 
are determined is truly astound- 
ing ; a ten-billionth of an inch ! 
These numerical wave lengths 
save all necessity for referring to 
the color of any part of the spec- 
trum, and pictures of spectra for 
scientific use are not usually 
printed in colors. 

87. Absorption spectra. There 
is another kind of spectrum, of 


greater importance than either of those above considered, 
which is well illustrated by the spectrum of sunlight (Fig. 
50). This is a nearly continuous spectrum crossed by nu- 
merous dark lines due to absorption of radiant energy in a 
comparatively cool gas through which it passes on its way 
to the spectroscope. Fraunhofer, who made the first care- 
ful study of spectra, designated some of the more conspicu- 
ous of these lines by letters of the alphabet which are shown 
in the plate, and which are still in common use as names 
for the lines, not only in the spectrum of sunlight but 
wherever they occur in other spectra. Thus the double 
line marked Z>, wave length 5893, falls at precisely the same 
place in the spectrum as does the double (sodium) line 
which we have already seen in the yellow part of the arc- 
light spectrum, which line is also called D and bears a very 
intimate relation to the dark D line of the solar spectrum. 

The student who has access to colored crayons should 
color one edge of Fig. 50 in accordance with the lettering 
there given and, so far as possible, he should make the 
transition from one color to the next a gradual one, as it is 
in the rainbow. 

Fig. 50 is far from being a complete representation of 
the spectrum of sunlight. Xot only does this spectrum ex- 
tend both to the right and to the left into regions invisible 
to the human eye, but within the limits of the figure, in- 
stead of the seventy-five lines there shown, there are liter- 
ally thousands upon thousands of lines, of which only the 
most conspicuous can be shown in such a cut as this. 

The dark lines which appear in the spectrum of sun- 
light can, under proper conditions, be made to appear in 
the spectrum of an arc light, and Fig. 51 shows a magnified 
representation of a small part of such a spectrum adjacent 
to the D (sodium) lines. Down the middle of each of these 
lines runs a black streak whose position (wave length) is 
precisely that of the D lines in the spectrum of sunlight, 
and whose presence is explained as follows : 


The very hot sodium vapor at the center of the arc gives 
off its characteristic light, which, shining through the outer 
and cooler layers of sodium vapor, is partially absorbed by 
these, resulting in a fine dark line corresponding exactly in 
position and wave length to the bright lines, and seen 
against these as a background, since the higher tempera- 
ture at the center of the arc tends to broaden the bright 
lines and make them diffuse. Similarly the dark lines in 
the spectrum of the sun (Fig. 50) point to the existence of 


FIG. 51. The lines reversed. 

a surrounding envelope of relatively cool gases, which absorb 
from the sunlight precisely those kinds of radiant energy 
which they would themselves emit if incandescent. The 
resulting dark lines in the spectrum are to be interpreted 
by the same set of principles which we have above applied 
to the bright lines of a discontinuous spectrum, and they 
may be used to determine the chemical composition of the 
sun, just as the bright lines serve to determine the chemi- 
cal elements present in the electric arc. With reference to 
the mode of their formation, bright-line and dark-line spec- 
tra are sometimes called respectively emission and absorp- 
tion spectra. 

88. Types of spectrum, The sun presents by far the 
most complex spectrum known, and Fig. 50 shows only a 
small number of the more conspicuous lines which appear 


in it. Spectra of stars, per contra, appear relatively simple, 
since their feeble light is insufficient to bring out faint 
details. In Chapters XIII and XIV there are shown types 
of the different kinds of spectra given by starlight, and 
these are to be interpreted by the principles above estab- 
lished. Thus the spectrum of the bright star ft Aurigse 
shows a continuous spectrum crossed by a few heavy ab- 
sorption lines which are known from laboratory experi- 
ments to be produced only by hydrogen. There must 
therefore be an atmosphere of relatively cool hydrogen 
surrounding this star. The spectrum of Pollux is quite 
similar to that of the sun and is to be interpreted as show- 
ing a physical condition similar to that of the sun, while 
the spectrum of a Herculis is quite different from either of 
the others. In subsequent chapters we shall have occasion 
to consider more fully these different types of spectrum. 

89. The Doppler principle. This important principle of 
the spectrum analysis is most readily appreciated through 
the following experiment : 

Listen to the whistle of a locomotive rapidly approach- 
ing, and observe how the pitch changes and the note be- 
comes more grave as the locomotive passes by and com- 
mences to recede. During the approach of the whistle 
each successive sound wave has a shorter distance to travel 
in coming to the ear of the listener than had its predeces- 
sor, and in consequence the waves appear to come in 
quicker succession, producing a higher note with a corre- 
spondingly shorter wave length than would be heard if the 
same whistle were blown with the locomotive at rest. On 
the other hand, the wave length is increased and the pitch 
of the note lowered by the receding motion of the whistle. 
A similar effect is produced upon the wave length of light 
by a rapid change of distance between the source from 
which it comes and the instrument which receives it, so 
that a diminishing distance diminishes very slightly the 
wave length of every line in the spectrum produced by the 


light, and an increasing distance increases these wave 
lengths, and this holds true whether the change of dis- 
tance is produced by motion of the source of light or by 
motion of the instrument which receives it. 

This change of wave length is sometimes described by 
saying that when a body is rapidly approaching, the lines 
of its spectrum are all displaced toward the violet end of 
the spectrum, and are correspondingly displaced toward the 
red end by a receding motion. The amount of this shift- 
ing, when it can be measured, measures the velocity of the 
body along the line of sight, but the observations are ex- 
ceedingly delicate, and it is only in recent years that it has 
been found possible to make them with precision. For this 
purpose there is made to pass through the spectroscope 
light from an artificial source which contains one or more 
chemical elements known to be present in the star which 
is to be observed, and the corresponding lines in the 
spectrum of this light and in the spectrum of the star 
are examined to determine whether they exactly match 
in position, or show, as they sometimes do, a slight dis- 
placement, as if one spectrum had been slipped past 
the other. The difficulty of the observations lies in the 
extremely small amount of this slipping, which rarely if 
ever in the case of a moving star amounts to one sixth part 
of the interval between the close parallel lines marked D 
in Fig. 50. The spectral lines furnished by the headlight 
of a locomotive running at the rate of a hundred miles 
per hour would be displaced by this motion less than one 
six-thousandth part of the space between the D lines, 
an amount absolutely imperceptible in the most powerful 
spectroscope yet constructed. But many of the celestial 
bodies have velocities so much greater than a hundred 
miles per hour that these may be detected and measured 
by means of the Doppler principle. 

90. Other instruments. Other instruments of impor- 
tance to the astronomer, but of which only casual mention 


can here be made, are the meridian-circle ; the transit, one 
form of which is shown in Fig. 52, and the zenith tele- 
scope, which furnish refined methods for making observa- 
tions similar in kind to those which the student has already 
learned to make with plumb line and protractor ; the sex- 
tant, which is pre-eminently the sailor's instrument for 
finding the latitude and longitude at sea, by measuring the 

FIG. 52. A combined transit instrument and zenith telescope. 

altitudes of sun and stars above the sea horizon ; the heli- 
ometer, which serves for the very accurate measurement of 
small angles, such as the angular distance between two stars 
not more than one or two degrees apart ; and the photom- 
eter, which is used for measuring the amount of light re- 
ceived from the celestial bodies. 



91. Results of observation with the unaided eye, The 
student who has made the observations of the moon which 
are indicated in Chapter III has in hand data from which 
much may be learned about the earth's satellite. Perhaps 
the most striking feature brought out by them is the mo- 
tion of the moon among the stars, always from west toward 
east, accompanied by that endless series of changes in 
shape and brightness new moon, first quarter, full moon, 
etc. whose successive stages we represent by the words, 
the phase of the moon. From his own observation the 
student should be able to verify, at least approximately, 
the following statements, although the degree of numer- 
ical precision contained in some of them can be reached 
only by more elaborate apparatus and longer study than he 
has given to the subject : 

A. The phase of the moon depends upon the distance 
apart of sun and moon in the sky, new moon coming 
when they are together, and full moon when they are as 
far apart as possible. 

B. The moon is essentially a round, dark body, giving 
off no light of its own, but shining solely by reflected sun- 
light. The proof of this is that whenever we see a part of 
the moon which is turned away from the sun it looks dark 
e. g., at new moon, sun and moon are in nearly the same 
direction from us and we see little or nothing of the moon, 
since the side upon which the sun shines is turned away 
from us. At full moon the earth is in line between sun 



From a photograph made at the Paris Observatory. 


and moon, and we see, round and bright, the face upon 
which the sun shines. At other phases, such as the quar- 
ters, the moon turns toward the earth a part of its night 
hemisphere and a part of its day hemisphere, but in gen- 
eral only that part which belongs to the day side of the 
moon is visible and the peculiar curved line which forms 
the boundary the " ragged edge," or terminator, as it is 
called, is the dividing line between day and night upon 
the moon. 

A partial exception to what precedes is found for a few 
days after new moon when the moon and sun are not very 
far apart in the sky, for then the whole round disk of the 
moon may often be seen, a small part of it brightly illu- 
minated by the sun and the larger part feebly illuminated 
by sunlight which fell first upon the earth and was by it 
reflected back to the moon, giving the pleasing effect which 
is sometimes called the old moon in the new moon's arms. 
The new moon i. e., the part illumined by the sun usu- 
ally appears to belong to a sphere of larger radius than the 
old moon, but this is purely a trick played by the eyes of 
the observer, and the effect disappears altogether in a tele- 
scope. Is there any similar effect in the few days before 
new moon ? 

C. The moon makes the circuit of the sky from a given 
star around to the same star again in a little more than 
27 days (27.32166), but the interval between successive new 
moons i. e., from the sun around to the sun again is 
more than 29 days (29.53059). This last interval, which is 
called a lunar month or synodical month, indicates what 
we have learned before that the sun has changed its place 
among the stars during the month, so that it takes the 
moon an extra two days to overtake him after having 
made the circuit of the sky, just as it takes the minute 
hand of a clock an extra 5 minutes to catch up with 
the hour hand after having made a complete circuit of the 


D. Wherever the moon may be in the sky, it turns 
always the same face toward the earth, as is shown by the 
fact that the dark markings which appear on its surface 
stand always upon (nearly) the same part of its disk. It 
does not always turn the same face toward the sun, for 
the boundary line between the illumined and unillumined 
parts of the moon shifts from one side to the other as the 
phase changes, dividing at each moment day from night 
upon the moon and illustrating by its slow progress that 
upon the moon the day and the month are of equal length 
(29.5 terrestrial days), instead of being time units of differ- 
ent lengths as with us. 

92. The moon's motion, The student should compare the 
results of his own observations, as well as the preceding 
section, with Fig. 53, in which the lines with dates printed 
on them are all supposed to radiate from the sun and to 
represent the direction from the sun of earth and moon 
upon the given dates which are arbitrarily assumed for 
the sake of illustration, any other set would do equally 
well. The black dots, small and large, represent the 
moon revolving about the earth, but having the circular 
path shown in Fig. 34 (ellipse) transformed by the earth's 
forward motion into the peculiar sinuous line here shown. 
With respect to both earth and sun, the moon's orbit 
deviates but little from a circle, since the sinuous curve 
of Fig. 53 follows very closely the earth's orbit around 
the sun and is almost identical with it. For clearness 
of representation the distance between earth and moon 
in the figure has been made ten times too great, and to 
get a proper idea of the moon's orbit with reference to 
the sun, we must suppose the moon moved up toward the 
earth until its distance from the line of the earth's orbit is 
only a tenth part of what it is in the figure. When this is 
done, the moon's path becomes almost indistinguishable 
from that of the earth, as may be seen in the figure, where 
the attempt has been made to show both lines, and it 

PIG. 53. Motion of moon and earth relative to the sun. 


is to be especially noted that this real orbit of the moon is 
everywhere concave toward the sun. 

The phase presented by the moon at different parts of 
its path is indicated by the row of circles at the right, and 
the student should show why a new moon is associated 
with June 30th and a full moon with July 15th, etc. What 
was the date of first quarter ? Third quarter ? 

We may find in Fig. 53 another effect of the same 
kind as that noted above in C. Between noon, June 30th, 
and noon, July 3d, the earth makes upon its axis three com- 
plete revolutions with respect to the sun, but the meridian 
which points toward the moon at noon on June 30th will 
not point toward it at noon on July 3d, since the moon has 
moved into a new position and is now 37 away from the 
meridian. Verify this statement by measuring, in Fig. 53, 
with the protractor, the moon's angular distance from the 
meridian at noon on July 3d. When will the meridian 
overtake the moon ? 

93. Harvest moon. The interval between two successive 
transits of the meridian past the moon is called a lunar 
day, and the student should show from the figure that on 
the average a lunar day is 51 minutes longer than a solar 
day i. e., upon the average each day the moon comes to 
the meridian 51 minutes of solar time later than on the 
day before. It is also true that on the average the moon 
rises and sets 51 minutes later each day than on the day 
before. But there is a good deal of irregularity in the 
retardation of the time of moonrise and moonset, since 
the time of rising depends largely upon the particular 
point of the horizon at which the moon appears, and be- 
tween two days this point may change so much on account 
of the moon's orbital motion as to make the retardation 
considerably greater or less than its average value. In 
northern latitudes this effect is particularly marked in the 
month of September, when the eastern horizon is nearly 
parallel with the moon's apparent path in the sky, and near 


the time of full moon in that month the moon rises on 
several successive nights at nearly the same hour, and in 
less degree the same is true for October. This highly 
convenient arrangement of moonlight has caused the full 
moons of these two months to be christened respectively 
the Harvest Moon and the Hunter's Moon. 

94. Size and mass of the moon. It has been shown in 
Chapter I how the distance of the moon from the earth 
may be measured and its diameter determined by means of 
angles, and without enlarging upon the details of these ob- 
servations, we note as their result that the moon is a globe 
2,163 miles in diameter, and distant from the earth on the 
average about 240,000 miles. But, as we have seen in 
Chapter VII, this distance changes to the extent of a few 
thousand miles, sometimes less, sometimes greater, mainly 
on account of the elliptic shape of the moon's orbit about 
the earth, but also in part from the disturbing influence of 
other bodies, such as the sun, which pull the moon to and 
fro, backward and forward, to quite an appreciable extent. 

From the known diameter of the moon it is a matter of 
elementary geometry to derive in miles the area of its sur- 
face and its volume or solid contents. Leaving this as an 
exercise for the student, we adopt the earth as the standard 
of comparison and find that the diameter of the moon is 
rather more than a quarter, u /g," that of the earth, the area 
of its surface is a trifle more than -^ that of the earth, 
and its volume a little more than V of the earth's. So 
much is pure geometry, but we may combine with it some 
mechanical principles which enable us to go a step farther 
and to " weigh " the moon i. e., determine its mass and 
the average density of the material of which it is made. 

We have seen that the moon moves around the sun in a 
path differing but little from the smooth curve shown in 
Fig. 53, with arrows indicating the direction of motion, 
and it would follow absolutely such a smooth path were 
it not for the attraction of the earth, and in less degree 


of some of the other planets, which swing it about first 
to one side then to the other. But action and reaction 
are equal ; the moon pulls as strongly upon the earth 
as does the earth upon the moon, and if earth and moon 
were of equal mass, the deviation of the earth from the 
smooth curve in the figure would be just as large as that 
of the moon. It is shown in the figure that the moon does 
displace the earth from this curve, and we have only to 
measure the amount of this displacement of the earth and 
compare it with the displacement suffered by the moon to 
find how much the mass of the one exceeds that of the 
other. It may be seen from the figure that at first quarter, 
about July 7th, the earth is thrust ahead in the direction 
of its orbital motion, while at the third quarter, July 22d, it 
is pulled back by the action of the moon, and at all times 
it is more or less displaced by this action, so that, in order 
to be strictly correct, we must amend our former statement 
about the moon moving around the earth and make it read, 
Both earth and moon revolve around a point on line be- 
tween their centers. This point is called their center of 
gravity, and the earth and the moon both move in ellipses 
having this center of gravity at their common focus. 
Compare this with Kepler's First Law. These ellipses are 
similarly shaped, but of very different size, corresponding 
to Newton's third law of motion (Chapter IV), so that the 
action of the earth in causing the small moon to move 
around a large orbit is just equal to the reaction of the 
moon in causing the larger earth to move in the smaller 
orbit. This is equivalent to saying that the dimensions of 
the two orbits are inversely proportional to the masses of 
the earth and the moon. 

By observing throughout the month the direction from 
the earth to the sun or to a near planet, such as Mars or 
Venus, astronomers have determined that the diameter of 
the ellipse in which the earth moves is about 5,850 miles, 
so that the distance of the earth from the center of gravity 


is 2,925 miles, and the distance of the moon from it is 
240,000 2,925 = 237,075. We may now write in the form 
of a proportion 

Mass of earth : Mass of moon : : 237,075 : 2,925, 

and find from it that the mass of the earth is 81 times 
as great as the mass of the moon i. e., leaving kind and 
quality out of account, there is enough material in the 
earth to make 81 rnoons. We may note in this con- 
nection that the diameter of the earth, 7,926 miles, is 
greater than the diameter of the monthly orbit in which 
the moon causes it to move, and therefore the center of 
gravity of earth and moon always lies inside the body of 
the earth, about 1,000 miles below the surface. 

95. Density of the moon. It is believed that in a general 
way the moon is made of much the same kind of material 
which goes to make up the earth metals, minerals, rocks, 
etc. and a part of the evidence upon which this belief is 
based lies in the density of the moon. By density of a 
substance we mean the amount of it which is contained in 
a given volume i. e., the weight of a bushel or a cubic 
centimeter of the stuff. The density of chalk is twice as 
great as the density of water, because a cubic centimeter 
of chalk weighs twice as much as an equal volume of 
water, and similarly in other cases the density is found by 
dividing the mass or weight of the body by the mass or 
weight of an equal volume of water. 

We know the mass of the earth ( 40), and knowing 
the mass of a cubic foot of water, it is easy, although a 
trifle tedious, to compute what would be the mass of a vol- 
ume of water equal in size to the earth. The quotient 
obtained by dividing one of these masses by the other (mass 
of earth -5- mass of water) is the average density of the ma- 
terial composing the earth, and we find numerically that 
this is 5.6 i. e., it would take 5.6 water earths to attract as 
strongly as does the real one. From direct experiment we 


know that the average density of the principal rocks which 
make up the crust of the earth is only about half of this, 
showing that the deep-lying central parts of the earth are 
denser than the surface parts, as we should expect them to 
be, because they have to bear the weight of all that lies 
above them and are compressed by it. 

Turning now to the moon, we find in the same way as 
for the earth that its average density is 3.4 as great as that 
of water. 

96. Force of gravity upon the moon. This number, 3.4, 
compared with the 5.6 which we found for the earth, shows 
that on the whole the moon is made of lighter stuff than is 
the body of the earth, and this again is much what we should 
expect to find, for weight, the force which tends to com- 
press the substance of the moon, is less there than here. 
The weight of a cubic yard of rock at the surface of either 
earth or moon is the force with which the earth or moon 
attracts it, and this by the law of gravitation is for the 


and for the moon 



w = k. _?L; 
(1081) 2 

from which we find by division 

TF/3963X 2 
W = 81 - 

The cubic yard of rock, which upon the earth weighs two 
tons, would, if transported to the moon, weigh only one 
third of a ton, and would have only one sixth as much 
influence in compressing the rocks below it as it had upon 
the earth. Xote that this rock when transported to the 
moon would be still attracted by the earth and would have 
weight toward the earth, but it is not this of which we are 


speaking ; by its weight in the moon we mean the force 
with which the moon attracts it. Making due allowance 
for the difference in compression produced by weight, we 
may say that in general, so far as density goes, the moon is 
very like a piece of the earth of equal mass set off by itself 

97. Albedo. In another respect the lunar stuff is like 
that of which the earth is made : it reflects the sunlight in 
much the same way and to the same amount. The con- 
trast of light and dark areas on the moon's surface shows, 
as we shall see in another section, the presence of different 
substances upon the moon which reflect the sunlight in 
different degrees. This capacity for reflecting a greater or 
less percentage of the incident sunlight is called albedo 
(Latin, whiteness), and the brilliancy of the full moon might 
lead one to suppose that its albedo is very great, like that 
of snow or those masses of summer cloud which we call 
thunderheads. But this is only an effect of contrast with 
the dark background of the sky. The same moon by day 
looks pale, and its albedo is, in fact, not very different 
from that of our common rocks weather-beaten sandstone 
according to Sir John Herschel so that it would be pos- 
sible to build an artificial moon of rock or brick which 
would shine in the sunlight much as does the real moon. 

The effect produced by the differences of albedo upon 
the moon's face is commonly called the " man in the moon," 
but, like the images presented by glowing coals, the face in 
the moon is anything which we choose to make it. Among 
the Chinese it is said to be a monkey pounding rice ; in 
India, a rabbit ; in Persia, the earth reflected as in a mir- 
ror, etc. 

98. Librations. We have already learned that the moon 
turns always the same face toward the earth, and we have 
now to modify this statement and to find that here, as in 
so many other cases, the thing we learn first is only ap- 
proximately true and needs to be limited or added to or 


modified in some way. In general, Nature is too complex 
to be completely understood at first sight or to be per- 
fectly represented by a simple statement. In Fig. 55 we 
have two photographs of the moon, taken nearly three years 
apart, the right-hand one a little after first quarter and the 
left-hand one a little before third quarter. They there- 
fore represent different parts of the moon's surface, but 
along the ragged edge the same region is shown on both 
photographs, and features common to both pictures may 
readily be found e. g., the three rings which form a right- 
angled triangle about one third of the way down from the 
top of the cut, and the curved mountain chain just below 
these. If the moon turned exactly the same face toward 
us in the two pictures, the distance of any one of these 
markings from any part of the moon's edge must be the 
same in both pictures ; but careful measurement will show 
that this is not the case, and that in the left-hand pic- 
ture the upper edge of the moon is tipped toward us and 
the lower edge away from us, as if the whole moon had 
been rotated slightly about a horizontal line and must be 
turned back a little (about 7) in order to match perfectly 
the other part of the picture. 

This turning is called a libration, and it should be borne 
in mind that the moon librates not only in the direction 
above measured, north and south, but also at right angles 
to this, east and west, so that we are able to see a little 
farther around every part of the moon's edge than would 
be possible if it turned toward us at all times exactly the 
same face. But in spite of the librations there remains on 
the farther side of the moon an area of 6,000,000 square 
miles which is forever hidden from us, and of whose char- 
acter we have no direct knowledge, although there is no 
reason to suppose it very different from that which is visi- 
ble, despite the fact that some of the books contain quaint 
speculations to the contrary. The continent of South 
America is just about equal in extent to this unknown re- 



gion, while North America is a fair equivalent for all the 
rest of the moon's surface, both those central parts which 
are constantly visible, and the zone around the edge whose 
parts sometimes come into sight and are sometimes hidden. 

An interesting consequence of the peculiar rotation of 
the moon is that from our side of it the earth is always 
visible. Sun, stars, and planets rise and set there as well 
as here, but to an observer on the moon the earth swings 
always overhead, shifting its position a few degrees one 
way or the other on account of the libration but running 
through its succession of phases, new earth, first quarter, 
etc., without ever going below the horizon, provided the 
observer is anywhere near the center of the moon's disk. 

99. Cause of librations. That the moon should librate 
is by no means so remarkable a fact as that it should at all 
times turn very nearly the 
same face toward the earth. 
This latter fact can have but 
one meaning : the moon re- 
volves about an axis as does 
the earth, but the time re- 
quired for this revolution is 
just equal to the time re- 
quired to make a revolution 
in its orbit. Place two coins 
upon a table with their heads 
turned toward the north, as 
in Fig. 54, and move the 
smaller one around the larger 

in such a way that its face shall always look away from the 
larger one. In making one revolution in its orbit the head 
on this small coin will be successively directed toward every 
point of the compass, and when it returns to its initial 
position the small coin will have made just one revolu- 
tion about an axis perpendicular to the plane of its or- 
bit. In no other way can it be made to face always away 

FIG. 54. Illustrating the moon's 


from the figure at the center of its orbit while moving 
around it. 

We are now in a position to understand the moon's 
librations, for, if the small coin at any time moves faster or 
slower in its orbit than it turns about its axis, a new side 
will be turned toward the center, and the same may happen 
if the central coin itself shifts into a new position. This is 
what happens to the moon, for its orbital motion, like that 
of Mercury (Fig. 16), is alternately fast and slow, and in 
addition to this there are present other minor influences, 
such as the fact that its rotation axis is not exactly per- 
pendicular to the plane of its orbit ; in addition to this the 
observer upon the earth is daily carried by its rotation from 
one point of view to another, etc., so that it is only in a gen- 
eral way that the rotation upon the axis and motion in the 
orbit keep pace with each other. In a general way a cable 
keeps a ship anchored in the same place, although wind and 
waves may cause it to " librate " about the anchor. 

How the moon came to have this exact equality be- 
tween its times of revolution and rotation constitutes a 
chapter of its history upon which we shall not now enter ; 
but the equality having once been established, the mechan- 
ism by which it is preserved is simple enough. 

The attraction of the earth for the moon has very 
slightly pulled the latter out of shape ( 42), so that the 
particular diameter, which points toward the earth, is a lit- 
tle longer than any other, and thus serves as a handle which 
the earth lays hold of and pulls down into its lowest possible 
position i. e., the position in which it points toward the 
center of the earth. Just how long this handle is, remains 
unknown, but it may be shown from the law of gravitation 
that less than a hundred yards of elongation would suffice 
for the work it has to do. 

100. The moon as a world. Thus far we have considered 
the moon as a satellite of the earth, dependent upon the 
earth, and interesting chiefly because of its relation to it. 


But the moon is something more than this ; it is a world in 
itself, very different from the earth, although not wholly 
unlike it. The most characteristic feature of the earth's 
surface is its division into land and water, and 'nothing of 
this kind can be found upon the moon. It is true that the 
first generation of astronomers who studied the moon with 
telescopes fancied that the large dark patches shown in 
Fig. 55 were bodies of water, and named them oceans, 
seas, lakes, and ponds, and to the present day we keep 
those names, although it is long since recognized that these 
parts of the moon's surface are as dry as any other. Their 
dark appearance indicates a different kind of material from 
that composing the lighter parts of the moon, material 
with a different albedo, just as upon the earth we have 
light-colored and dark-colored rocks, marble and slate, 
which seen from the moon must present similar contrasts 
of brightness. Although these dark patches are almost 
the only features distinguishable with the unaided eye, it 
is far otherwise in the telescope or the photograph, espe- 
cially along the ragged edge where great numbers of rings 
can be seen, which are apparently depressions in the moon 
and are called craters. These we find in great number 
all over the moon, but, as the figure shows, they are seen 
to the best advantage near the terminator i. e., the divid- 
ing line between day and night, since the long shadows 
cast here by the rising or setting sun bring out the details 
of the surface better than elsewhere. Carefully examine 
Fig. 55 with reference to these features. 

Another feature which exists upon both earth and 
moon, although far less common there than here, is illus- 
trated in the chain of mountains visible near the termina- 
tor, a little above the center of the moon in both parts of 
Fig. 55. This particular range of mountains, which is 
called the Lunar Apennines, is by far the most prominent 
one upon the moon, although others, the Alps and Cauca- 
sus, exist. But for the most part the lunar mountains 


stand alone, each by itself, instead of being grouped into 
ranges, as on the earth. Note in the figure that some of 
the lunar mountains stretch out into the night side of the 
moon, their peaks projecting up into the sunlight, and 
thus becoming visible, while the lowlands are buried in the 

A subordinate feature of the moon's surface is the sys- 
tem of rays which seem to radiate like spokes from some 
of the larger craters, extending over hill and valley some- 
times for hundreds of miles. A suggestion of these rays 
may be seen in Fig. 55, extending from the great crater 
Copernicus a little southwest of the end of the Apennines, 
but their most perfect development is to be seen at the 
time of full moon around the crater Tycho, which lies near 
the south pole of the moon. Look for them with an opera 

Another and even less conspicuous feature is furnished 
by the rills, which, under favorable conditions of illumina- 
tion, appear like long cracks on the moon's surface, per- 
haps analogous to the canons of our Western country. 

101. The map of the moon. Fig. 55 furnishes a fairly 
good map of a limited portion of the moon near the termi- 
nator, but at the edges little or no detail can be seen. This 
is always true ; the whole of the moon can not be seen to 
advantage at any one time, and to remedy this we need to 
construct from many photographs or drawings a map which 
shall represent the several parts of the moon as they appear 
at their best. Fig. 56 shows such a map photographed from 
a relief model of the moon, and representing the principal 
features of the lunar surface in a way they can never be 
seen simultaneously. Perhaps its most striking feature is 
the shape of the craters, which are shown round in the cen- 
tral parts of the map and oval at the edges, with their long 
diameters parallel to the moon's edge. This is, of course, 
an eif ect of the curvature of the moon's surface, for we look 
very obliquely at the edge portions, and thus see their for- 



mations much foreshortened in the direction of the moon's 

The north and south poles of the moon are at the top 
and bottom of the map respectively, and a mere inspection 

FIG. 56. Eelief map of the moon's surface. After NASMTTH and CARPENTER. 

of the regions around them will show how much more 
rugged is the southern hemisphere of the moon than the 
northern. It furnishes, too, some indication of how numer- 
ous are the lunar craters, and how in crowded regions they 
overlap one another. 

The student should pick out upon the map those features 
which he has learned to know in the photograph (Fig. 55) 
the Apennines, Copernicus, and the continuation of the 
Apennines, extending into the dark part of the moon. 


102. Size of the lunar features. We may measure dis- 
tances here in the same way as upon a terrestrial map, re- 
membering that near the edges the scale of the map is very 
much distorted parallel to the moon's diameter, and meas- 
urements must not be taken in this direction, but may be 
taken parallel to the edge. Measuring with a millimeter 
scale, we find on the map for the diameter of the crater 
Copernicus, 2.1 millimeters. To turn this into the diam- 
eter of the real Copernicus in miles, we measure upon the 
same map the diameter of the moon, 79.7 millimeters, and 
then have the proportion 

Diameter of Copernicus in miles : 2,163 : : 2.1 : 79.7, 

which when solved gives 57 miles. The real diameter of 
Copernicus is a trifle over 56 miles. At the eastern edge 

FIG. 57. Mare Imbrium. Photographed at Goodsell Observatory. 

of the moon, opposite the Apennines, is a large oval spot 
called the Mare Crisium (Latin, ma-re = sea). Measure its 



length. The large crater to the northwest of the Apen- 
nines is called Archimedes. Measure its diameter both in 
the map and in the photograph (Fig. 55), and see how the 
two results agree. The true diameter of this crater, east 
and west, is very approximately 50 miles. The great smooth 
surface to the west of Archimedes is the Mare Imbrium. Is 

it larger or smaller than 
Lake Superior ? Fig. 
57 is from a photo- 
graph of the Mare Im- 
brium, and the amount 
of detail here shown at 
the bottom of the sea 
is a sufficient indica- 
tion that, in this case 
at least, the water has 
been drawn off, if in- 
deed any was ever pres- 

Fig. 58 is a repre- 
sentation of the Mare 
Crisium at a time when 
night was beginning to 
encroach upon its east- 
ern border, and it 
serves well to show the 
rugged character of the ring-shaped wall which incloses 
this area. 

With these pictures of the smoother parts of the moon's 
surface we may compare Fig. 59, which shows a region 
near the north pole of the moon, and Fig. 60, giving an 
early morning view of Archimedes and the Apennines. 
Note how long and sharp are the shadows. 

103. The moon's atmosphere. Upon the earth the sun 
casts no shadows so sharp and black as those of Fig. 60, 
because his rays are here scattered and reflected in all direc- 

FIG. 58. Mare Crisium. 
Lick Observatory photographs. 



tions by the dust and vapors of the atmosphere ( 51), 
so that the place from which direct sunlight is cut off 
is at least partially illumined by this reflected light. The 
shadows of Fig. 60 show that upon the moon it must be 
otherwise, and suggest that if the moon has any atmosphere 
whatever, its density must be utterly insignificant in com- 
parison with that of the earth. In its motion around the 
earth the moon fre- 
quently eclipses stars 
(occults is the tech- 
nical word), and if the 
moon had an atmos- 
phere such as is shown 
in Fig. 61, the light 
from the star A must 
shine through this at- 
mosphere just before 
the moon's advancing 
body cuts it off, and it 
must be refracted by 
the atmosphere so that 
the star would appear 
in a slightly different 
direction (nearer to 
B) than before. The 
earth's atmosphere re- 
fracts the starlight 

under such circumstances by more than a degree, but no 
one has been able to find in the case of the moon any effect 
of this kind amounting to even a fraction of a second of 
arc. While this hardly justifies the statement sometimes 
made that the moon has no atmosphere, we shall be entire- 
ly safe in saying that if it has one at all its density is less 
than a thousandth part of that of the earth's atmosphere. 
Quite in keeping with this absence of an atmosphere is the 
fact that clouds never float over the surface of the moon. 

FIG. 59. Illustrating the rugged character of the 
moon's surface. NASMYTH and CARPENTER. 



Its features always stand out hard and clear, without any 
of that haze and softness of outline which our atmosphere 
introduces into all terrestrial landscapes. 

104. Height of the lunar mountains. Attention has al- 
ready been called to the detached mountain peaks, which 

in Fig. 55 pro- 
long the range of 
Apennines into 
the lunar night. 
These are the be- 
ginnings of the 
Caucasus moun- 
tains, and from 
the photograph 
we may measure 
as follows the 
height to which 
they rise above 
the surrounding 
level of the moon : 
Fig. 62 repre- 
sents a part of 

the lunar surface along the boundary line between night 
and day, the horizontal line at the top of the figure repre- 
senting a level ray of sunlight which just touches the moon 
at T and barely illuminates the top of the mountain, M, 
whose height, /i, is to be determined. If we let R stand for 
the radius of the moon and s for the distance, T M, we shall 
have in the right-angled triangle M T C, 

FIG. 60. Archimedes and Apennines. 

and we need only to measure s that is, the distance from 
the terminator to the detached mountain peak to make 
this equation determine ^, since R is already known, being 
half the diameter of the moon 1,081 miles. Practically it 
is more convenient to use instead of this equation another 



form, which the student who is expert in algebra may show 
to be very nearly equivalent to it : 

s 2 
h (miles) = ^-77^, or h (feet) = 2.44 s 2 . 

FIG. 61. Occultations and the moon's 

The distance s must be expressed in miles in all of these 
equations. In Fig. 55 the distance from the terminator 
to the first detached peak 
of the Caucasus moun- 
tains is 1.7 millimeters = 
52 miles, from which we 
find the height of the 
mountain to be 1.25 
miles, or 6,600 feet. 

Two things, however, 
need to be borne in mind 
in this connection. On 
the earth we measure the 

heights of mountains above sea level, while on the moon 
there is no sea, and our 6,600 feet is simply the height of 

the mountain top above 
the level of that par- 
ticular point in the 
terminator, from which 
we measure its distance. 
So too it is evident 
from the appearance of 
things, that the sun- 
light, instead of just 
touching the top of the 
particular mountain 
whose height we have 
measured, really extends 
some little distance down from its summit, and the 6,600 
feet is therefore the elevation of the lowest point on the 
mountains to which the sunlight reaches. The peak itself 


FIG. 62. Determining the height of a lunar 


may be several hundred feet higher, and our photograph 
must be taken at the exact moment when this peak appears 
in the lunar morning or disappears in the evening if we are 
to measure the altitude of the mountain's summit. Meas- 
ure the height of the most northern visible mountain of 
the Caucasus range. This is one of the outlying spurs of 
the great mountain Calippus, whose principal peak, 19,000 
feet high, is shown in Fig. 55 as the brightest part of the 
Caucasus range. 

The highest peak of the lunar Apennines, Huyghens, 
has an altitude of 18,000 feet, and the Leibnitz and Doerfel 
Mountains, near the south pole of the moon, reach an alti- 
tude 50 per cent greater than this, and are probably the 
highest peaks on the moon. This falls very little short of 
the highest mountain on the earth, although the moon is 
much smaller than the earth, and these mountains are con- 
siderably higher than anything on the western continent of 
the earth. 

The vagueness of outline of the terminator makes it 
difficult to measure from it with precision, and somewhat 
more accurate determinations of the heights of lunar 
mountains can be obtained by measuring the length of 
the shadows which they cast, and the depths of craters 
may also be measured by means of the shadows which fall 
into them. 

105. Craters. Fig. 63 shows a typical lunar crater, and 
conveys a good idea of the ruggedness of the lunar land- 
scape. Compare the appearance of this crater with the 
following generalizations, which are based upon the accurate 
measurement of many such : 

A. A crater is a real depression in the surface of the 
moon, surrounded usually by an elevated ring which rises 
above the general level of the region outside, while the bot- 
tom of the crater is about an equal distance below that 

B. Craters are shallow, their diameters ranging from 


five times to more than fifty times their depth. Archi- 
medes, whose diameter we found to be 50 miles, has an 
average depth of about 4,000 feet below the crest of its 
surrounding wall, and is relatively a shallow crater. . 

FIG. 63. A typical lunar crater. NASMYTH and CARPENTER. 

C. Craters frequently have one or more hills rising 
within them which, however, rarely, if ever, reach up to the 
level of the surrounding wall. 

D. Whatever may have been the mode of their forma- 
tion, the craters can not have been produced by scooping 
out material from the center and piling it up to make the 
wall, for in three cases out of four the volume of the exca- 
vation is greater than the volume of material contained in 
the wall. 

106. Moon and earth. We have gone far enough now 
to appreciate both the likeness and the unlikeness of the 
moon and earth. They may fairly enough be likened to 
offspring of the same parent who have followed very differ- 
ent careers, and in the fullness of time find themselves in 
very different circumstances. The most serious point of 
difference in these circumstances is the atmosphere, which 
gives to the earth a wealth of phenomena altogether lack- 


ing in the moon. Clouds, wind, rain, snow, dew, frost, and 
hail are all dependent upon the atmosphere and can not be 
found where it is not. There can be nothing upon the 
moon at all like that great group of changes which we 
call weather, and the unruffled aspect of the moon's face 
contrasts sharply with the succession of cloud and sunshine 
which the earth would present if seen from the moon. 

The atmosphere is the chief agent in the propagation 
of sound, and without it the moon must be wrapped in 
silence more absolute than can be found upon the surface 
of the earth. So, too, the absence of an atmosphere shows 
that there can be no water or other liquid upon the moon, 
for if so it would immediately evaporate and produce a 
gaseous envelope which we have seen does not exist. With 
air and water absent there can be of course no vegetation 
or life of any kind upon the moon, and we are compelled 
to regard it as an arid desert, utterly waste. 

107. Temperature of the moon. A characteristic feature 
of terrestrial deserts, which is possessed in exaggerated de- 
gree by the moon, is the great extremes of temperature to 
which they and it are subject. Owing to its slow rotation 
about its axis, a point on the moon receives the solar radia- 
tion uninterruptedly for more than a fortnight, and that 
too unmitigated by any cloud or vaporous covering. Then 
for a like period it is turned away from the sun and allowed 
to cool off, radiating into interplanetary space without hin- 
drance its accumulated store of heat. It is easy to see that 
the range of temperature between day and night must be 
much greater under these circumstances than it is with us 
where shorter days and clouded skies render day and night 
more nearly alike, to say nothing of the ocean whose waters 
serve as a great balance wheel for equalizing temperatures. 
Just how hot or how cold the moon becomes is hard to 
determine, and very different estimates are to be found in 
the books. Perhaps the most reliable of these are fur- 
nished by the recent researches of Professor Very, whose 


experiments lead him to conclude that " its rocky surface at 
midday, in latitudes where the sun is high, is probably hotter 
than boiling water and only the most terrible of earth's des- 
erts, where the burning sands blister the skin, and men, 
beasts, and birds drop dead, can approach a noontide on 
the cloudless surface of our satellite. Only the extreme 
polar latitudes of the moon can have an endurable tem- 
perature by day, to say nothing of the night, when we 
should have to become troglodytes to preserve ourselves 
from such intense cold." 

While the night temperature of the moon, even very 
soon after sunset, sinks to something like 200 below zero 
on the centigrade scale, or 320 below zero on the Fahren- 
heit scale, the lowest known temperature upon the earth, 
according to General Greely, is 90 Fahr. below zero, re- 
corded in Siberia in January, 1885. 

Winter and summer are not markedly different upon 
the moon, since its rotation axis is nearly perpendicular to 
the plane of the earth's orbit about the sun, and the sun 
never goes far north or south of the moon's equator. The 
month is the one cycle within which all seasonal changes in 
its physical condition appear to run their complete course. 

108. Changes in the moon. It is evidently idle to look 
for any such changes in the condition of the moon's sur- 
face as with us mark the progress of the seasons or 
the spread of civilization over the wilderness. But minor 
changes there may be, and it would seem that the violent 
oscillations of temperature from day to night ought to have 
some effect in breaking down and crumbling the sharp 
peaks and crags which are there so common and so pro- 
nounced. For a century past astronomers have searched 
carefully for changes of this kind the filling up of some 
crater or the fall of a mountain peak; but while some 
things of this kind have been reported from time to time, 
the evidence in their behalf has not been altogether conclu- 
sive. At the present time it is an open question whether 



changes of this sort large enough to be seen from the 
earth are in progress. A crater much less than a mile 
wide can be seen in the telescope, but it is not easy to 
tell whether so minute an object has changed in size or 
shape during a year or a decade, and even if changes are 
seen they may be apparent rather than real. Fig. 64 con- 
tains two views of the crater Archimedes, taken under a 


FIG. 64. Archimedes in the lunar morning and afternoon. WEINEK. 

morning and an afternoon sun respectively, and shows a 
very pronounced difference between the two which pro- 
ceeds solely from a difference of illumination. In the pres- 
ence of such large fictitious changes astronomers are slow 
to accept smaller ones as real. 

r ' "^ It is this absence of change that is responsible for the 

\ rugged and sharp-cut features of the moon which continue 

\ substantially as they were made, while upon the earth rain 

I and frost are continually wearing down the mountains and 

\ spreading their substance upon the lowland in an unending 

\ process of smoothing off the roughnesses of its surface. 

\ Upon the moon this process is almost if not wholly want- 

} ing, and the moon abides to-day much more like its primi- 

; tive condition than is the earth. 

109. The moon's influence upon the earth. There is a 
"widespread popular belief that in many ways the moon exer- 


cises a considerable influence upon terrestrial affairs : that 
it affects the weather for good or ill, that crops must be 
planted and harvested, pigs must be killed, and timber cut 
at the right time of the moon, etc. Our common word 
lunatic means moonstruck i. e., one upon whom the moon 
has shone while sleeping. There is not the slightest scien- 
tific basis for any of these beliefs, and astronomers every- 
where class them with tales of witchcraft, magic, and pop- 
ular delusion. For the most part the moon's influence 
upon the earth is limited to the light which it sends and 
the effect of its gravitation, chiefly exhibited in the ocean 
tides. We receive from the moon a very small amount of 
second-hand solar heat and there is also a trifling magnetic 
influence, but neither of these last effects comes within the 
range of ordinary observation, and we shall not go far wrong 
in saying that, save the moonlight and the tides, every sup- 
posed lunar influence upon the earth is either fictitious or 
too small to be readily detected. 



110. Dependence of the earth upon the sun. There is no 
better introduction to the study of the sun than Byron's 
Ode to Darkness, beginning with the lines 

" I dreamed a dream 
That was not all a dream. 
The bright sun was extinguished," 

and proceeding to depict in vivid words the consequences 
of this extinction. The most matter-of-fact language of 
science agrees with the words of the poet in declaring the 
earth's dependence upon the sun for all those varied forms 
of energy which make it a fit abode for living beings. The 
winds blow and the rivers run ; the crops grow, are gathered 
and consumed, by virtue of the solar energy. Factory, 
locomotive, beast, bird, and the human body furnish types 
of machines run by energy derived from the sun ; and the 
student will find it an instructive exercise to search for 
kinds of terrestrial energy which are not derived either 
directly or indirectly from the sun. There are a few such, 
but they are neither numerous nor important. 

111. The sun's distance from the earth. To the astron- 
omer the sun presents problems of the highest consequence 
and apparently of very diverse character, but all tending 
toward the same goal : the framing of a mechanical explana- 
tion of the sun considered as a machine, what it is, and 
how it does its work. In the forefront of these problems 
stand those numerical determinations of distance, size, 


THE SUN 179 

mass, density, etc., which we have already encountered in 
connection with the moon, but which must here be dealt 
with in a different manner, because the immensely greater 
distance of the sun makes impossible the resort to any such 
simple method as the triangle used for determining the 
moon's distance. It would be like determining the distance' 
of a steeple a mile away by observing its 'direction first 
from one eye, then from the other ; too short a base for the 
triangle. In one respect, however, we stand upon a better 
footing than in the case of the moon, for the mass of the 
earth has already been found (Chapter IV) as a fractional 
part of the sun's mass, and we have only to invert the 
fraction in order to find that the sun's mass is 329,000 
times that of the earth and moon combined, or 333,000 
times that of the earth alone. 

If we could rely implicitly upon this number we might 
make it determine for us the distance of the sun through 
the law of gravitation as follows : It was suggested in 38 
that Newton proved Kepler's three laws to be imperfect 
corollaries from the law of gravitation, requiring a little 
amendment to make them strictly correct, and below we 
give in the form of an equation Kepler's statement of the 
Third Law together with Newton's amendment of it. In 
these equations 

T = Periodic time of any planet ; 

a = One half the major axis of its orbit ; 

m = Its mass ; 

M = The mass of the sun ; 

Tc The gravitation constant corresponding to the par- 
ticular set of units in which J 7 , #, m, and M are expressed. 

(Kepler) ~ = h ; (Newton) ^-= k (M+ m). 

Kepler's idea was : For every planet which moves 
around the sun, a 3 divided by T 2 always gives the same 
quotient, h ; and he did not concern himself with the sig- 


nificance of this quotient further than to note that if the 
particular a and T which belong to any planet e. g., the 
earth be taken as the units of length and time, then the 
quotient will be 1. Newton, on the other hand, attached 
a meaning to the quotient, and showed that it is equal to 
the product obtained by multiplying the sum of the two 
masses, planet and sun, by a number which is always the 
same when we are dealing with the action of gravitation, 
whether it be between the sun and planet, or between 
moon and earth, or between the earth and a roast of beef 
in the butcher's scales, provided only that we use always 
the same units with which to measure times, distances, 
and masses. 

Numerically, Newton's correction to Kepler's Third 
Law does not amount to much in the motion of the 
planets. Jupiter, which shows the greatest effect, makes 
the circuit of his orbit in 4,333 days instead of 4,335, which 
it would require if Kepler's law were strictly true. But in 
another respect the change is of the utmost importance, 
since it enables us to extend Kepler's law, which relates 
solely to the sun and its planets, to other attracting bodies, 
such as the earth, moon, and stars. Thus for the moon's 
motion around the earth we write 

from which we may find that, with the units here employed, 
the earth's mass as the unit of mass, the mean solar day as 
the unit of time, and the mile as the unit of distance 

k = 1830 X 10 10 . 

If we introduce this value of Jc into the corresponding 
equation, which represents the motion of the earth around 
the sun, we shall have 

= 1830 X 10 10 (333,000 + 1), 


THE SUN 181 

where the large number in the parenthesis represents the 
number of times the mass of the sun is greater than the 
mass of the earth. We shall find by solving this equation 
that , the mean distance of the sun from the earth, is 
very approximately 93,000,000 miles. 

113. Another method of determining the sun's distance, N 
This will be best appreciated by a reference to Fig. 16. It 
appears here that the earth makes its nearest approach to the 
orbit of Mars in the month of August, and if in any August 
Mars happens to be in opposition, its distance from the earth 
will be very much less than the distance of the sun from 
the earth, and may be measured by methods not unlike 
those which served for the moon. If now the orbits of 
Mars and the earth were circles having their centers at the 
sun this distance between them, which we may represent by 
Z>, would be the difference of the radii of these orbits 

D = a" - ', i(ff ' 

where the accents " ' represent Mars and the earth respec- 
tively. Kepler's Third Law furnishes the relation 

and since the periodic times of the earth and Mars, T', T", 
are known to a high degree of accuracy, these two equa- 
tions are sufficient to determine the two unknown quanti- 
ties, 0', a" i. e., the distance of the sun from Mars as well 
as from the earth. The first of these equations is, of 
course, not strictly true, on account of the elliptical shape 
of the orbits, but this can be allowed for easily enough. 

In practice it is found better to apply this method of 
determining the sun's distance through observations of an 
asteroid rather than observations of Mars, and great inter- 
est has been aroused among astronomers by the discovery, 
in 1898, of an asteroid, or planet, Eros, which at times comes 
much closer to the earth than does Mars or any other heav- 


enly body except the moon, and which will at future oppo- 
sitions furnish a more accurate determination of the sun's 
distance than any hitherto available. Observations for this 
purpose are being made at the present time (October, 1900). 

Many other methods of measuring the sun's distance 
have been devised by astronomers, some of them extremely 
ingenious and interesting, but every one of them has its 
weak point e. g., the determination of the mass of the 
earth in the first method given above and the measurement 
of D in the second method, so that even the best results at 
present are uncertain to the extent of 200,000 miles or more, 
and astronomers, instead of relying upon any one method, 
must use all of them, and take an average of their results, 
According to Professor Harkness, this average value is 92,- 
796,950 miles, and it seems certain that a line of this length 
drawn from the earth toward the sun would end somewhere 
within the body of the sun, but whether on the nearer or 
the farther side of the center, or exactly at it, no man 

114. Parallax and distance. It is quite customary among 
astronomers to speak of the sun's parallax, instead of its 
distance from the earth, meaning by parallax its difference 
of direction as seen from the center and surface of the 
earth i. e., the angle subtended at the sun by a radius of 
the earth placed at right angles to the line of sight. The 
greater the sun's distance the smaller will this angle be, 
and it therefore makes a substitute for the distance which 
has the advantage of being represented by a small number, 
8".8, instead of a large one. 

The books abound with illustrations intended to help 
the reader comprehend how great is a distance of 93,000,000 
miles, but a single one of these must suffice here. To ride 
100 miles a day 365 days in the year would be counted a 
good bicycling record, but the rider who started at the be- 
ginning of the Christian era and rode at that rate toward 
the sun from the year 1 A. D. down to the present moment 



would not yet have reached his destination, although his 
journey would be about three quarters done. He would 
have crossed the orbit of Venus about the time of Charle- 
magne, and that of 
Mercury soon after 
the discovery of 

115. Size and 
density of the sun, 
Knowing the dis- 
tance of the sun, 
it is easy to find 
from the angle sub- 
tended by its di- 
ameter (32 minutes 
of arc) that the 
length of that di- 
ameter is 865,000 
miles. We recall 
in this connection 
that the diameter 
of the moon's or- 
bit is only 480,000 
miles, but little 
more than half the 
diameter of the 
sun, thus affording 
abundant room in- 
side the sun, and 

to spare, for the moon to perform the monthly revolution 
about its orbit, as shown in Fig. 65. 

In the same manner in which the density of the moon 
was found from its mass and diameter, the student may 
find from the mass and diameter of the sun given above 
that its mean density is 1.4 times that of water. This is 
about the same as the density of gravel or soft coal, and 

FIG. 65. The sun's size. YOUNG. 


is just about one quarter of the average density of the 

We recall that the small density of the moon was ac- 
counted for by the diminished weight of objects upon it, 
but this explanation can not hold in the case of the sun, 
for not only is the density less but the force of gravity 
(weight) is there 28 times as great as upon the earth. The 
athlete who here weighs 175 pounds, if transported to the 
surface of the sun would weigh more than an elephant does 
here, and would find his bones break under his own weight 
if his muscles were strong enough to hold him upright. 
The tremendous pressure exerted by gravity at the surface 
of the sun must be surpassed below the surface, and as it 
does not pack the material together and make it dense, we 
are driven to one of two conclusions : Either the stuff of 
which the sun is made is altogether unlike that of the 
earth, not so readily compressed by pressure, or there is 
some opposing influence at work which more than balances 
the effect of gravity and makes the solar stuff much lighter 
than the terrestrial. 

116. Material of which the sun is made. As to the first 
of these alternatives, the spectroscope comes to our aid and 
shows in the sun's spectrum (Fig. 50) the characteristic 
line marked D, which we know always indicates the pres- 
ence of sodium and identifies at least one terrestrial sub- 
stance as present in the sun in considerable quantity. The 
lines marked C and F are produced by hydrogen, which is 
one of the constituents of water, E shows calcium to be 
present in the sun, b magnesium, etc. In this way it has 
been shown that about one half of our terrestrial elements, 
mainly the metallic ones, are present as gases on or near the 
sun's surface, but it must not be inferred that elements not 
found in this way are absent from the sun. They may be 
there, probably are there, but the spectroscopic proof of 
their presence is more difficult to obtain. Professor Row- 
land, who has been prominent in the study of the solar 

THE SUN 185 

spectrum, says : " Were the whole earth heated to the tem- 
perature of the sun, its spectrum would probably resemble 
that of the sun very closely." 

Some of the common terrestrial elements found in the 
sun are : 

Aluminium. Nickel. 

Calcium. Potassium. 

Carbon. Silicon. 

Copper. Silver. 

Hydrogen. Sodium. 

Iron. Tin. 

Lead. Zinc. 
Oxygen (?) 

Whatever differences of chemical structure may exist 
between the sun and the earth, it seems that we must re- 
gard these bodies as more like than unlike to each other in 
substance, and we are brought back to the second of our 
alternatives : there must be some influence opposing the 
force of gravity and making the substance of the sun light 
instead of heavy, and we need not seek far to find it in 

117. The heat of the sun. That the sun is hot is too 
evident to require proof, and it is a familiar fact that heat 
expands most substances and makes them less dense. The 
sun's heat falling upon the earth expands it and diminishes 
its density in some small degree, and we have only to im- 
agine this process of expansion continued until the earth's 
diameter becomes 58 per cent larger than it now is, to find 
the earth's density reduced to a level with that of the sun. 
Just how much the temperature of the earth must be raised 
to produce this amount of expansion we do not know, 
neither do we know accurately the temperature of the sun, 
but there can be no doubt that heat is the cause of the 
sun's low density and that the corresponding temperature 
is very high. 

Before we inquire more closely into the sun's tempera- 


ture, it will be well to draw a sharp distinction between the 
two terms heat and temperature, which are often used as if 
they meant the same thing. Heat is a form of energy 
which may be found in varying degree in every substance, 
whether warm or cold a block of ice contains a consider- 
able amount of heat while temperature corresponds to our 
sensations of warm and cold, and measures the extent to 
which heat is concentrated in the body. It is the amount 
of heat per molecule of the body. A barrel of warm water 
contains more heat than the flame of a match, but its tem- 
perature is not so high. Bearing in mind this distinction, 
we seek to determine not the amount of heat contained in 
the sun but the sun's temperature, and this involves the 
same difficulty as does the question, What is the tempera- 
ture of a locomotive ? It is one thing in the fire box and 
another thing in the driving wheels, and still another at 
the headlight ; and so with the sun, its temperature is cer- 
tainly different in different parts one thing at the center 
and another at the surface. Even those parts which we 
see are covered by a veil of gases which produce by absorp- 
tion the dark lines of the solar spectrum, and seriously 
interfere both with the emission of energy from the sun 
and with our attempts at measuring the temperature of 
those parts of the surface from which that energy streams. 

In view of these and other difficulties we need not be 
surprised that the wildest discordance has been found in 
estimates of the solar temperature made by different investi- 
gators, who have assigned to it values ranging from 1,400 C. 
to more than 5,000,000 C. Quite recently, however, im- 
proved methods and a better understanding of the problem 
have brought about a better agreement of results, and it 
now seems probable that the temperature of the visible 
surface of the sun lies somewhere between 5,000 and 
10,000 C., say 15,000 of the Fahrenheit scale. 

118. Determining the sun's temperature. One ingenious 
method which has been used for determining this tempera- 

THE SUN 187 

ture is based upon the principle stated above, that every 
object, whether warm or cold, contains heat and gives it 
off in the form of radiant energy. The radiation from a 
body whose temperature is lower than 500 C. is made up 
exclusively of energy whose wave length, is greater than 
7,600 tenth meters, and is therefore invisible to the eye, al- 
though a thermometer or even the human hand can often 
detect it as radiant heat. A brick wall in the summer sun- 
shine gives oif energy which can be felt as heat but can 
not be seen. When such a body is further heated it con- 
tinues to send off the same kinds (wave lengths) of energy 
as before, but new and shorter waves are added to its radia- 
tion, and when it begins to emit energy of wave length 7,500 
or 7,600 tenth meters, it also begins to shine with a dull- 
red light, which presently becomes brighter and less ruddy 
and changes to white as the temperature rises, and waves 
of still shorter length are thereby added to the radiation. 
We say, in common speech, the body becomes first red hot 
and then white hot, and we thus recognize in a general 
way that the kind or color of the radiation which a body 
gives off is an index to its temperature. The greater the 
proportion of energy of short wave lengths the higher is 
the temperature of the radiating body. In sunlight the 
maximum of brilliancy to the eye lies at or near the wave 
length, 5,600 tenth meters, but the greatest intensity of 
radiation of all kinds (light included) is estimated to fall 
somewhere between green and blue in the spectrum at or 
near the wave length 5,000 tenth meters, and if we can ap- 
ply to this wave length Paschen's law temperature reck- 
oned in degrees centigrade from the absolute zero is always 
equal to the quotient obtained by dividing the number 
27,000,000 by the wave length corresponding to maximum 
radiation we shall find at once for the absolute tempera- 
ture of the sun's surface 5,400 C. 

Paschen's law has been shown to hold true, at least 
approximately, for lower temperatures and longer wave 


lengths than are here involved, but as it is not yet certain 
that it is strictly true and holds for all temperatures, too 
great reliance must not be attached to the numerical result 
furnished by it. 

119. The sun's surface. A marked contrast exists be- 
tween the faces of sun and moon in respect of the amount 


FIG. 66. The sun, August 11, 1894. Photographed at the Goodsell Observatory. 

of detail to be seen upon them, the sun showing nothing 
whatever to correspond with the mountains, craters, and 
seas of the moon. The unaided eye in general finds in the 
sun only a blank bright circle as smooth and unmarked as 
the surface of still water, and even the telescope at first 
sight seems to show but little more. There may usually be 
found upon the sun's face a certain number of black patches 
called sun spots, such as are shown in Figs. 66 to 69, and 

THE SUN 189 

occasionally these are large enough to be seen through a 
smoked glass without the aid of a telescope. When seen 
near the edge of the sun they are quite frequently accom- 
panied, as in Fig. 69, by vague patches called faculce (Latin, 
facula = a little torch), which look a little brighter than 
the surrounding parts of the sun. So, too, a good photo- 


FIG. 67. The sun, August 14, 1894. Photographed at the Goodsell Observatory. 

graph of the sun usually shows that the central parts of 
the disk are rather brighter than the edge, as indeed we 
should expect them to be, since the absorption lines in the 
sun's spectrum have already taught us that the visible sur- 
face of the sun is enveloped by invisible vapors which in 
some measure absorb the emitted light and render it feebler 
at the edge where it passes through a greater thickness of 
this envelope than at the center (see Fig. 70), where it is 



shown that the energy coming from the edge of the sun to 
the earth has to traverse a much longer path inside the 
vapors than does that coming from the center. 

Examine the sun spots in the four photographs, Figs. 
66 to 69, and note that the two spots which appear at the 
extreme left of the first photograph, very much distorted 

FIG. 68. The sun, August 18, 1894. Photographed at the Goodsell Observatory. 

and foreshortened by the curvature of the sun's surface, are 
seen in a different part of the second picture, and are not 
only more conspicuous but show better their true shape. 

120. The sun's rotation. The changed position of these 
spots shows that the sun rotates about an axis at right 
angles to the direction of the spot's motion, and the posi- 
tion of this axis is shown in the figure by a faint line ruled 
obliquely across the face of the sun nearly north and south 



THE SL T N 191 

in each of the four photographs. This rotation in the 
space of three days has carried the spots from the edge 
halfway to the center of the disk, and the student should 
note the progress of the spots in the two later photographs, 
that of August 21st showing them just ready to disappear 
around the farther edge of the sun. 

FIG. 69. The sun, August 21, 1894. Photographed at the Goodsell Observatory. 

Plot accurately in one of these figures the positions of 
the spots as shown in the other three, and observe whether 
the path of the spots across the sun's face is a straight line. 
Is there any reason why it should not be straight ? 

These four pictures may be made to illustrate many 
things about the sun. Thus the sun's axis is not parallel 
to that of the earth, for the letters N S mark the direction 
of a north and south line across the face of the sun, and 


this line, of course, is parallel to the earth's axis, while it is 
evidently not parallel to the sun's axis. The group of 

spots took more than 
ten days to move 
across the sun's face, 
and as at least an 
equal time must be 
required to move 
around the opposite 
side of the sun, it is 
evident that the pe- 

FIG. 70. Absorption at the sun's edge. 

nod of the sun s ro- 
tation is something more than 20 days. It is, in fact, a 
little more than 25 days, for this same group of spots reap- 
peared again on the left-hand edge of the sun on Septem- 
ber 5th. 

121. Sun spots. Another significant fact comes out 
plainly from the photographs. The spots are not perma- 
nent features of the sun's face, since they changed their 
size and shape very appreciably in the few days covered by 
the pictures. Compare particularly the photographs of 
August 14th and August 18th, where the spots are least 
distorted by the curvature of the sun's surface. By Sep- 
tember 16th this group of spots had disappeared absolutely 
from the sun's face, although when at its largest the group 
extended more than 80,000 miles in length, and several of 
the individual spots were large enough to contain the 
earth if it had been dropped upon them. From Fig. 67 
determine in miles the length of the group on August 
14th. Fig. 71 shows an enlarged view of these spots as 
they appeared on August 17th, and in this we find some 
details not so well shown in the preceding pictures. The 
larger spots consist of a black part called the nucleus or 
umbra (Latin, shadow), which is surrounded by an irregu- 
lar border called the penumbra (partial shadow), which is 
intermediate in brightness between the nucleus and the 



surrounding parts of the sun. It should not be inferred 
from the picture that the nucleus is really black or even 
dark. It shines, in 
fact, with a brilliancy 
greater than that of 
an electric lamp, but 
the background fur- 
nished by the sun's 
surface is so much 
brighter that by con- 
trast with it the nu- 
cleus and penumbra 
appear relatively dark. 
The bright shining 
surface of the sun, the 
background for the 
spots, is called the 
photosphere (Greek, 
light sphere), and, as Fig. 71 shows, it assumes under a 
suitable magnifying power a mottled aspect quite different 

FIG. 71. Sun spots, August 17, 1894. 
Goodsell Observatory. 

FIG. 72. Sun spot of March 5, 1873. From LANGLKY, The New Astronomy. 
By permission of the publishers. 

from the featureless expanse shown in the earlier pictures. 
The photosphere is, in fact, a layer of little clouds with 



darker spaces between them, and the fine detail of these 
clouds, their complicated structure, and the way in which, 
when projected against the background of a sun spot, they 
produce its penumbra, are all brought out in Fig. 72. 
Note that the little patch in one corner of this picture 
represents North and South America drawn to the same 
scale as the sun spots. 

122. Faculse. We have seen in Fig. 69 a few of the 
bright spots called faculae. At the telescope or in the 
ordinary photograph these can be seen only at the edge of 

the sun, because else- 
where the background 
furnished by the pho- 
tosphere is so bright 
that they are lost in it. 
It is possible, however, 
by an ingenious appli- 
cation of the spectro- 
scope to break up the 
sunlight into a spec- 
trum in such a way as 
to diminish the bright- 
ness of this back- 
ground, much more 
than the brightness of 
the faculae is dimin- 
ished, and in this way to obtain a photograph of the sun's 
surface which shall show them wherever they occur, and 
such a photograph, showing faintly the spectral lines, is 
reproduced in Fig. 73. The faculae are the bright patches 
which stretch inconspicuously across the face of the sun, 
in two rather irregular belts with a comparatively empty 
lane between them. This lane lies along the sun's equa- 
tor, and it is upon either side of it between latitudes 5 
and 40 that faculae seem to be produced. It is significant 
of their connection with sun spots that the spots occur 

FIG. 73. Spectroheliograph, showing distribu- 
tion of faculae upon the sun. HALE. 


in these particular zones and are rarely found outside 

123. Invisible parts of the sun. The Corona. Thus far 
we have been dealing with parts of the sun that may be 
seen and photographed under all ordinary conditions. 

FIG. 75. Eclipse of April 16, 1893. SCHAEBERLE. 

But outside of and surrounding these parts is an envelope, 
or rather several envelopes, of much greater extent than 
the visible sun. These envelopes are for the most part 
invisible save at those times when the brighter central 
portions of the sun are hidden in a total eclipse. 

Fig. 74 is from a drawing, and Figs. 75 and 76 are from 
eclipse photographs showing this region, in which the most 



conspicuous object is the halo of soft light called the corona, 
that completely surrounds the sun but is seen to be of dif- 

FIG. 76. Eclipse of January 21, 1898. CAMPBELL. 

fering shapes and differing extent at the several eclipses 
here shown, although a large part of these apparent differ- 
ences is due to technical difficulties in photographing, and 
reproducing an object with outlines so vague as those of 
the corona. The outline of the corona is so indefinite and 
its outer portions so faint that it is impossible to assign to 
it precise dimensions, but at its greatest extent it reaches 
out for several millions of miles and fills a space more than 
twenty times as large as the visible part of the sun. De- 
spite its huge bulk, it is of most unsubstantial character, 



FIG. 77. Solar prominence of March 25, 
1895. HALE. 

an airy nothing through which comets have been known 
to force their way around the sun from one side to the 
other, literally for millions of miles, without having their 

course influenced or their 
velocity checked to any 
appreciable extent. This 
would hardly be possible 
if the density even at the 
bottom of the corona were 
greater than that of the 
best vacuum which we 
are able to produce in lab- 
oratory experiments. It 
seems odd that a vacuum 
should give off so bright 
a light as the coronal pic- 
tures show, and the exact character of that light and the 
nature of the corona are still subjects of dispute among 
astronomers, although it is generally agreed that, in part 
at least, its light is ordinary sunlight faintly reflected 
from the widely scattered molecules composing the sub- 
stance of the corona. It is also probable that in part the 
light has its origin in the corona itself. A curious and at 
present unconfirmed result announced by one of the ob- 
servers of the eclipse of May 28, 1900, is that the corona is 
not hot, its effective temperature being lower than that of 
the instrument used for the observation. 

124. The chromosphere. Between the corona and the 
photosphere there is a thin separating layer called the 
chromosphere (Greek, color sphere), because when seen at 
an eclipse it shines with a brilliant red light quite unlike 
anything else upon the sun save the prominences which are 
themselves only parts of the chromosphere temporarily 
thrown above its surface, as in a fountain a jet of water is 
thrown up from the basin and remains for a few moments 
suspended in mid-air. Not infrequently in such a foun- 



tain foreign matter is swept up by the rush of the water 
dirt, twigs, small fish, etc.^-and in like manner the promi- 
nences often carry along with them parts of the under- 
lying layers of the sun, photosphere, faculae, etc., which 
reveal their presence in the prominence by adding their 
characteristic lines to the spectrum, like that of the chro- 
mosphere, which the prominence presents when they are 
absent. None of the eclipse photographs (Figs. 74 to 76) 
show the chromosphere, because the color effect is lacking 
in them, but a great curving prominence may be seen near 
the bottom of Fig. 75, and smaller ones at other parts of 
the sun's edge. 

125. Prominences. Fig. 77 shows upon a larger scale one 
of these prominences rising to a height of 160,000 miles 
above the photo- 
sphere ; and an- 
other photograph, 
taken 18 minutes 
later, but not re- 
produced here, 
showed the same 
prominence grown 
in this brief inter- 
val to a stature 
of 280,000 miles. 
These pictures 
were not taken 
during an eclipse, 
but in full sun- 
light, using the 
same spectroscop- 
ic apparatus which 
was employed in 
connection with 

the faculae to diminish the brightness of the background 
without much enfeebling the brilliancy of the prominence 

FIG. 78. A solar prominence. HALE. 


itself. The dark base from which the prominence seems 
to spring is not the sun's edge, but a part of the appara- 
tus used to cut off the direct sunlight. 

Fig. 78 contains a series of photographs of another 
prominence taken within an interval of 1 hour 47 minutes 
and showing changes in size and shape which are much 
more nearly typical of the ordinary prominence than was 
the very unusual change in the case of Fig. 77. 

The preceding pictures are from photographs, and with 
them the student may compare Fig. 79, which is con- 

FIG. 79. Contrasted forms of solar prominences. ZOELLNEB. 

structed from drawings made at the spectroscope by the 
German astronomer Zoellner. The changes here shown 
are most marked in the prominence at the left, which is 
shaped like a broken tree trunk, and which appears to be 
vibrating from one side to the other like a reed shaken 
in the wind. Such a prominence is frequently called an 
eruptive one, a name suggested by its appearance of hav- 
ing been blown out from the sun by something like an 
explosion, while the prominence at the right in this series 
of drawings, which appears much less agitated, is called by 
contrast with the other a quiescent prominence. These 
quiescent prominences are, as a rule, much longer-lived 

THE SUN 201 

than the eruptive ones. One more picture of prominences 
(Fig. 80) is introduced to show the continuous stretch of 
chromosphere out of which they spring. 

Prominences are seen only at the edge of the sun, be- 
cause it is there alone that the necessary background can 
be obtained, but they must occur at the center of the sun 
and elsewhere quite as well as at the edge, and it is prob- 
able that quiescent prominences are distributed over all 

FIG. 80. Prominences and chromosphere. HALE. 

parts of the sun's surface, but eruptive prominences show 
a strong tendency toward the regions of sun spots and 
faculae as if all three were intimately related phenomena. 

126. The sun as a machine. Thus far we have consid- 
ered the anatomy of the sun, dissecting it into its several 
parts, and our next step should be a consideration of its 
physiology, the relation of the parts to each other, and 
their function in carrying on the work of the solar organ- 
ism, but this step, unfortunately, must be a lame one. 
The science of astronomy to-day possesses no comprehen- 
sive and well-established theory of this kind, but looks to 
the future for the solution of this the greatest pending 


problem of solar physics. Progress has been made toward 
its solution, and among the steps of this progress that we 
shall have to consider, the first and most important is the 
conception of the sun as a kind of heat engine. 

In a steam engine coal is burned under the boiler, and 
its chemical energy, transformed into heat, is taken up by 
the water and delivered, through steam as a medium, to 
the engine, which again transforms and gives it out as 
mechanical work in the turning of shafts, the driving of 
machinery, etc. Now, the function of the sun is exactly 
opposite to that of the engine and boiler : it gives out, 
instead of receiving, radiant energy ; but, like the engine, 
it must be fed from some source ; it can not be run upon 
nothing at all any more than the engine can run day after 
day without fresh supplies of fuel under its boiler. We 
know that for some thousands of years the sun has been 
furnishing light and heat to the earth in practically un- 
varying amount, and not to the earth alone, but it has 
been pouring forth these forms of energy in every direc- 
tion, without apparent regard to either use or economy. 
Of all the radiant energy given off by the sun, only two 
parts out of every thousand million fall upon any planet 
of the solar system, and of this small fraction the earth 
takes about one tenth for the maintenance of its varied 
forms of life and action. Astronomers and physicists have 
sought on every hand for an explanation of the means by 
which this tremendous output of energy is maintained 
century after century without sensible diminution, and 
have come with almost one mind to the conclusion that 
the gravitative forces which reside in the sun's own mass 
furnish the only adequate explanation for it, although 
they may be in some small measure re-enforced by minor 
influences, such as the fall of meteoric dust and stones 
into the sun. 

Every boy who has inflated a bicycle tire with a hand 
pump knows that the pump grows warm during the opera- 

THE SUN 203 

tion, on account of the compression of the air within the 
cylinder. A part of the muscular force (energy) expended 
in working the pump reappears in the heat which warms 
both air and pump, and a similar process is forever going on 
in the sun, only in place of muscular force we must there sub- 
stitute the tremendous attraction of gravitation, 23 times 
as great as upon the earth. " The matter in the interior 
of the sun must be as a shuttlecock between the stupen- 
dous pressure and the enormously high temperature," the 
one tending to compress and the other to expand it, but 
with this important difference between them : the tem- 
perature steadily tends to fall as the heat energy is wasted 
away, while the gravitative force suffers no corresponding 
diminution, and in the long run must gain the upper 
hand, causing the sun to shrink and become more dense. 
It is this progressive shrinking and compression of its 
molecules into a smaller space which supplies the energy 
contained in the sun's output of light and heat. Accord- 
ing to Lord Kelvin, each centimeter of shrinkage in the 
sun's diameter furnishes the energy required to keep up 
its radiation for something more than an hour, and,, on 
account of the sun's great distance, the shrinkage might 
go on at this rate for many centuries without producing 
any measurable effect in the sun's appearance. 

127. Gaseous constitution of the sun. But Helmholtz's dy- 
namical theory of the maintenance of the sun's heat, which 
we are here considering, includes one essential feature 
that is not sufficiently stated above. In order that the 
explanation may hold true, it is necessary that the sun 
should be in the main a gaseous body, composed from cen- 
ter to circumference of gases instead of solid or liquid 
parts. Pumping air warms the bicycle pump in a way 
that pumping water or oil will not. 

The high temperature of the sun itself furnishes suffi- 
cient reason for supposing the solar material to be in the 
gaseous state, but the gas composing those parts of the 


sun below the photosphere must be very different in some 
of its characteristics from the air or other gases with which 
we are familiar at the earth, since its average density is 
1,000 times as great as that of air, and its consistence and 
mechanical behavior must be more like that of honey or tar 
than that of any gas with which we are familiar. It is 
worth noting, however, that if a hole were dug into the 
crust of the earth to a depth of 15 or 20 miles the air at 
the bottom of the hole would be compressed by that above 
it to a density comparable with that of the solar gases. 

128. The sun's circulation. It is plain that under the 
conditions which exist in the sun the outer portions, which 
can radiate their heat freely into space, must be cooler than 
the inner central parts, and this difference of temperature 
must set up currents of hot matter drifting upward and out- 
ward from within the sun and counter currents of cooler 
matter settling down to take its place. So, too, there must 
be some level at which the free radiation into outer space 
chills the hot matter sufficiently to condense its less refrac- 
tory gases into clouds made up of liquid drops, just as on a 
cloudy day there is a level in our own atmosphere at which 
the vapor of water condenses into liquid drops which form 
the thin shell of clouds that hovers above the earth's surface, 
while above and below is the gaseous atmosphere. In the 
case of the sun this cloud layer is always present and is that 
part which we have learned to call the photosphere. Above 
the photosphere lies the chromosphere, composed of gases 
less easily liquefied, hydrogen is the chief one, while be- 
tween photosphere and chromosphere is a thin layer of me- 
tallic vapors, perhaps indistinguishable from the top crust 
of the photosphere itself, which by absorbing the light 
given off from the liquid photosphere produces the greater 
part of the Fraunhofer lines in the solar spectrum. 

From time to time the hot matter struggling up from 
below breaks through the photosphere and, carrying with 
it a certain amount of the metallic vapors, is launched into 

THE SUN 205 

the upper and cooler regions of the snn, where, parting 
with its heat, it falls back again upon the photosphere and 
is absorbed into it. It is altogether probable that the 
corona is chiefly composed of fine particles ejected from 
the sun with velocities sufficient to carry them to a height 
of millions of miles, or even sufficient to carry them off 
never to return. The matter of the corona must certainly 
be in a state of the most lively agitation, its particles being 
alternately hurled up from the photosphere and falling 
back again like fireworks, the particles which make up the 
corona of to-day being quite a different set from those of 
yesterday or last week. It seems beyond question that 
the prominences and faculae too are produced in some 
way by this up-and-down circulation of the sun's matter, 
and that any mechanical explanation of the sun must be 
worked out along these lines ; but the problem is an exceed- 
ingly difficult one, and must include and explain many other 
features of the sun's activity of which only a few can be con- 
sidered here. 

129. The sun-spot period. Sun spots come and go, and 
at best any particular spot is but short-lived, rarely lasting 
more than a month or two, and more often its duration is 
a matter of only a few days. They are not equally numer- 
ous at all times, but, like swarms of locusts, they seem to 
come and abound for a season and then almost to disap- 
pear, as if the forces which produced them were of a peri- 
odic character alternately active and quiet. The effect of 
this periodic activity since 1870 is shown in Fig. 81, where 
the horizontal line is a scale of times, and the distance of 
the curve above this line for any year shows the relative 
number of spots which appeared upon the sun in that 
year. This indicates very plainly that 1870, 1883, and 
1893 were years of great sun-spot activity, while 1879 and 
1889 were years in which few spots appeared. The older 
records, covering a period of two centuries, show the same 
fluctuations in the frequency of sun spots and from these 



records curves (which may be found in Young's, The Sun) 
have been plotted, showing a succession of waves extend- 
ing back for many years. 

The sun-spot period is the interval of time from the 
crest or hollow of one wave to the corresponding part of 
the next one, and on the average this appears to be a little 
more than eleven years, but is subject to considerable varia- 
tion. In accordance with this period there is drawn in 

1870 1SSO 1890 4900 19iO 

FIG. 81. The curve of sun-spot frequency. 

broken lines at the right of Fig. 81 a predicted continua- 
tion of the sun-spot curve for the first decade of the twen- 
tieth century. The irregularity shown by the three pre- 
ceding waves is such that we must not expect the actual 
course of future sun spots to correspond very closely to 
the prediction here made ; but in a general way 1901 and 
1911 will probably be years of few sun spots, while they 
will be numerous in 1905, but whether more or less numer- 
ous than at preceding epochs of greatest frequency can not 
be foretold with any approach to certainty so long as we 
remain in our present ignorance of the causes which make 
the sun-spot period. 

Determine from Fig. 81 as accurately as possible the 
length of the sun-spot period. It is hard to tell the ex- 
act position of a crest or hollow of the curve. Would it 
do to draw a horizontal line midway between top and bot- 
tom of the curve and determine the length of the period 



from its intersections with the curve e. g., in 1874 and 

130. The sun-spot zones. It has been already noted that 
sun spots are found only in certain zones of latitude upon 
the sun, and that faculse and eruptive prominences abound 

FIG. 82. Illustrating change of the sun-spot zones. 

in these zones more than elsewhere, although not strictly 
confined to them. We have now to note a peculiarity of 
these zones which ought to furnish a clew to the sun's 
mechanism, although up to the present time it has not 
been successfully traced out. Just before a sun-spot mini- 
mum the few spots which appear are for the most part 
clustered near the sun's equator. As these spots die out 


two new groups appear, one north the other south of the 
sun's equator and about 25 or 30 distant from it, and as 
the period advances toward a maximum these groups shift 
their positions more and more toward the equator, thus ap- 
proaching each other but leaving between them a vacant 
lane, which becomes steadily narrower until at the close 
of the period, when the next minimum is at hand, it 
reaches its narrowest dimensions, but does not altogether 
close up even then. In Fig. 82 these relations are shown 
for the period falling between 1879 and 1890, by means of 
the horizontal lines ; for each year one line in the north- 
ern and one in the southern hemisphere of the sun, their 
lengths being proportional to the number of spots which 
appeared in the corresponding hemisphere during the year, 
and their positions on the sun's disk showing the average 
latitude of the spots in question. It is very apparent from 
the figure that during this decade the sun's southern hemi- 
sphere was much more active than the northern one in the 
production of spots, and this appears to be generally the 
case, although the difference is not usually as great as in 
this particular decade. 

131. Influence of the sun-spot period. Sun spots are cer- 
tainly less hot than the surrounding parts of the sun's sur- 
face, and, in view of the intimate dependence of the earth 
upon the solar radiation, it would be in no way surprising 
if their presence or absence from the sun's face should 
make itself felt in some degree upon the earth, raising and 
lowering its temperature and quite possibly affecting it in 
other ways. Ingenious men have suggested many such 
kinds of influence, which, according to their investigations, 
appear to run in cycles of eleven years. Abundant and 
scanty harvests, cyclones, tornadoes, epidemics, rainfall, 
etc., are among these alleged effects, and it is possible that 
there may be a real connection between any or all of them 
and the sun-spot period, but for the most part astronomers 
are inclined to hold that there is only one case in which 


the evidence is strong enough to really establish a connec- 
tion of this kind. The magnetic condition of the earth 
and its disturbances, which are called magnetic storms, do 
certainly follow in a very marked manner the course of 
sun-spot activity, and perhaps there should be added to 
this the statement that auroras (northern lights) stand in 
close relation to these magnetic disturbances and are most 
frequent at the times of sun-spot maxima. 

Upon the sun, however, the influence of the spot period 
is not limited to things in and near the photosphere, but 
extends to the outermost limits of the corona. Determine 
from Fig. 81 the particular part of the sun-spot period 
corresponding to the date of each picture of the corona 
and note how the pictures which were taken near times of 
sun-spot minima present a general agreement in the shape 
and extent of the corona, while the pictures taken at a time 
of maximum activity of the sun spots show a very differ- 
ently shaped and much smaller corona. 

132. The law of the sun's rotation. We have seen in a 
previous part of the chapter how the time required by the 
sun to make a complete rotation upon its axis may be de- 
termined from photographs showing the progress of a spot 
or group of spots across its disk, and we have now to add 
that when this is done systematically by means of many 
spots situated in different solar latitudes it leads to a 
very peculiar and extraordinary result. Each particular 
parallel of latitude has its own period of rotation different 
from that of its neighbors on either side, so that there can 
be no such thing as a fixed geography of the sun's surface. 
Every part of it is constantly taking up a new position 
with respect to every other part, much as if the Gulf of 
Mexico should be south of the United States this year, 
southeast of it next year, and at the end of a decade should 
have shifted around to the opposite side of the earth from 
us. A meridian of longitude drawn down the Mississippi 
Valley remains always a straight line, or, rather, great 


circle, upon the surface of the earth, while Fig. 83 shows 
what would become of such a meridian drawn through 
the equatorial parts of the sun's disk. In the first dia- 
gram it appears as a straight line running down the mid- 
dle of the sun's disk. Twenty-five days later, when the 
same face of the sun comes back into view again, after 
making a complete revolution about the axis, the equa- 
torial parts will have moved so much faster and far- 
ther than those in higher latitudes that the meridian 

FIG. 83. Effect of the sun's peculiar rotation in warping a meridian, originally 


will be warped as in the second diagram, and still more 
warped after another and another revolution, as shown in 
the figure. 

At least such is the case if the spots truly represent the 
way in which the sun turns round. There is, however, a 
possibility that the spots themselves drift with varying 
speeds across the face of the sun, and that the differences 
which we find in their rates of motion belong to them 
rather than to the photosphere. Just what happens in the 
regions near the poles is hard to say, for the sun spots only 
extend about halfway from the equator to the poles, and 
the spectroscope, which may be made to furnish a certain 
amount of information bearing upon the case, is not as yet 
altogether conclusive, nor are the faculae which have also 
been observed for this purpose. 

The simple theory that the solar phenomena are caused 
by an interchange of hotter and cooler matter between the 
photosphere and the lower strata of the sun furnishes in 

THE SUN 211 

its present shape little or no explanation of such features 
as the sun-spot period, the variations in the corona, the 
peculiar character of the sun's rotation, etc., and we have 
still unsolved in the mechanical theory of the sun one of 
the noblest problems of astronomy, and one upon which 
both observers and theoretical astronomers are assiduously 
working at the present time. A close watch is kept upon 
sun spots and prominences, the corona is observed at every 
total eclipse, and numerous are the ingenious methods 
which are being suggested and tried for observing it with- 
out an eclipse in ordinary daylight. Attempts, more or 
less plausible, have been made and are now pending to 
explain photosphere, spots and the reversing layer by means 
of the refraction of light within the sun's outer envelope 
of gases, and it seems altogether probable, in view of these 
combined activities, that a considerable addition to our 
store of knowledge concerning the sun may be expected in 
the not distant future. 



133. Planets. Circling about the sun, under the influ- 
ence of his attraction, is a family of planets each member 
of which is, like the moon, a dark body shining by reflected 
sunlight, and therefore presenting phases ; although only 
two of them, Mercury and Venus, run through the com- 
plete series new, first quarter, full, last quarter which 
the moon presents. The way in which their orbits are 
grouped about the sun has been considered in Chapter 
III, and Figs. 16 and 17 of that chapter may be completed 
so as to represent all of the planets by drawing in Fig. 16 
two circles with radii of 7.9 and 12.4 centimeters respec- 
tively, to represent the orbits of the planets Uranus and 
Neptune, which are more remote from the sun than Sat- 
urn, and by introducing a little inside the orbit of Jupiter 
about 500 ellipses of different sizes, shapes, and positions to 
represent a group of minor planets or asteroids as they are 
often called. It is convenient to regard these asteroids as 
composing by themselves a class of very small planets, while 
the remaining 8 larger planets fall naturally into two other 
classes, a group of medium-sized ones Mercury, Venus, 
Earth, and Mars called inner planets by reason of their 
nearness to the sun ; and the outer planets Jupiter, Sat- 
urn, Uranus, Neptune each of which is much larger and 
more massive than any planet of the inner group. Com- 
pare in Figs. 84 and 85 their relative sizes. The earth, E, is 
introduced into Fig. 85 as a connecting link between the 
two figures. 

Some of these planets, like the earth, are attended by 



one or more moons, technically called satellites, which also 
shine by reflected sunlight and which move about their 
respective planets in accordance with the law of gravitation, 
much as the moon moves around the earth. 

Force of Gravity 0.43 
Diameter .3030 





"Density 6.3 


FIG. 84. The inner planets and the moon. 

134. Distances of the planets from the sun. It is a com- 
paratively simple matter to observe these planets year after 
year as they move among the stars, and to find from these 
observations how long each one of them requires to make 
its circuit around the sun that is, its periodic time, T 7 , 
which figures in Kepler's Third Law, and when these peri- 
odic times have been ascertained, to use them in connection 
with that law to determine the mean distance of each 

force of Gravity 
Mean Diameter 

0.9 0.9 

32000 35000 




FIG. 85. The outer planets. 

planet from the sun. Thus, Jupiter requires 4,333 days to 
move completely around its orbit ; and comparing this with 
the periodic time and mean distance of the earth we find 

fl 3 _ (93 ? 000,000) 3 ; 
(4333) 2 ~ (365.S5) 2 


which when solved gives as the mean distance of Jupiter 
from the sun, 483,730,000 miles, or 5.20 times as distant as 
the earth. If we make a similar computation for each 
planet, we shall find that their distances from the sun show 
a remarkable agreement with an artificial series of numbers 
called Bode's law. We write down the numbers contained 
in the first line of figures below, each of which, after the 
second, is obtained by doubling the preceding one, add 4 
to each number and point off one place of decimals; the 
resulting number is (approximately) the distance of the 
corresponding planet from the sun. 















































The last line of figures shows the real distance of the 
planet as determined from Kepler's law, the earth's mean 
distance from the sun being taken as the unit for this pur- 
pose. With exception of Neptune, the agreement between 
Bode's law and the true distances is very striking, but most 
remarkable is the presence in the series of a number, 2.8, 
with no planet corresponding to it. This led astronomers 
at the time Bode published the law, something more than 
a century ago, to give new heed to a suggestion made long 
before by Kepler, that there might be an unknown planet 
moving between the orbits of Mars and Jupiter, and a num- 
ber of them agreed to search for such a planet, each in a 
part of the sky assigned him for that purpose. But they 
were anticipated by Piazzi, an Italian, who found the new 
planet, by accident, on the first day of the nineteenth cen- 
tury, moving at a distance from the sun represented by the 
number 2.77. 


This planet was the first of the asteroids, and in the 
century that has elapsed hundreds of them have been dis- 
covered, while at the present time no year passes by with- 
out several more being added to the number. While some 
of these are nearer to the sun than is the first one discov? 
ered, and others are farther from it, their average distance 
is fairly represented by the number 2.8. 

Why Bode's law should hold true, or even so nearly 
true as it does, is an unexplained riddle, and many astron- 
omers are inclined to call it no law at all, but only a chance 
coincidence an illustration of the " inherent capacity of 
figures to be juggled with " ; but if so, it is passing strange 
that it should represent the distance of the asteroids and 
of Uranus, which was also an undiscovered planet at the 
time the law was published. 

135. The planets compared with each other. When we 
pass from general considerations to a study of the indi- 
vidual peculiarities of the planets, we find great differences 
in the extent of knowledge concerning them, and the reason 
for this is not far to seek. Neptune and Uranus, at the 
outskirts of the solar system, are so remote from us and so 
feebly illumined by the sun that any detailed study of them 
can go but little beyond determining the numbers which 
represent their size, mass, density, the character of their 
orbits, etc. The asteroids are so small that in the telescope 
they look like mere points of light, absolutely indistinguish- 
able in appearance from the fainter stars. Mercury, al- 
though closer at hand and presenting a disk of considerable 
size, always stands so near the sun that its observation is 
difficult on this account. Something of the same kind is 
true for Venus, although in much less degree ; while Mars, 
Jupiter, and Saturn are comparatively easy objects for tele- 
scopic study, and our knowledge of them, while far from 
complete, is considerably greater than for the other planets. 

Figs. 84 and 85 show the relative sizes of the planets 
composing the inner and outer groups respectively, and fur- 


nish the numerical data concerning their diameters, masses, 
densities, etc., which are of most importance in judging of 
their physical condition. Each planet, save Saturn, is 
represented by two circles, of which the outer is drawn 
proportional to the size of the planet, and the inner shows 
the amount of material that must be subtracted from the 
interior in order that the remaining shell shall just float in 
water. Note the great difference in thickness of shell 
between the two groups. Saturn, having a mean density 
less than that of water, must have something loaded upon 
it, instead of removed, in order that it should float just 


136. Appearance, Commencing our consideration of the 
individual planets with Jupiter, which is by far the largest 
of them, exceeding both in bulk and mass all the others 
combined, we have in Fig. 86 four representations of 
Jupiter and his family of satellites as they may be seen in 
a very small telescope e. g., an opera glass save that the 
little dots which here represent the satellites are numbered 
j?, #, $, 4-> i n order to preserve their identity in the succes- 
sive pictures. 

The chief interest of these pictures lies in the satellites, 
but, reserving them for future consideration, we note that 
the planet itself resembles in shape the full moon, although 
in respect of brightness it sends to us less than ^Vo P ar ^ 
as much light as the moon. From a consideration of the 
motion of Jupiter and the earth in Fig. 16, show that 
Jupiter can not present any such phases as does the moon, 
but that its disk must be at all times nearly full. As seen 
from Saturn, what kind of phases would Jupiter present ? 

137. The belts. Even upon the small scale of Fig. 86 
we detect the most characteristic feature of Jupiter's ap- 
pearance in the telescope, the two bands extending across 
his face parallel to the line of the satellites, and in Fig. 87 
these same dark bands may be recognized amid the abun- 


dance of detail which is here brought out by a large tele- 
scope. Photography does not succeed as a means of repro- 
ducing this detail, and for it we have to rely upon the skill 
of the artist astronomer. The lettering shows the Pacific 

FIG. 86. Jupiter and his satellites. 

Standard time at which the sketches were made, and also 
the longitude of the meridian of Jupiter passing down the 
center of the planet's disk. 

The dark bands are called technically the belts of Jupi- 
ter ; and a comparison of these belts in the second and third 
pictures of the group, in which nearly the same face of the 
planet is turned toward us, will show that they are subject 
to considerable changes of form and position even within 
the space of a few days. So, too, by a comparison of such 
markings as the round white spots in the upper parts of 
the disks, and the indentations in the edges of the belts, 
we may recognize that the planet is in the act of turning 
round, and must therefore have an axis about which it 
turns, and poles, an equator, etc. The belts are in fact 
parallel to the planet's equator ; and generalizing from what 
appears in the pictures, we may say that there is always a 
strongly marked belt on each side of the equator with a 

FIG. 87. Drawings of Jupiter made at the 36-inch telescope of the Lick 
Observatory. KEELER. 


lighter colored streak between them, and that farther from 
the equator are other belts variable in number, less con- 
spicuous, and less permanent than the two first seen. Com- 
pare the position of the principal belts with the position of 
the zones of sun-spot activity in the sun. A feature of 
the planet's surface, which can not be here reproduced, is 
the rich color effect to be found upon it. The principal 
belts are a brick-red or salmon color, the intervening spaces 
in general white but richly mottled, and streaked with 
purples, browns, and greens. 

The drawings show the planet as it appeared in the 
telescope, inverted, and they must be turned upside down 
if we wish the points of the compass to appear as upon a 
terrestrial map. Bearing this in mind, note in the last 
picture the great oval spot in the southern hemisphere of 
Jupiter. This is a famous marking, known from its color 
as the great red spot, which appeared first in 1878 and has 
persisted to the present day (1900), sometimes the most 
conspicuous marking on the planet, at others reduced to a 
mere ghost of itself, almost invisible save for the inden- 
tation which it makes in the southern edge of the belt 
near it. 

138. Rotation and flattening at the poles, One further 
significant fact with respect to Jupiter may be obtained 
from a careful measurement of the drawings ; the planet is 
flattened at the poles, so that its polar diameter is about 
one sixteenth part shorter than the equatorial diameter. 
The flattening of the earth amounts to only one three- 
hundredth part, and the marked difference between these 
two numbers finds its explanation in the greater swiftness 
of Jupiter's rotation about its axis, since in both cases it is 
this rotation which makes the flattening. 

It is not easy to determine the precise dimensions of the 
planet, since this involves a knowledge both of its distance 
from us and of the angle subtended by its diameter, but 
the most recent determinations of this kind assign as the 


equatorial diameter 90,200 miles, and for the polar diam- 
eter 84,400 miles. Determine from either of these num- 
bers the size of the great red spot. 

The earth turns on its axis once in 24 hours but no 
such definite time can be assigned to Jupiter, which, like 
the sun, seems to have different rotation periods in differ- 
ent latitudes 9h. 50m. in the equatorial belt and 9h. 56m. 
in the dark belts and higher latitudes. There is some indi- 
cation that the larger part of the visible surface rotates in 
9h. 55.6m., while a broad stream along the equator flows 
eastward some 270 miles per hour, and thus comes back to 
the center of the planet, as seen from the earth, five or six 
minutes earlier than the parts which do not share in this 
motion. Judged by terrestrial standards, 270 miles per 
hour is a great velocity, but Jupiter is constructed on a 
colossal scale, and, too, we have to compare this movement, 
not to a current flowing in the ocean, but to a wind blow- 
ing in the upper regions of the earth's atmosphere. The 
visible surface of Jupiter is only the top of a cloud forma- 
tion, and contains nothing solid or permanent, if indeed 
there is anything solid even at the core of the planet. The 
great red spot during the first dozen years of its existence, 
instead of remaining fixed relative to the surrounding for- 
mations, drifted two thirds of the way around the planet, 
and having come to a standstill about 1891, it is now slowly 
retracing its path. 

139. Physical condition. For a better understanding of 
the physical condition of Jupiter, we have now to consider 
some independent lines of evidence which agree in point- 
ing to the conclusion that Jupiter, although classed with 
the earth as a planet, is in its essential character much 
more like the sun. 

Appearance. The formations which we see in Fig. 87 
look like clouds. They gather and disappear, and the only 
element of permanence about them is their tendency to 
group themselves along zones of latitude. If we measure 


the light reflected from the planet we find that its albedo 
is very high, like that of snow or our own cumulus clouds, 
and it is of course greater from the light parts of the disk 
than from the darker bands. The spectroscope shows that 
the sunlight reflected from these darker belts is like that 
reflected from the lighter parts, save that a larger portion of 
the blue and violet rays has been absorbed out of it, thus 
producing the ruddy tint of the belts, as sunset colors are 
produced on the earth, and showing that here the light has 
penetrated farther into the planet's atmosphere before 
being thrown back by reflection from lower-lying cloud sur- 
faces. The dark bands are therefore to be regarded as rifts 
in the clouds, reaching down to some considerable distance 
and indicating an atmosphere of great depth. The great 
red spot, 28,000 miles long, and obviously thrusting back 
the white clouds on every side of it, year after year, can 
hardly be a mere patch on the face of the planet, but indi- 
cate? a ome considerable depth of atmosphere. 

Density. So, too, the small mean density of the planet, 
only 1.3 times that of water and actually less than the den- 
sity of the sun, suggests that the larger part of the planet's 
bulk may be made of gases and clouds, with very little solid 
matter even at the center ; but here we get into a difficulty 
from which there seems but one escape. The force of 
gravity at the visible surface of Jupiter may be found 
from its mass and dimensions to be 2.6 times as great as 
at the surface of the earth, and the pressure exerted upon 
iis atmosphere by this force ought to compress the lower 
strata into something more dense than we find in the 
)lanet. Some idea of this compression may be obtained 
from Fig. 88, where the line marked E shows approximately 
low the density of the air increases as we move from its 
ipper strata down toward the surface of the earth through 
distance of 16 miles, the density at any level being pro- 
>rtional to the distance of the curved line from the straight 
oiae near it. The line marked J in the same figure shows 


how the density would increase if the force of gravity were 
as great here as it is in Jupiter, and indicates a much 
greater rate of increase. Starting from the upper surface 
of the cloud in Jupiter's atmosphere, if we descend, 
not 16 miles, but 1,600 or 16,000, what must the den- 
sity of the atmosphere become and how is this to be 
reconciled with what we know to be the very small 
mean density of the planet ? 

We are here in a dilemma between density on the 
one hand and the effects of gravity on the other, and 
the only escape from it lies in the assumption that 
the interior of Jupiter is tremendously hot, and that 
this heat expands the substance of the planet in spite 
of the pressure to which it is subject, making a large 
planet with a low density, possibly gaseous at 
the very center, but in its outer part surrounded 
by a shell of clouds con- 
densed from the gases by 
radiating their heat into 

FIG. 88-Increase of density in the atmos- the Cold of Outer space. 

pheres of Jupiter and the earth. This is essentially the 

same physical condition 

that we found for the sun, and we may add, as further 
points of resemblance between it and Jupiter, that there 
seems to be a circulation of matter from the hot interior of 
the planet to its cooler surface that is more pronounced in 
the southern hemisphere than in the northern, and that has 
its periods of maximum and minimum activity, which, cu- 
riously enough, seem to coincide with periods of maximum 
and minimum sun-spot development. Of this, however, we 
can not be entirely sure, since it is only in recent years that 
it has been studied with sufficient care, and further obser- 
vations are required to show whether the agreement is 
something more than an accidental and short-lived coin- 

Temperature. The temperature of Jupiter must, of 


course, be much lower than that of the sun, since the sur- 
face which we see is not luminous like the sun's ; but below 
the clouds it is not improbable that Jupiter may be incan- 
descent, white hot, and it is surmised with some show of 
probability that a little of its light escapes through the 
clouds from time to time, and helps to produce the striking 
brilliancy with which this planet shines. 

140. The satellites of Jupiter. The satellites bear much 
the same relation to Jupiter that the moon bears to the 
earth, revolving about the planet in accordance with the 
law of gravitation, and conforming to Kepler's three laws, 
as do the planets in their courses about the sun. Observe in 
Fig. 86 the position of satellite No. 1 on the four dates, and 
note how it oscillates back and forth from left to right of 
Jupiter, apparently making a complete revolution in about 
two days, while No. 4 moves steadily from left to right dur- 
ing the entire period, and has evidently made only a frac- 
tion, of a revolution in the time covered by the pictures. 
This quicker motion, of course, means that No. 1 is nearer 
to Jupiter than No. 4, and the numbers given to the satel- 
lites show the order of their distances from the planet. 
The peculiar way in which the satellites are grouped, always 
standing nearly in a straight line, shows that their orbits 
must lie nearly in the same plane, and that this plane, which 
is also the plane of the planets' equator, is turned edgewise 
toward the earth. 

These satellites enjoy the distinction of being the first 
objects ever discovered with the telescope, having been 
found by Galileo almost immediately after its invention, 
A. D. 1610. It is quite possible that before this time they 
may have been seen with the naked eye, for in more recent 
years reports are current that they have been seen under 
favorable circumstances by sharp-eyed persons, and very 
little telescopic aid is required to show them. Look for 
them with an opera or field glass. They bear the names 
lo, Europa, Ganymede, Callisto, which, however, are rarely 



used, and, following the custom of astronomers, we shall 
designate them by the Eoman numerals I, II, III, IV. 

For nearly three centuries (1610 to 1892) astronomers 
spoke of the four satellites of Jupiter ; but in September, 
1892, a fifth one was added to the number by Professor Bar- 
nard, who, observing with the largest telescope then extant, 
found very close to Jupiter a tiny object only ^ part as 

/C.754 days 

FIG. 89. Orbits of Jupiter's satellites. 

bright as the other satellites, but, like them, revolving around 
Jupiter, a permanent member of his system. This is called 
the fifth satellite, and Fig. 89 shows the orbits of these satel- 
lites around Jupiter, which is here represented on the same 
scale as the orbits themselves. The broken line just inside 
the orbit of I represents the size of the moon's orbit. The 
cut shows also the periodic times of the satellites expressed 
in days, and furnishes in this respect a striking illustra- 
tion of the great mass of Jupiter. Satellite I is a little 


farther from Jupiter than is the moon from the earth, but 
under the influence of a greater attraction it makes the cir- 
cuit of its orbit in 1.77 days, instead of taking 29.53 days, 
as does the moon. Determine from the figure by the method 
employed in 111 how much more massive is Jupiter than 
the earth. 

Small as these satellites seem in Fig. 86, they are really 
bodies of considerable size, as appears from Fig. 90, where 
their dimensions are compared with those of the earth 
and moon, save that the fifth satellite is not included. 
This one is so small as to escape all attempts at measuring 
its diameter, but, judging from the amount of light it re- 
flects, the period printed with the legend of the figure 
represents a gross exaggeration of this satellite's size. 

FIG. 90. Jupiter's satellites compared with the earth and moon. 

Like the moon, each of these satellites may fairly be 
considered a world in itself, and as such a fitting object of 
detailed study, but, unfortunately, their great distance from 
us makes it impossible, even with the most powerful tele- 
scope, to see more upon their surfaces than occasional vague 
markings, which hardly suffice to show the rotations of the 
satellites upon their axes. 

One striking feature, however, comes out from a study 
of their influence in disturbing each other's motion about 
Jupiter. Their masses and the resulting densities of the 
satellites are smaller than we should have expected to find, 
the density being less than that of the moon, and aver- 
aging only a little greater than the density of Jupiter 


itself. At the surface of the third satellite the force of 
gravity is but little less than on the moon, although the 
moon's density is nearly twice as great as that of III, and 
there can be no question here of accounting for the low 
density through expansion by great heat, as in the case of 
the sun and Jupiter. It has been surmised that these satel- 
lites are not solid bodies, like the earth and moon, but only 
shoals of rock and stone, loosely piled together and kept 
from packing into a solid mass by the action of Jupiter in 
raising tides within them. But the explanation can hardly 
be regarded as an accepted article of astronomical belief, 
although it is supported by some observations which tend 
to show that the apparent shapes of the satellites change un- 
der the influence of the tidal forces impressed upon them. 
141. Eclipses of the satellites, It may be seen from Fig. 
89 that in their motion around the planet Jupiter's satellites 
must from time to time pass through his shadow and be 
eclipsed, and that the shadows of the satellites will occasion- 
ally fall upon the planet, producing to an observer upon 
Jupiter an eclipse of the sun, but to an observer on the earth 
presenting only the appearance of a round black spot mov- 
ing slowly across the face of the planet. Occasionally also 
a satellite will pass exactly between the earth and Jupiter, 
and may be seen projected against the planet as a back- 
ground. All of these phenomena are duly predicted and 
observed by astronomers, but the eclipses are the only ones 
we need consider here. The importance of these eclipses 
was early recognized, and astronomers endeavored to con- 
struct a theory of their recurrence which would permit 
accurate predictions of them to be made. But in this they 
met with no great success, for while it was easy enoug.h 
to foretell on what night an eclipse of a given satellite 
would occur, and even to assign the hour of the night, it 
was not possible to make the predicted minute agree with 
the actual time of eclipse until after Roemer, a Danish 
astronomer of the seventeenth century, found where lay the 


trouble. His discovery was, that whenever the earth was 
on the side of its orbit toward Jupiter the eclipses really 
occurred before the predicted time, and when the earth 
was on the far side of its orbit they came a few minutes 
later than the predicted time. He correctly inferred thatx 
this was to be explained, not by any influence which the 
earth exerted upon Jupiter and his satellites, but through 
the fact that the light by which we see the satellite and its 
eclipse requires an appreciable time to cross the interven- 
ing space, and a longer time when the earth is far from 
Jupiter than when it is near. 

For half a century Roemer's views found little credence, 
but we know now that he was right, and that on the 
average the eclipses come 8m. 18s. early when the earth is 
nearest to Jupiter, and 8m. 18s. late when it is on the op- 
posite side of its orbit. This is equivalent to saying that 
light takes 8m. 18s. to cover the distance from the sun to 
the earth, so that at any moment we see the sun not as it 
then is, but as it was 8 minutes earlier. It has been found 
possible in recent years to measure by direct experiment 
the velocity with which light travels 186,337 miles per 
second and multiplying this number by the 498s. (= 8m. 
18s.) we obtain a new determination of the sun's distance 
from the earth. The product of the two numbers is 
92,795,826, in very fair agreement with the 93,000,000 
miles found in Chapter X ; but, as noted there, this method, 
like every other, has its weak side, and the result may be a 
good many thousands of miles in error. 

It is worthy of note in this connection that both meth- 
ods of obtaining the sun's distance which were given in 
Chapter X involve Kepler's Third Law, while the result 
obtained from Jupiter's satellites is entirely independent 
of this law, and the agreement of the several results is 
therefore good evidence both for the truth of Kepler's laws 
and for the soundness of Eoemer's explanation of the 
eclipses. This mode of proof, by comparing the numerical 



results furnished by two or more different principles, and 
showing that they agree or disagree, is of wide application 
and great importance in physical science. 


142. The ring of Saturn, In respect of size and mass 
Saturn stands next to Jupiter, and although far inferior to 
him in these respects, it contains more material than all 
the remaining planets combined. But the unique feature 
of Saturn which distinguishes it from every other known 

body in the heavens is 
its ring, which was long 
a puzzle to the astrono- 
mers who first studied 
the planet with a tele- 
scope (one of them called 
Saturn a planet with 
ears), but, was after 
nearly half a century 
correctly understood and 
described by Huyghens, 
whose Latin text we 
translate into " It is 
surrounded by a ring, 
thin, flat, nowhere touch- 
ing it, and making quite 
an angle with the eclip- 

Compare with this 
description Fig. 91, which shows some of the appearances 
presented by the ring at different positions of Saturn in 
its orbit. It was their varying aspects that led Huyghens 
to insert the last words of his description, for, if the plane 
of the ring coincided with the plane of the earth's orbit, 
then at all times the ring must be turned edgewise toward 
the earth, as shown in the middle picture of the group. 

FIG. 91. Aspects of Saturn's rings. 



Fig. 92 shows the sun and the orbit of the earth placed 
near the center of Saturn's orbit, across whose circumfer- 
ence are ruled some oblique lines representing the plane 
of the ring, the right end always tilted up, no matter where 

FIG. 92. Aspects of the ring in their relation to Saturn's orbital motion. 

the planet is in its orbit. It is evident that an observer 
upon the earth will see the N side of the ring when the 
planet is at N and the 8 side when it is at $, as is shown 
in the first and third pictures of Fig. 91, while midway be- 
tween these positions the edge of the ring will be presented 
to the earth. 

The last occasion of this kind was in October, 1891, and 
with the large telescope of the Washburn Observatory the 


writer at that time saw Saturn without a trace of a ring 
surrounding it. The ring is so thin that it disappears 
altogether when turned edgewise. The names of the zo- 
diacal constellations are inserted in Fig. 92 in their proper 
direction from the sun, and from these we learn that the 
ring will disappear, or be exceedingly narrow, whenever 
Saturn is in the constellation Pisces or near the boundary 
line between Leo and Virgo. It will be broad and show its 
northern side when Saturn is in Scorpius or Sagittarius, and 
its southern face when the planet is in Gemini. What will 
be its appearance in 1907 at the date marked in the figure? 

143. Nature of the ring. It is apparent from Figs. 91 
and 93 that Saturn's ring is really made up of two or more 
rings lying one inside of the other and completely sepa- 
rated by a dark space which, though narrow, is as clean and 
sharp as if cut with a knife. Also, the inner edge of the 
ring fades off into an obscure border called the dusky ring 
or crape ring. This requires a pretty good telescope to 
show it, as may be inferred from the fact that it escaped 
notice for more than two centuries during which the planet 
was assiduously studied with telescopes, and was discovered 
at the Harvard College Observatory as recently as 1850. 

Although the rings appear oval in all of the pictures, 
this is mainly an effect of perspective, and they are in fact 
nearly circular with the planet at their center. The ex- 
treme diameter of the ring is 172,000 miles, and from this 
number, by methods already explained (Chapter IX), the 
student should obtain the width of the rings, their distance 
from the ball of the planet, and the diameter of the ball. 
As to thickness, it is evident, from the disappearance of the 
ring when its edge is turned toward the earth, that it is 
very thin in comparison with its diameter, probably not 
more than 100 miles thick, although no exact measurement 
of this can be made. 

From theoretical reasons based upon the law of gravita- 
tion astronomers have held that the rings of Saturn could 

FIG. 93. Saturn. 


not possibly be solid or liquid bodies. The strains im- 
pressed upon them by the planet's attraction would tear 
into fragments steel rings made after their size and shape. 
Quite recently Professor Keeler has shown, by applying the 
spectroscope (Doppler's principle) to determine the velocity 
of the ring's rotation about Saturn, that the inner parts of 
the ring move, as Kepler's Third Law requires, more rapidly 
than do the outer parts, thus furnishing a direct proof that 
they are not solid, and leaving no doubt that they are made 
up of separate fragments, each moving about the planet in 
its own orbit, like an independent satellite, but standing so 
close to its neighbors that the whole space reflects the sun- 
light as completely as if it were solid. With this under- 
standing of the rings it is easy to see why they are so thin. 
Like Jupiter, Saturn is greatly flattened at the poles, and 
this flattening, or rather the protuberant mass about the 
equator, lays hold of every satellite near the planet and 
exerts upon it a direct force tending to thrust it down 
into the plane of the planet's equator and hold it there. 
The ring lies in the plane of Saturn's equator because each 
particle is constrained to move there. 

The division of the ring into two parts, an outer and an 
inner ring, is usually explained as follows : Saturn is sur- 
rounded by a numerous brood of satellites, which by their 
attractions produce perturbations in the material compos- 
ing the rings, and the dividing line between the outer and 
inner rings falls at the place where by the law of gravita- 
tion the perturbations would have their greatest effect. 
The dividing line between the rings is therefore a narrow 
lane, 2,400 miles wide, from which the fragments have been 
swept clean away by the perturbing action of the satellites. 
Less conspicuous divisions are seen from time to time in 
other parts of the ring, where the perturbations, though 
less, are still appreciable. But it is open to some question 
whether this explanation is sufficient. 

The curious darkness of the inner or crape ring is easily 


explained. The particles composing it are not packed to- 
gether so closely as in the outer ring, and therefore reflect 
less sunlight. Indeed, so sparsely strewn are the particles 
in this ring that it is in great measure transparent to the 
sunlight, as is shown by a recorded observation of one of the* 
satellites which was distinctly although faintly seen while 
moving through the shadow of the dark ring, but disap- 
peared in total eclipse when it entered the shadow cast by 
the bright ring. 

144. The ball of Saturn. The ball of the planet is in 
most respects a smaller copy of Jupiter. With an equa- 
torial diameter of 76,000 miles, a polar diameter of 69,000 
miles, and a mass 95 times that of the earth, its density 
is found to be the least of any planet in the solar system, 
only 0.70 of the density of water, and about one half as 
great as is the density of Jupiter. The force of gravity at 
its surface is only a little greater (1.18) than on the earth ; 
and this, in connection with the low density, leads, as in the 
case of Jupiter, to the conclusion that the planet must be 
mainly composed of gases and vapors, very hot within, but 
inclosed by a shell of clouds which cuts off their glow from 
our eyes. 

Like Jupiter in another respect, the planet turns very 
swiftly upon its axis, making a revolution in 10 hours 14 
minutes, but up to the present it remains unknown whether 
different parts of the surface have different rotation times. 

145. The satellites. Saturn is attended by a family of 
nine satellites, a larger number than belongs to any other 
planet, but with one exception they are exceedingly small 
and difficult to observe save with a very large telescope. 
Indeed, the latest one to be discovered was found in 1898 by 
means of the image which it impressed upon a photographic 
plate, and it has never been seen. 

Titan, the largest of them, is distant 771,000 miles from 
the planet and bears much the same relation to Saturn that 
Satellite III bears to Jupiter, the similarity in distance, size, 


and mass being rather striking, although, of course, the 
smaller mass of Saturn as compared with Jupiter makes the 
periodic time of Titan 15 days 23 hours much greater 
than that of III. Can you apply Kepler's Third Law to 
the motion of Titan so as to determine from the data given 
above, the time required for a particle at the outer or inner 
edge of the ring to revolve once around Saturn ? 

Japetus, the second satellite in point of size, whose dis- 
tance from Saturn is about ten times as great as the moon's 
distance from the earth, presents the remarkable peculiar- 
ity of being always brighter in one part of its orbit than 
in another, three or four times as bright when west of 
Saturn as when east of it. This probably indicates that, 
like our own moon, the satellite turns always the same face 
toward its planet, and further, that one side of the satellite 
reflects the sunlight much better than the other side i. e., 
has a higher albedo. With these two assumptions it 
is easily seen that the satellite will always turn toward 
the earth one face when west, and the other face when 
east of Saturn, and thus give the observed difference of 


146. Chief characteristics. The two remaining large 
planets are interesting chiefly as modern additions to the 
known members of the sun's family. The circumstances 
leading to the discovery of Neptune have been touched 
upon in Chapter IV, and for Uranus we need only note 
that it was found by accident in the year 1781 by William 
Herschel, who for some time after the discovery considered 
it to be only a comet. It was the first planet ever discov- 
ered, all of its predecessors having been known from pre- 
historic times. 

Uranus has four satellites, all of them very faint, which 
present only one feature of special importance. Instead of 
moving in orbits which are approximately parallel to the 

WILLIAM HEESCHEL (1738-1822). 


plane of the ecliptic, as do the satellites of the other planets, 
their orbit planes are tipped up nearly perpendicular to the 
planes of the orbits of both Uranus and the earth. The 
one satellite which Neptune possesses has the same pecul- 
iarity in even greater degree, for its motion around the 
planet takes place in the direction opposite to that in 
which all the planets move around the sun, much as if the 
orbit of the satellite had been tipped over through an angle 
of 150. Turn a watch face down and note how the hands 
go round in the direction opposite to that in which they 
moved before the face was turned through 180. 

Both Uranus and Neptune are too distant to allow 
much detail to be seen upon their surfaces, but the pres- 
ence of broad absorption bands in their spectra shows that 
they must possess dense atmospheres quite different in con- 
stitution from the atmosphere of the earth. In respect of 
density and the force of gravity at their surfaces, they are 
not very unlike Saturn, although their density is greater 
and gravity less than his, leading to the supposition that 
they are for the most part gaseous bodies, but cooler and 
probably more nearly solid than either Jupiter or Saturn. 

Under favorable circumstances Uranus may be seen 
with the naked eye by one who knows just where to look 
for it. Neptune is never visible save in a telescope. 

147. The inner planets. In sharp contrast with the giant 
planets which we have been considering stands the group 
of four inner planets, or five if we count the moon as an 
independent body, which resemble each other in being all 
small, dense, and solid bodies, which by comparison with 
the great distances separating the outer planets may fairly 
be described as huddled together close to the sun. Their 
relative sizes are shown in Fig. 84, together with the nu- 
merical data concerning size, mass, density, etc., which we 
have already found important for the understanding of a 
planet's physical condition. 




148. Appearance, Omitting the earth, Venus is by far 
the most conspicuous member of this group, and when at its 
brightest is, with exception of the sun and moon, the most 
brilliant object in the sky, and may be seen with the naked 
eye in broad daylight if the observer knows just where to 
look for it. But its brilliancy is subject to considerable 
variations on account of its changing distance from the 

FIG. 94. The phases of Venus. ANTONIADI. 

earth, and the apparent size of its disk varies for the same 
reason, as may be seen from Fig. 94. These drawings bring 
out well the phases of the planet, and the student should 
determine from Fig. 17 what are the relative positions in 
their orbits of the earth and Venus at which the planet 
would present each of these phases. As a guide to this, 
observe that the dark part of Venus's earthward side is 
always proportional in area to the angle at Venus between 
the earth and sun. In the first picture of Fig. 94 about 


two thirds of the surface corresponding to the full hemi- 
sphere of the planet is dark, and the angle at Venus 
between earth and sun is therefore two thirds of 180 i. e., 
120. In Fig. 17 find a place on the orbit of Venus from 
which if lines be drawn to the sun and earth, as there 
shown, the angle between them will be 120. Make a simi- 
lar construction for the fourth picture in Fig. 94. Which 
of these two positions is farther from the earth ? How do 
the distances compare with the apparent size of Venus in 
the two pictures ? What is the phase of Venus to-day ? 

The irregularities in the shading of the illuminated 
parts of the disk are too conspicuous in Fig. 94, on account 
of difficulties of reproduction; these shadings are at the 
best hard to see in the telescope, and distinct permanent 
markings upon the planet are wholly lacking. This absence 
of markings makes almost impossible a determination of 
the planet's time of rotation about its axis, and -astrono- 
mers are divided in this respect into two parties, one of 
which maintains that Venus, like the earth, turns upon its 
axis in some period not very different from 24 hours, while 
the other contends that, like the moon, it turns always the 
same face toward the center of its orbit, making a rotation 
upon its axis in the same period in which it makes a revo- 
lution about the sun. The reason why no permanent mark- 
ings are to be seen on this planet is easily found. Like 
Jupiter and Saturn, its atmosphere is at all times heavily 
cloud-laden, so that we seldom, if ever, see down to the 
level of its solid parts. There is, however, no reason here 
to suppose the interior parts hot and gaseous. It is much 
more probable that Venus, like the earth, possesses a solid 
crust whose temperature we should expect to be consider- 
ably higher than that of the earth, because Venus is nearer 
the sun. But the cloud layer in its atmosphere must modify 
the temperature in some degree, and we have practically 
no knowledge of the real temperature conditions at the 
surface of the planet. 


It is the clouds of Venus which in great measure are 
responsible for its marked brilliancy, since they are an ex- 
cellent medium for reflecting the sunlight, and give to its 
surface an albedo greater than that of any other planet, 
although Saturn is nearly equal to it. 

Of course, the presence of such cloud formations indi- 
cates that Venus is surrounded by a dense atmosphere, and 
we have independent evidence of this in the shape of its 
disk when the planet is very nearly between the earth and 
sun. The illuminated part, from tip to tip of the horns ? 
then stretches more than halfway around the planet's cir- 
cumference, and shows that a certain amount of light must 
have been refracted through its atmosphere, thus making 
the horns of the crescent appear unduly prolonged. This 
atmosphere is shown by the spectroscope to be not unlike 
that of the earth, although probably more dense. 


149. Chief characteristics. Mercury, on account of its 
nearness to the sun, is at all times a difficult object to ob- 
serve, and Copernicus, who spent most of his life in Poland, 
is said, despite all his efforts, to have gone to his grave with- 
out ever seeing it. In our more southern latitude it can 
usually be seen for about a fortnight at the time of each 
elongation i. e., when at its greatest angular distance from 
the sun and the student should find from Fig. 16 the time 
at which the next elongation occurs and look for the planet, 
shining like a star of the first magnitude, low down in the 
sky just after sunset or before sunrise, according as the 
elongation is to the east or west of the sun. When seen in 
the morning sky the planet grows brighter day after day 
until it disappears in the sun's rays, while in the evening 
sky its brilliancy as steadily diminishes until the planet is 
lost. It should therefore be looked for in the evening as 
soon as possible after it emerges from the sun's rays. 

Mercury, as the smallest of the planets, is best compared 


with the moon, which it does not greatly surpass in size 
and which it strongly resembles in other respects. Careful 
comparisons of the amount of light reflected by the planet 
in different parts of its orbit show not only that its albedo 
agrees very closely with that of the moon, but also that its 
light changes with the varying phase of the planet in al- 
most exactly the same way as the amount of moonlight 
changes. We may therefore infer that its surface is like 
that of the moon, a rough and solid one, with few or no 
clouds hanging over it, and most probably covered with 
very little or no atmosphere. Like Venus, its rotation pe- 
riod is uncertain, with the balance of probability favoring 
the view that it rotates upon its axis once in 88 days, and 
therefore always turns the same face toward the sun. 

If such is the case, its climate must be very peculiar : 
one side roasted in a perpetual day, where the direct heat- 
ing power of the sun's rays, when the planet is at perihelion, 
is ten times as great as on the moon, and which six weeks 
later, when the planet is at its farthest from the sun, has 
fallen off to less than half of this. On the opposite side of 
the planet there must reign perpetual night and perpetual 
cold, mitigated by some slight access of warmth from the 
day side, and perhaps feebly imitating the rapid change of 
season which takes place on the day side of the planet. 
This view, however, takes no account of a possible devia- 
tion of the planet's axis from being perpendicular to the 
plane of its orbit, or of the librations which must be pro- 
duced by the great eccentricity of the orbit, either of which 
would complicate without entirely destroying the ideal 
conditions outlined above. 


150. Appearance. The one remaining member of the 
inner group, Mars, has in recent years received more atten- 
tion than any other planet, and the newspapers and maga- 
zines have announced marvelous things concerning it : that 



it is inhabited by a race of beings superior in intelligence 
to men ; that the work of their hands may be seen upon 
the face of the planet ; that we should endeavor to com- 
municate with them, if indeed they are not already sending 
messages to us, etc. all of which is certainly important, 
if true, but it rests upon a very slender foundation of evi- 
dence, a part of which we shall have to consider. 

Beginning with facts of which there is no doubt, this 
ruddy-colored planet, which usually shines about as brightly 

as a star of the first mag- 
nitude, sometimes dis- 
plays more than tenfold 
this brilliancy, surpass- 
ing every other planet 
save Venus and present- 
ing at these times espe- 
cially favorable opportu- 
nities for the study of 
its surface. The expla- 
nation of this increase 
of brilliancy is, of course, 
that the planet approach- 
es unusually near to the 
earth, and we have al- 
ready seen from a con- 
sideration of Fig. 17 
that this can only hap- 
pen in the months of August and September. The last 
favorable epoch of this kind was in 1894. From Fig. 17 
the student should determine when the next one will 

Fig. 95 presents nine drawings of the planet made at 
one of the epochs of close approach to the earth, and shows 
that its face bears certain faint markings which, though 
inconspicuous, are fixed and permanent features of the 
planet. The dark triangular projection in the lower half 




of the second drawing was seen and sketched by Huyghens. 
1659 A. D. In Fig. 96 some of these markings are shown 
much more plainly, but Fig. 95 gives a better idea of their 
usual appearance in the telescope. 

151. Rotation. It may be seen readily enough, from a 
comparison of the first two sketches of Fig. 95, that the 
planet rotates about an 
axis, and from a more 
extensive study it is 
found to be very like 
the earth in this re- 
spect, turning once in 
24h. 37m. around an 
axis tipped from being 
perpendicular to the 
plane of its orbit about 
a degree and a half 
more than is the earth's 
axis. Since it is this 
inclination of the axis 
which is the cause of 
changing seasons upon 
the earth, there must 
be similar changes, 

winter and summer, as well as day and night, upon Mars, 
only each season is longer there than here in the same pro- 
portion that its year is longer than ours i. e., nearly two 
to one. It is summer in the northern hemisphere of Mars 
whenever the sun, as seen from Mars, stands in that con- 
stellation which is nearest the point of the sky toward 
which the planet's axis points. But this axis points toward 
the constellation Cygnus, and Alpha Cygni is the bright 
star nearest the north pole of Mars. As Pisces is the 
zodiacal constellation nearest to Cygnus, it must be sum- 
mer in the northern hemisphere of Mars when the sun is in 
Pisces, or, turning the proposition about, it must be summer 

FIG. 96. Four views of Mars differing 90 in 
longitude. BARNARD. 



in the southern hemisphere of Mars when the planet, as 
seen from the sun, lies in the direction of Pisces. 

152. The polar caps. One effect of the changing seasons 
upon Mars is shown in Fig. 97, where we have a series of 
drawings of the region about its south pole made in 1894, 
on dates between May 21st and December 10th. Show 
from Fig. 16 that during this time it was summer in the 
region here shown. Mars crossed the prime radius in 1894 
on September 5th. The striking thing in these pictures is 
the white spot surrounding the pole, which shrinks in size 

from the beginning to 
near the end of the se- 
ries, and then disappears 
altogether. The spot 
came back again a year 
later, and like a similar 
spot at the north pole of 
the planet it waxes in the 
winter and wanes during 
the summer of Mars in 
endless succession. 

Sir W. Herschel, who 
studied these appear- 
ances a century ago, com- 
pared them with the snow 
fields which every winter 

FIG. 97. The south polar cap of Mars in .. . , 

1894.-BABNARD. spread out from the re- 

gion around the terres- 
trial pole, and in the summer melt and shrink, although 
with us they do not entirely disappear. This explanation of 
the polar caps of Mars has been generally accepted among 
astronomers, and from it we may draw one interesting con- 
clusion : the temperature upon Mars between summer and 
winter oscillates above and below the freezing point of 
water, as it does in the temperate zones of the earth. But 
this conclusion plunges us into a serious difficulty. The 


temperature of the earth is made by the sun, and at the 
distance of Mars from the sun the heating effect of the 
latter is reduced to less than half what it is at the earth, 
so that, if Mars is to be kept at the same temperature as 
the earth, there must be some peculiar means for storing 
the solar heat and using it more economically than is done 
here. Possibly there is some such mechanism, although 
no one has yet found it, and some astronomers are very 
confident that it does not exist, and assert that the com- 
parison of the polar caps with snow fields is misleading, 
and that the temperature upon Mars must be at least 100, 
and perhaps 200 or more, below zero. 

153. Atmosphere and climate. In this connection one 
feature of Mars is of importance. The markings upon its 
surface are always visible when turned toward the earth, 
thus showing that the atmosphere contains no such amount 
of cloud as does our own, but on the whole is decidedly 
clear and sunny, and presumably much less dense than 
ours. AVe have seen in comparing the earth and the moon 
how important is the service which the earth's atmosphere 
renders in storing the sun's heat and checking those great 
vicissitudes of temperature to which the moon is subject ; 
and with this in mind we must regard the smaller density 
and cloudless character of the atmosphere of Mars as un- 
favorable to the maintenance there of a temperature like 
that of the earth. Indeed, this cloudlessness must mean 
one of two things : either the temperature is so low that 
vapors can not exist in any considerable quantity, or the 
surface of Mars is so dry that there is little water or other 
liquid to be evaporated. The latter alternative is adopted 
by those astronomers who look upon the polar caps as true 
snow fields, which serve as the chief reservoir of the planet's 
water supply, and who find in Fig. 98 evidence that as the 
snow melts and the water flows away over the flat, dry sur- 
face of the planet, vegetation springs up, as shown by the 
dark markings on the disk, and gradually dies out with 



the advancing season. Note that in the first of these pic- 
tures the season upon Mars corresponds to the end of May 
with us, and in the last picture to the beginning of August, 
a period during which in much of our western country the 
luxuriant vegetation of spring is burned out by the scorch- 
ing sun. From this point of view the permanent dark 
spots are the low-lying parts of the planet's surface, in 
which at all times there is a sufficient accumulation of 
water to support vegetable life. 

154. The canals. In Fig. 98 the lower part of the disk 
of Mars shows certain faint dark lines which are generally 
called canals, and in Plate III there is given a map of Mars 

FIG. 98. The same face of Mars at three different seasons. LOWELL. 

showing many of these canals running in narrow, dusky 
streaks across the face of the planet according to a pattern 
almost as geometrical as that of a spider's web. This must 
not be taken for a picture of the planet's appearance in a 
telescope. No man ever saw Mars look like this, but the 
map is useful as a plain representation of things dimly 
seen. Some of the regions of this map are marked Mare 
(sea), in accordance with the older view which regarded 
the darker parts of the planet and of themotm as bodies 
of water, but this is now known to be an error in both 
cases. The curved surface of a planet can not be accurately 
reproduced upon the flat surface of paper, but ifi always 
more or less distorted by the various methods of/" project- 
ing " it which are in use. Compare the map/of Mars in 


Plate III with Fig. 99, in which the projection represents 
very well the equatorial parts of the planet, but enormously 
exaggerates the region arou nd the poles. 

It is a remarkable feature of the canals that they all 
begin and end in one of these dark parts of the planetV 
surface ; they show no loose ends lying on the bright parts 
of the planet. Another even more remarkable feature is 
that while the larger canals are permanent features of the 
planet's surface, they at times appear " doubled " i. e., in 
place of one canal two parallel ones side by side, lasting 
for a time and then giving place again to a single canal. 

It is exceedingly difficult to frame any reasonable ex- 
planation of these canals and the varied appearances which 
they present. The source of the wild speculations about 
Mars, to which reference is made above, is to be found in 
the suggestion frequently made, half in jest and half in 
earnest, that the canals are artificial water courses con- 
structed upon a scale vastly exceeding any public works 
upon the earth, and testifying to the presence in Mars of 
an advanced civilization. The distinguished Italian as- 
tronomer, Schiaparelli, who has studied these formations 
longer than any one else, seems inclined to regard them as 
water courses lined on either side by vegetation, which 
flourishes as far back from the central channel as water 
can be supplied from it a plausible enough explanation if 
the fundamental difficulty about temperature can be over- 

155. Satellites. In 1877, one of the times of near ap- 
proach, Professor Hall, of Washington, discovered two tiny 
satellites revolving about Mars in orbits so small that the 
nearer one, Phobos, presents the remarkable anomaly of 
completing the circuit of its orbit in less time than the 
planet takes for a rotation about its axis. This satellite, in 
fact, makes three revolutions in its orbit while the planet 
turns once upon its axis, and it therefore rises in the west 
and sets in the east, as seen from Mars, going from one 

3 S SS?g2o2SS?3S? 


horizon to the other in a little less than 6 hours. The 
other satellite, Deimos, takes a few hours more than a day 
to make the circuit of its orhit, but the difference is so 
small that it remains continuously above the horizon of 
any given place upon Mars for more than 60 hours at a 
time, and during this period runs twice through its com- 
plete set of phases new, first quarter, full, etc. In ordi- 
nary telescopes these satellites can be seen only under espe- 
cially favorable circumstances, and are far too small to 
permit of any direct measurement of their size. The 
amount of light which they reflect has been compared 
with that of Mars and found to be as much inferior to it 
as is Polaris to two full moons, and, judging from this com- 
parison, their diameters can not much exceed a half dozen 
miles, unless their albedo is far less than that of Mars, 
which does not seem probable. 


156. Minor planets. These may be dismissed with few 
words. There are about 500 of them known, all discovered 
since the beginning of the nineteenth century, and new 
ones are still found every year. No one pretends to 
remember the names which have been assigned them, and 
they are commonly represented by a number inclosed in a 
circle, showing the order in which they were discovered 
e. g., Q = Ceres, @ Eros, etc. For the most part they 
are little more than chips, world fragments, adrift in space, 
and naturally it was the larger and brighter of them that 
were first discovered. The size of the first four of them 
Ceres, Pallas, Juno, and Vesta compared with the size of 
the moon, according to Professor Barnard, is shown in Fig. 
100. The great majority of them must be much smaller 
than the smallest of these, perhaps not more than a score 
of miles in diameter. 

A few of the asteroids present problems of special in- 
terest, such as Eros, on account of its close approach to the 



earth ; Polyhymnia, whose very eccentric orbit makes it a 
valuable means for determining the mass of Jupiter, etc.; 
but these are special cases and the average asteroid now 
receives scant attention, although half a century ago, when 
only a few of them were known, they were regarded with 
much interest, and the discovery of a new one was an event 
of some consequence. 

It was then a favorite speculation that they were in fact 
fragments of an ill-fated planet which once filled the gap 

between the orbits of Mars 
and Jupiter, but which, by 
some mischance, had been 
blown into pieces. This is 
now known to be well-nigh 
impossible, for every frag- 
ment which after the explo- 
sion moved in an elliptical 
orbit, as all the asteroids do 
move, would be brought 
back once in every revolu- 
tion to the place of the ex- 
plosion, and all the asteroid 
orbits must therefore inter- 
sect at this place. But there is no such common point of 

157. Life on the planets. There is a belief firmly 
grounded in the popular mind, and not without its ad- 
vocates among professional astronomers, that the planets 
are inhabited by living and intelligent beings, and it seems 
proper at the close of this chapter to inquire briefly how 
far the facts and principles here developed are consistent 
with this belief, and what support, if any, they lend to it. 

At the outset we must observe that the word life is an 
elastic term, hard to define in any satisfactory way, and yet 
standing for something which we know here upon the 
earth. It is this idea, our familiar though crude knowl- 

FIG. 100. The size of the first four 
asteroids. BARNARD. 


edge of life, which lies at the root of the matter. Life, if 
it exists in another planet, must be in its essential char- 
acter like life upon the earth, and must at least possess 
those features which are common to all forms of terrestrial 
life. It is an abuse of language to say that life in Mars- 
may be utterly unlike life in the earth ; if it is absolutely 
unlike, it is not life, whatever else it may be. Now, every 
form of life found upon the earth has for its physical basis 
a certain chemical compound, called protoplasm, which 
can exist and perpetuate itself only within a narrow range 
of temperature, roughly speaking, between and 100 
centigrade, although these limits can be considerably over- 
stepped for short periods of time. Moreover, this proto- 
plasm can be active only in the presence of water, or water 
vapor, and we may therefore establish as the necessary con- 
ditions for the continued existence and reproduction of 
life in any place that its temperature must not be perma- 
nently above 100 or below 0, C., and water must be pres- 
ent in that place in some form. 

With these conditions before us it is plain that life can 
not exist in the sun on account of its high temperature. 
It is conceivable that active and intelligent beings, salaman- 
ders, might exist there, but they could not properly be said 
to live. In Jupiter and Saturn the same condition of high 
temperature prevails, and probably also in Uranus and 
Xeptune, so that it seems highly improbable that any of 
these planets should be the home of life. 

Of the inner planets, Mercury and the moon seem desti- 
tute of any considerable atmospheres, and are therefore 
lacking in the supply of water necessary for life, and the 
same is almost certainly true of all the asteroids. There 
remain Venus, Mars, and the satellites of the outer planets, 
which latter, however, we must drop from consideration as 
being too little known. On Venus there is an atmosphere 
probably containing vapor of water, and it is well within 
the range of possibility that liquid water should exist upon 


the surface of this planet and that its temperature should 
fall within the prescribed limits. It would, however, be 
straining our actual knowledge to affirm that such is the 
case, or to insist that if such were the case, life would ne- 
cessarily exist upon the planet. 

On Mars we encounter the fundamental difficulty of 
temperature already noted in 152. If in some unknown 
way the temperature is maintained sufficiently high for the 
polar caps to be real snow, thawing and forming again with 
the progress of the seasons, the necessary conditions of life 
would seem to be fulfilled here and life if once introduced 
upon the planet might abide and flourish. But of positive 
proof that such is the case we have none. 

On the whole, our survey lends little encouragement to 
the belief in planetary life, for aside from the earth, of all 
the hundreds of bodies in the solar system, not one is found 
in which the necessary conditions of life are certainly ful- 
filled, and only two exist in which there is a reasonable 
probability that these conditions may be satisfied. 



158. Visitors in the solar system. All of the objects 
sun, moon, planets, stars which we have thus far had to 
consider, are permanent citizens of the sky, and we have no 
reason to suppose that their present appearance differs ap- 
preciably from what it was 1,000 years or 10,000 years ago. 
But there is another class of objects comets, meteors 
which appear unexpectedly, are visible for a time, and then 
vanish and are seen no more. On account of this temporary 
character the astronomers of ancient and mediaeval times 
for the most part refused to regard them as celestial bodies 
but classed them along with clouds, fogs, Jack-o'-lanterns, 
and fireflies, as exhalations from the swamps or the vol- 
cano ; admitting them to be indeed important as harbingers 
of evil to mankind, but having no especial significance for 
the astronomer. 

The comet of 1018 A. D. inspired the lines 

" Eight things there be a Comet brings, 
When it on high doth horrid range : 
Wind, Famine, Plague, and Death to Kings, 

War, Earthquakes, Floods, and Direful Change," 

which, according to White (History of the Doctrine of 
Comets), were to be taught in all seriousness to peasants 
and school children. 

It was by slow degrees, and only after direct measure- 
ments of parallax had shown some of them to be more dis- 
tant than the moon, that the tide of old opinion was turned 
and comets were transferred from the sublunary to the 




celestial sphere, and in more recent times meteors also 
have been recognized as coming to us from outside the 
earth. A meteor, or shooting star as it is often called, is 
one of the commonest of phenomena, and one can hardly 
watch the sky for an hour on any clear and moonless night 
without seeing several of those quick flashes of light which 
look as if some star had suddenly left its place, dashed 
swiftly across a portion of the sky and then vanished. It 
is this misleading appearance that prohably is responsible 
for the name shooting star. 

159. Comets, Comets are less common and much longer- 
lived than meteors, lasting usually for several weeks, and 
may be visible night after night for many months, but 
never for many years, at a time. During the last decade 

FIG. 101. Douati's comet. BOND. 

there is no year in which less than three comets have 
appeared, and 1898 is distinguished by the discovery of 
ten of these bodies, the largest number ever found in 
one year. On the average, we may expect a new comet to 



be found about once in every ten weeks, but for the most 
part they are small affairs, visible only in the telescope, and 
a fine large one, like Donati's comet of 1858 (Fig. 101), or 
the Great Comet of Septem- 
ber, 1882, which was visible in 
broad daylight close beside the 
sun, is a rare spectacle, and as 
striking and impressive as it 
is rare. 

Note in Fig. 102 the great 
variety of aspect presented 
by some of the more famous 
comets, which are here repre- 
sented upon a very small scale. 

Fig. 103 is from a photo- 
graph of one of the faint 
comets of the year 1893, which 
appears here as a rather feeble 
streak of light amid the stars 
which are scattered over the 
background of the picture. 

An apparently detached portion of this comet is shown at 
the extreme left of the picture, looking almost like another 
independent comet. The clean, straight line running diag- 
onally across the picture is the flash of a bright meteor 
that chanced to pass within the range of the camera while 
the comet was being photographed. 

A more striking representation of a moderately bright 
telescopic comet is contained in Figs. 104 and 105, which 
present two different views of the same comet, showing a 
considerable change in its appearance. A striking feature 
of Fig. 105 is the star images, which are here drawn out into 
short lines all parallel with each other. During the expos- 
ure of 2h. 20m. required to imprint this picture upon the 
photographic plate, the comet was continually changing its 
position among the stars on account of its orbital motion, 

FIG. 102. Some famous comets. 



and the plate was therefore moved from time to time, so as 
to follow the comet and make its image always fall at the 
same place. Hence the plate was continually shifted rela- 
tive to the stars whose images, drawn out into lines, show 
the direction in which the plate was moved i. e., the direc- 
tion in which the comet was moving across the sky. The 
same effect is shown in the other photographs, but less 
conspicuously than here on account of their shorter expos- 
ure times. 

These pictures all show that one end of the comet is 
brighter and apparently more dense than the other, and it 

is customary to call 
this bright part the 
head of the comet, 
while the brushlike 
appendage that 
streams away from 
it is called the 
comet's tail. 

160. The parts 
of a comet. It is 
not every comet 
that has a tail, 
though all the 
large ones do, and 
in Fig. 103 the de- 
tached piece of 
cometary matter at 
the left of the 
picture represents 

very well the appearance of a tailless comet, a rather large 
but not very bright star of a fuzzy or hairy appearance. 
The word comet means long-haired or hairy star. Some- 
thing of this vagueness of outline is found in all comets, 
whose exact boundaries are hard to define, instead of being 
sharp and clean-cut like those of a planet or satellite. 

FIG. 103. Brooke's comet, November 13, 1893. 


Often, however, there is found in the head of a comet a 
much more solid appearing part, like the round white ball 
at the center of Fig. 106, which is called the nucleus of 

FIG. 104. Swift's comet, April 17, 1892. BAKNARD. 

the comet, and appears to be in some sort the center from 
which its activities radiate. As shown in Figs. 106 and 
107, the nucleus is sometimes surrounded by what are 
called envelopes, which have the appearance of successive 
wrappings or halos placed about it, and odd, spurlike pro- 
jections, called jets, are sometimes found in connection 
with the envelopes or in place of them. These figures also 
show what is quite a common characteristic of large 
comets, a dark streak running down the axis of the tail, 
showing that the tail is hollow, a mere shell surrounding 
empty space. 

The amount of detail shown in Figs. 106 and 107 is, 
however, quite exceptional, and the ordinary comet is much 
more like Fig. 103 or 104. Even a great comet when it 


first appears is not unlike the detached fragment in Fig. 
103, a faint and roundish patch of foggy light which grows 
through successive stages to its maximum estate, develop- 
ing a tail, nucleus, envelopes, etc., only to lose them again 
as it shrinks and finally disappears. 

161. The orbits of comets, It will be remembered that 
Newton found, as a theoretical consequence of the law of 
gravitation, that a body moving under the influence of the 
sun's attraction might have as its orbit any one of the 
conic sections, ellipse, parabola, or hyperbola, and among 
the 400 and more comet orbits which have been deter- 
mined every one of these orbit forms appear, but curiously 
enough there is not a hyperbola among them which, if 
drawn upon paper, could be distinguished by the unaided 

FIG. 105. Swift's comet, April 24, 1892. BARNARD. 

eye from a parabola, and the ellipses are all so long and 
narrow, not one of them being so nearly round as is the 
most eccentric planet orbit, that astronomers are accus- 
tomed to look upon the parabola as being the normal type 



of comet orbit, and to regard a comet whose motion differs 
much from a parabola as being abnormal and calling for 
some special explanation. 

The fact that comet orbits are parabolas, or differ but 
little from them, explains at once the temporary character 
and speedy disappearance 
of these bodies. They 
are visitors to the solar 
system and visible for 
only a short time, because 
the parabola in which 
they travel is not a closed 
curve, and the comet, hav- 
ing passed once along 
that portion of it near the 
earth and the sun, moves 
off along a path which 
ever thereafter takes it 
farther and farther away, 
beyond the limit of visi- 
bility. The development 
of the comet during the 
time it is visible, the 
growth and disappearance 

of tail, nucleus, etc., depend upon its changing distance 
from the sun, the highest development and most complex 
structure being presented when it is nearest to the sun. 

Fig. 108 shows the path of the Great Comet of 1882 
during the period in which it was seen, from September 3, 
1882, to May 26, 1883. These dates IX, 3, and V, 26 are 
marked in the figure opposite the parts of the orbit in 
which the comet stood at those times. Similarly, the posi- 
tions of the earth in its orbit at the beginning of Septem- 
ber, October, Xovember, etc., are marked by the Roman 
numerals IX, X, XI, etc. The line S V shows the direction 
from the sun to the vernal equinox, and S& is the line 

FIG. 106. Head of Coggia's comet, 
July 13, 1874. BOND. 



along which the plane of the comet's orbit intersects the 
plane of the earth's orbit i. e., it is the line of nodes of the 
comet orbit. Since the comet approached the sun from 
the south side of the ecliptic, all of its orbit, save the little 
segment which falls to the left of $Q, lies below (south) of 
the plane of the earth's orbit, and the part which would 
be hidden if this plane were opaque is represented by a 
broken line. 

162. Elements of a comet's orbit, There is a theorem of 
geometry to the effect that through any three points not 
in the same straight line one circle, and only one, can be 
drawn. Corresponding to this there is a theorem of celes- 
tial mechanics, that through any three positions of a comet 

one conic section, and 
only one, can be passed 
along which the comet 
can move in accordance 
with the law of gravita- 
tion. This conic section 
is, of course, its orbit, and 
at the discovery of a com- 
et astronomers always 
hasten to observe its po- 
sition in the sky on dif- 
ferent nights in order to 
obtain the three positions 
(right ascensions and de- 
clinations) necessary for 
determining the particu- 
lar orbit in which it 
moves. The circle, to 
which reference was made 
above, is completely as- 
certained and defined when we know its radius and the 
position of its center. A parabola is not so simply defined, 
and five numbers, called the elements of its orbit, are 

FIG. 107. Head of Donati's comet, Septem- 
ber 30, October 2, 1858. BOND. 



required to fix accurately a comet's path around the sun. 
Two of these relate to the position of the line of nodes and 
the angle which the orbit plane makes with the plane of the 
ecliptic ; a third fixes the direction of the axis of the orbit 

FIG. 108. Orbits of the earth and the 
Great Comet of 1882. 

in its plane, and the remaining two, which are of more 
interest to us, are the date at which the comet makes its 
nearest approach to the sun (perihelion passage) and its 
distance from the sun at that date (perihelion distance). 
The date, September 17th, placed near the center of Fig. 
108, is the former of these elements, while the latter, which 
is too small to be accurately measured here, may be found 
from Fig. 109 to be 0.82 of the sun's diameter, or, in terms 
of the earth's distance from the sun, C.008. 

Fig. 109 shows on a large scale the shape of that part of 
the orbit near the sun and gives the successive positions of 
the comet, at intervals of T 2 of a day, on September 16th 
and 17th, showing that in less than 10 hours 17.0 to 17.4 
the comet swung around the sun through an angle of 



more than 240. When at its perihelion it was moving 
with a velocity of 300 miles per second ! This very unusual 
velocity was due to the comet's extraordinarily close ap- 
proach to the sun. The earth's velocity in its orbit is only 
19 miles per second, and the velocity of any comet at any 
distance from the sun, provided its orbit is a parabola, may 
be found by dividing this number by the square root of 
half the comet's distance e. g., 300 miles per second equals 

Most of the visible comets have their perihelion dis- 
tances included between ^ and f of the earth's distance 
from the sun, but occasionally one is found, like the 
second comet of 1885, whose nearest approach to the sun 

FIG. 109. Motion of the Great Comet of 1882 in passing around the sun. 

lies far outside the earth's orbit, in this case half-way 
out to the orbit of Jupiter; but such a comet must be a 
very large one in order to be seen at all from the earth. 



FIG. 110. The Great Comet of 1843. 

There is, however, some reason for believing that the num- 
ber of comets which move around the sun without ever 
coming inside the orbit of Jupiter, or even that of Saturn, 
is much larger than the number of those which come close 
enough to be discovered from the earth. In any case we 
are reminded of Kepler's saying, that comets in the sky are 
as plentiful as fishes in the sea, which seems to be very little 
exaggerated when we consider that, according to Kleiber, 
out of all the comets which enter the solar system probably 
not more than 2 or 3 per cent are ever discovered. 

163. Dimensions of comets, The comet whose orbit is 
shown in Figs. 108 and 109 is the finest and largest that 
has appeared in recent years. Its tail, which at its maxi- 
mum extent would have more than bridged the space be- 
tween sun and earth (100,000,000 miles), is made very much 
too short in Fig. 109, but when at its best was probably not 
inferior to that of the Great Comet in 1843, shown in Fig. 


110. As we shall see later, there is a peculiar and special 
relationship between these two comets. 

The head of the comet of 1882 was not especially large 
about twice the diameter of the ball of Saturn but its 
nucleus, according to an estimate made by Dr. Elkin when 
it was very near perihelion, was as large as the moon. The 
head of the comet shown in Fig. 107 was too large to be 
put in the space between the earth and the moon, and the 
Great Comet of 1811 had a head considerably larger than 
the sun itself. From these colossal sizes down to the 
smallest shred just visible in the telescope, comets of all 
dimensions may be found, but the smaller the comet the 
less the chance of its being discovered, and a comet as small 
as the earth would probably go unobserved unless it ap- 
proached very close to us. 

164. The mass of a comet, There is no known case in 
which the mass of a comet has ever been measured, yet 
nothing about them is more sure than that they are bodies 
with mass which is attracted by the sun and the planets, 
and which in its turn attracts both sun and planets and 
produces perturbations in their motion. These perturba- 
tions are, however, too small to be measured, although the 
corresponding perturbations in the comet's motion are 
sometimes enormous, and since these mutual perturbations 
are proportional to the masses of comet and planet, we are 
forced to say that, by comparison with even such small 
bodies as the moon or Mercury, the mass of a comet is 
utterly insignificant, certainly not as great as a ten-thou- 
'"salrdth part of the mass of the earth. In the case of the 
Great Comet of 1882, if we leave its hundred million miles 
of tail out^pf account and suppose the entire mass condensed 
into its head, we find by a little computation that the aver- 
age density of^ the head under these circumstances must 
have been less\ than T ^Vo- P art of tne density of air. In 
ordinary laboratory practice this would be called a pretty 
good vacuum. 


A striking observation made on September 17, 1882, 
goes to confirm the very small density of this comet. It 
is shown in Fig. 109 that early on that day the comet 
crossed the line joining earth and sun, and therefore passed 
in transit over the sun's disk. Two observers at the Cape 
of Good Hope saw the comet approach the sun, and fol- 
lowed it with their telescopes until the nucleus actually 
reached the edge of the sun and disappeared, behind it as 
they supposed, for no trace of the comet, not even its 
nucleus, could be seen against the sun, although it was care- 
fully looked for. Now, the figure shows that the comet 
passed between the earth and sun, and its densest parts 
were therefore too attenuated to cut off any perceptible 
fraction of the sun's rays. In other cases stars have been 
seen through the head of a comet, shining apparently with 
undimmed luster, although in some cases they seem to 
have been slightly refracted out of their true positions. 

165. Meteors. Before proceeding further with the study 
of comets it is well to turn aside and consider their hum- 
bler relatives, the shooting stars. On some clear evening, 
when the moon is absent from the sky, watch the heavens 
for an hour and count the meteors visible during that time. 
Note their paths, the part of the sky where they appear 
and where they disappear, their brightness, and whether 
they all move with equal swiftness. Out of such simple 
observations with the unaided eye there has grown a large 
and important branch of astronomical science, some parts 
of which we shall briefly summarize here. 

A particular meteor is a local phenomenon seen over 
only a small part of the earth's surface, although occasion- 
ally a very big and bright one may travel and be visible 
over a considerable territory. Such a one in December, 
1876, swept over the United States from Kansas to Penn- 
sylvania, and was seen from eleven different States. But the 
ordinary shooting star is much less conspicuous, and, as we 
know from simultaneous observations made at neighboring 


places, it makes its appearance at a height of some 75 miles 
above the earth's surface, occupies something like a second 
in moving over its path, and then disappears at a height 
of ahout 50 miles or more, although occasionally a big one 
comes down to the very surface of the earth with force 
sufficient to bury itself in the ground, from which it may 
be dug up, handled, weighed, and turned over to the chem- 
ist to be analyzed. The pieces thus found show that the 
big meteors, at least, are masses of stone or mineral ; iron 
is quite commonly found in them, as are a considerable 
number of other terrestrial substances combined in rather 
peculiar ways. But no chemical element not found on the 
earth has ever been discovered in a meteor. 

166. Nature of meteors. The swiftness with which the 
meteors sweep down shows that they must come from out- 
side the earth, for even half their velocity, if given to them 
by some terrestrial volcano or other explosive agent, would 
send them completely away from the earth never to return. 
We must therefore look upon them as so many projectiles, 
bullets, fired against the earth from some outside source 
and arrested in their motion by the earth's atmosphere, 
which serves as a cushion to protect the ground from the 
bombardment which would otherwise prove in the highest 
degree dangerous to both property and life. The speed of 
the meteor is checked by the resistance which the atmos- 
phere offers to its motion, and the energy represented by 
that speed is transformed into heat, which in less than a 
second raises the meteor and the surrounding air to incan- 
descence, melts the meteor either wholly or in part, and 
usually destroys its identity, leaving only an impalpable 
dust, which cools off as it settles slowly through the lower 
atmosphere to the ground. The heating effect of the air's 
resistance is proportional to the square of the meteor's 
velocity, and even at such a moderate speed as 1 mile per 
second the effect upon the meteor is the same as if it stood 
still in a bath of red-hot air. Now, the actual velocity of 


meteors through the air is often 30 or 40 times as great as 
this, and the corresponding effect of the air in raising its 
temperature is more than 1,000 times that of red heat. 
Small wonder that the meteor is brought to lively incan- 
descence and consumed even in a fraction of a second. 

167. The number of meteors. A single observer may 
expect to see in the evening hours about one meteor every 
10 minutes on the average, although, of course, in this 
respect much irregularity may occur. Later in the night 
they become more frequent, and after 2 A. M. there are 
about three times as many to be seen as in the evening 
hours. But no one person can keep a watch upon the 
whole sky, high and low, in front and behind, and experi- 
ence shows that by increasing the number of observers and 
assigning to each a particular part of the sky, the total 
number of meteors counted may be increased about five- 
fold. So, too, the observers at any one place can keep an 
effective watch upon only those meteors which come into the 
earth's atmosphere within some moderate distance of their 
station, say 50 or 100 miles, and to watch every part of that 
atmosphere would require a large number of stations, esti- 
mated at something more than 10,000, scattered systemat- 
ically over the whole face of the earth. If we piece to- 
gether the several numbers above considered, taking 14 as 
a fair average of the hourly number of meteors to be seen 
by a single observer at all hours of the night, we shall find 
for the total number of meteors encountered by the earth 
in 24 hours, 14 X 5 X 10,000 x 24 = 16,800,000. Without 
laying too much stress upon this particular number, we 
may fairly say that the meteors picked up by the earth 
every day are to be reckoned by millions, and since they 
come at all seasons of the year, we shall have to admit that 
the region through which the earth moves, instead of being 
empty space, is really a dust cloud, each individual particle 
of dust being a prospective meteor. 

On the average these individual particles are very small 


and very far apart ; a cloud of silver dimes each about 250 
miles from its nearest neighbor is perhaps a fair representa- 
tion of their average mass and distance from each other, 
but, of course, great variations are to be expected both in the 
size and in the frequency of the particles. There must be 
great numbers of them that are too small to make shooting 
stars visible to the naked eye, and such are occasionally 
seen darting by chance across the field of view of a tele- 

168. The zodiacal light is an effect probably due to the 
reflection of sunlight from the myriads of these tiny meteors 
which occupy the space inside the earth's orbit. It is a 
faint and diffuse stream of light, something like the Milky 
Way, which may be seen in the early evening or morning 
stretching up from the sunrise or sunset point of the 
horizon along the ecliptic and following its course for 
many degrees, possibly around the entire circumference of 
the sky. It may be seen at any season of the year, although 
it shows to the best advantage in spring evenings and 
autumn mornings. Look for it. 

169. Great meteors. But there are other meteors, veri- 
table fireballs in appearance, far more conspicuous and im- 
posing than the ordinary shooting star. Such a one ex- 
ploded over the city of Madrid, Spain, on the morning of 
February 10, 1896, giving in broad sunlight " a brilliant 
flash which was followed ninety seconds later by a succes- 
sion of terrific noises like the discharge of a battery of 
artillery." Fig. 110 shows a large meteor which was seen 
in California in the early evening of July 27, 1894, and 
which left behind it a luminous trail or cloud visible for 
more than half an hour. 

Not infrequently large meteors are found traveling 
together, two or three or more in company, making their 
appearance simultaneously as did the California meteor of 
October 22, 1896, which is described as triple, the trio fol- 
lowing one another like a train of cars, and Arago cites an 



instance, from the year 1830, where within a short space of 
time some forty brilliant meteors crossed the sky, all mov- 
ing in the same direction with a whistling noise and dis- 
playing in their flight all the colors of the rainbow. 

The mass of great meteors such as these must be meas- 
ured in hundreds if not thousands of pounds, and stories 
are current, although not 
very well authenticated, of 
even larger ones, many tons 
in weight, having been found 
partially buried in the ground. 
Of meteors which have been 
actually seen to fall from the 
sky, the largest single frag- 
ment recovered weighs about 
500 pounds, but it is only a 
fragment of the original me- 
teor, which must have been 
much more massive before it 
was broken up by collision 
with the atmosphere. 

170. The velocity of me- 
teors. Every meteor, big or 
little, is subject to the law of 
gravitation, and before it en- 
counters the earth must be 
moving in some kind of orbit 
having the sun at its focus, 
the particular species of orbit ellipse, parabola, hyperbola 
depending upon the velocity and direction of its motion. 
Xow, the direction in which a meteor is moving can be 
determined without serious difficulty from observations of 
its apparent path across the sky made by two or more ob- 
servers, but the velocity can not be so readily found, since 
the meteors go too fast for any ordinary process of timing. 
But by photographing one of them two or three times on 

FIG. 111. The California meteor of 
July 27, 1894. 


the same plate, with an interval of only a tenth of a second 
between exposures, Dr. Elkin has succeeded in showing, in 
a few cases, that their velocities varied from 20 to 25 miles 
per second, and must have been considerably greater than 
this before the meteors encountered the earth's atmosphere. 
This is a greater velocity than that of the earth in its orbit, 
19 miles per second, as might have been anticipated, since 
the mere fact that meteors can be seen at all in the evening 
hours shows that some of them at least must travel consid- 
erably faster than the earth, for, counting in the direction 
of the earth's motion, the region of sunset and evening is 
always on the rear side of the earth, and meteors in order 
to strike this region must overtake it by their swifter 
motion. We have here, in fact, the reason why meteors 
are especially abundant in the morning hours ; at this time 
the observer is on the front side of the earth which catches 
swift and slow meteors alike, while the rear is pelted only 
by the swifter ones which follow it. 

A comparison of the relative number of morning and 
evening meteors makes it probable that the average meteor 
moves, relative to the sun, with a velocity of about 26 miles 
per second, which is very approximately the average velocity 
of comets when they are at the earth's distance from the 
sun. Astronomers, therefore, consider meteors as well as 
comets to have the parabola and the elongated ellipse as 
their characteristic orbits. 

171. Meteor showers The radiant. There is evident 
among meteors a distinct tendency for individuals, to the 
number of hundreds or even hundreds of millions, to 
travel together in flocks or swarms, all going the same way 
in orbits almost exactly alike. This gregarious tendency is 
made manifest not only by the fact that from time to time 
there are unusually abundant meteoric displays, but also 
by a striking peculiarity of their behavior at such times. 
The meteors all seem to come from a particular part of the 
heavens, as if here were a hole in the sky through which 


they were introduced, and from which they flow away in 
every direction, even those which do not visibly start from 
this place having paths among the stars which, if prolong- 
ing backward, would pass through it. The cause of this 
appearance may be understood from Fig. 112, which repre-^ 

FIG. 112. Explanation of the radiant of a meteoric shower. DENNING. 

sents a group of meteors moving together along parallel 
paths toward an observer at D. Traveling unseen above 
the earth until they encounter the upper strata of its at- 
mosphere, they here become incandescent and speed on in 
parallel paths, -?, #, 3, ^, 5, 0, which, as seen by the observer, 
are projected back against the sky into luminous streaks 
that, as is shown by the arrowheads, #, c, d, all seem to 
radiate from the point a i. e., from the point in the sky 
whose direction from the observer is parallel to the paths 
of the meteors. 

Such a display is called a meteor shower, and the point 
a is called its radiant. Note how those meteors which 
appear near the radiant all have short paths, while those 
remote from it in the sky have longer ones. Query : As 
the night wears on and the stars shift toward the west, will 



the radiant share in their motion or will it be left behind ? 
Would the luminous part of the path of any of these me- 
teors pass across the radiant from one side to the other ? 
Is such a crossing of the radiant possible under any circum- 
stances ? Fig. 113 shows how the meteor paths are grouped 
around the radiant of a strongly marked shower. Select 
from it the meteors which do not belong to this shower. 

FIG. 113. The radiant of a meteoric shower, showing also the paths of three meteors 
which do not belong to this shower. DENNING. 

Many hundreds of these radiants have been observed in 
the sky, each of which represents an orbit along which a 
group of meteors moves, and the relation of one of these 


orbits to that of the earth is shown in Fig. 114. The orbit 
of the meteors is an ellipse extending out beyond the orbit 
of Uranus, but so eccentric that a part of it comes inside 
the orbit of the earth, and the figure shows only that part 
of it which lies nearest the sun. The Eoman numerals 

Fia. 114. The orbits of the earth and the November meteors. 

which are placed along the earth's orbit show the position 
of the earth at the beginning of the tenth month, eleventh 
month, etc. The meteors flow along their orbit in a long 
procession, whose direction of motion is indicated by the 
arrow heads, and the earth, coming in the opposite direc- 
tion, plunges into this stream and receives the meteor 
shower when it reaches the intersection of the two orbits. 
The long arrow at the left of the figure represents the 
direction of motion of another meteor shower which 
encounters the earth at this point. 

Can you determine from the figure answers to the fol- 
lowing questions ? On what day of the year will the earth 
meet each of these showers? Will the radiant points of 
the showers lie above or below the plane of the earth's 


orbit ? Will these meteors strike the front or the rear of 
the earth ? Can they be seen in the evening hours ? 

From many of the radiants year after year, upon the 
same day or week in each year, there comes a swarm of 
shooting stars, showing that there must be a continuous 
procession of meteors moving along this orbit, so that some 
are always ready to strike the earth whenever it reaches 
the intersection of its orbit with theirs. Such is the expla- 
nation of the shower which appears each year in the first 
half of August, and whose meteors are sometimes called 
Perseids, because their radiant lies in the constellation 
Perseus, and a similar explanation holds for all the star 
showers which are repeated year after year. 

172. The Leonids. There is, however, a kind of star 
shower, of which the Leonids (radiant in Leo) is the most 
conspicuous type, in which the shower, although repeated 
from year to year, is much more striking in some years 
than in others. Thus, to quote from the historian : " In 
1833 the shower was well observed along the whole eastern 
coast of North America from the Gulf of Mexico to Hali- 
fax. The meteors were most numerous at about 5 A. M. on 
November 13th, and the rising sun could not blot out all 
traces of the phenomena, for large meteors were seen now and 
then in full daylight. Within the scope that the eye could 
contain, more than twenty could be seen at a time shooting 
in every direction. Not a cloud obscured the broad expanse, 
and millions of meteors sped their way across in every 
point of the compass. Their coruscations were bright, 
gleaming, and incessant, and they fell thick as the flakes in 
the early snows of December." But, so far as is known, none 
of them reached the ground. An illiterate man on the fol- 
lowing day remarked : " The stars continued to fall until 
none were left. I am anxious to see how the heavens will 
appear this evening, for I believe we shall see no more stars." 

An eyewitness in the Southern States thus describes 
the effect of this shower upon the plantation negroes : 


" Upward of a hundred lay prostrate upon the ground, 
some speechless and some with the bitterest cries, but with 
their hands upraised, imploring God to save the world and 
them. The scene was truly awful, for never did rain fall 
much thicker than the meteors fell toward the earth east, 
west, north, and south it was the same." In the preceding 
year a similar but feebler shower from the same radiant 
created much alarm in France, and through the old historic 
records its repetitions may be traced back at intervals of 33 
or 34 years, although with many interruptions, to October 
12, 902, 0. S., when " an immense number of falling stars 
were seen to spread themselves over the face of the sky 
like rain." 

Such a star shower differs from the one repeated every 
year chiefly in the fact that its meteors, instead of being 
drawn out into a long procession, are mainly clustered in a 
single flock which may be long enough to require two or 
three or four years to pass a given point of its orbit, but 
which is far from extending entirely around it, so that me- 
teors from this source are abundant only in those years in 
which the flock is at or near the intersection of its orbit 
with that of the earth. The fact that the Leonid shower is 
repeated at intervals of 33 or 34 years (it appeared in 1799, 
1832-'33, 1866-'67) shows that this is the " periodic time " 
in its orbit, which latter must of course be an ellipse, and 
presumably a long and narrow one. It is this orbit which 
is shown in Fig. 114, and the student should note in this 
figure that if the meteor stream at the point where it cuts 
through the plane of the earth's orbit were either nearer to 
or farther from the sun than is the earth there could be no 
shower ; the earth and the meteors would pass by without a 
collision. Now, the meteors in their motion are subject to 
perturbations, particularly by the large planets Jupiter, 
Saturn, and Uranus, which slightly change the meteor orbit, 
and it seems certain that the changes thus produced will 
sometimes thrust the swarm inside or outside the orbit of 


the earth, and thus cause a failure of the shower at times 
when it is expected. The meteors were due at the crossing 
of the orbits in November, 1899 and 1900, and, although a 
few were then seen, the shower was far from being a bril- 
liant one, and its failure was doubtless caused by the outer 
planets, which switched the meteors aside from the path in 
which they had been moving for a century. Whether they 
will be again switched back so as to produce future showers 
is at the present time uncertain. 

173. Capture of the Leonids. But a far more striking 
effect of perturbations is to be found in Fig. 115, which 
shows the relation of the Leonid orbit to those of the prin- 
cipal planets, and illustrates a curious chapter in the his- 
tory of the meteor swarm that has been worked out by 
mathematical analysis, and is probably a pretty good ac- 
count of what actually befell them. Early in the second 
century of the Christian era this flock of meteors came 
down toward the sun from outer space, moving along a 
parabolic orbit which would have carried it just inside the 
orbit of Jupiter, and then have sent it off to return no 
more. But such was not to be its fate. As it approached 
the orbit of Uranus, in the year 126 A. D., that planet 
chanced to be very near at hand and perturbed the motion 
of the meteors to such an extent that the character of their 
orbit was completely changed into the ellipse shown in the 
figure, and in this new orbit they have moved from that 
time to this, permanent instead of transient members of 
the solar system. The perturbations, however, did not end 
with the year in which the meteors were captured and an- 
nexed to the solar system, but ever since that time Jupiter, 
Saturn, and Uranus have been pulling together upon the 
orbit, and have gradually turned it around into its present 
position as shown in the figure, and it is chiefly this shift- 
ing of the orbit's position in the thousand years that have 
elapsed since 902 A. D. that makes the meteor shower now 
come in November instead of in October as it did then. 


174. Breaking up a meteor swarm, How closely packed 
together these meteors were at the time of their annexation 
to the solar system is unknown, but it is certain that ever 
since that time the sun has been exerting upon them a 
tidal influence tending to break up the swarm and distribute 
its particles around the orbit, as the Perseids are distrib- 
uted, and, given sufficient time, it will accomplish this, but 
up to the present the work is only partly done. A certain 
number of the meteors have gained so much over the slower 
moving ones as to have made an extra circuit of the orbit 
and overtaken the rear of the procession, so that there is a 
thin stream of them extending entirely around the orbit 
and furnishing in every November a Leonid shower; but by 
far the larger part of the meteors still cling together, al- 
though drawn out into a stream or ribbon, which, though 
very thin, is so long that it takes some three years to pass 
through the perihelion of its orbit. It is only when the 
earth plunges through this ribbon, as it should in 1899, 
1900, 1901, that brilliant Leonid showers can be expected. 

175. Relation of comets and meteors. It appears from 
the foregoing that meteors and comets move in similar or- 
bits, and we have now to push the analogy a little further 
and note that in some, instances at least they move in iden- 
tically the same orbit, or at least in orbits so like that an 
appreciable difference between them is hardly to be found. 
Thus a comet which was discovered and observed early in 
the year 1866, moves in the same orbit with the Leonid 
meteors, passing its perihelion about ten months ahead of 
the main body of the meteors. If it were set back in its 
orbit by ten months' motion, it would be a part of the meteor 
swarm. Similarly, the Perseid meteors have a comet moving 
in their orbit actually immersed in the stream of meteor 
particles, and several other of the more conspicuous star 
showers have comets attending them. 

Perhaps the most remarkable case of this character is 
that of a shower which comes in the latter part of Govern- 


ber from the constellation Andromeda, and which from its 
association with the comet called Biela (after the name of 
its discoverer) is frequently referred to as the Bielid shower. 
This comet, an inconspicuous one moving in an unusually 
small elliptical orbit, had been observed at various times 
from 1772 down to 1846 without presenting anything re- 
markable in its appearance; but about the beginning of the 
latter year, with very little warning, it broke in two, and 
for three months the pieces were watched by astronomers 
moving off, side by side, something more than half as far 
apart as are the earth and moon. It disappeared, made the 
circuit of its orbit, and six years later came back, with the 
fragments nearly ten times as far apart as before, and after 
a short stay near the earth once more disappeared in the dis- 
tance, never to be seen again, although the fragments should 
have returned to perihelion at least half a dozen times since 
then. In one respect the orbit of the comet was remark- 
able : it passed through the place in which the earth stands 
on November 27th of each year, so that if the comet were at 
that particular part of its orbit on any November 27th, a 
collision between it and the earth would be inevitable. So 
far as is known, no such collision with the comet has ever 
occurred, but the Bielid meteors which are strung along 
its orbit do encounter the earth on that date, in greater or 
less abundance in different years, and are watched with 
much interest by the astronomers who look upon them as 
the final appearance of the debris of a worn-out comet. 

176. Periodic comets, The Biela comet is a specimen of 
the type which astronomers call periodic comets i. e., 
those which move in small ellipses and have correspond- 
ingly short periodic times, so that they return frequently 
and regularly to perihelion. The comets which accompany 
the other meteor swarms Leonids, Perseids, etc. also be- 
long to this class as do some 30 or 40 others which have 
periodic times less than a century. As has been already 
indicated, these deviations from the normal parabolic orbit 


call for some special explanation, and the substance of that 
explanation is contained in the account of the Leonid 
meteors and their capture by Uranus. Any comet may be 
thus captured by the attraction of a planet near which it 
passes. It is only necessary that the perturbing action 
of the planet should result in a diminution of the comet's 
velocity, for we have already learned that it is this velocity 
which determines the character of the orbit, and anything 
less than the velocity appropriate to a parabola must pro- 
duce an ellipse i. e., a closed orbit around which the body 
will revolve time after time in endless succession. We 
note in Fig. 115 that when the Leonid swarm encountered 
Uranus it passed in front of the planet and had its velocity 
diminished and its orbit changed into an ellipse thereby. 
It might have passed behind Uranus, it would have passed 
behind had it come a little later, and the effect would then 
have been just the opposite. Its velocity would have been 
increased, its orbit changed to a hyperbola, and it would 
have left the solar system more rapidly than it came into 
it, thrust out instead of held in by the disturbing planet. 
Of such cases we can expect no record to remain, but the 
captured comet is its own witness to what has happened, 
and bears imprinted upon its orbit the brand of the planet 
which slowed down its motion. Thus in Fig. 115 the changed 
orbit of the meteors has its aphelion (part remotest from 
the sun) quite close to the orbit of Uranus, and one of its 
nodes, y, the point in which it cuts through the plane of 
the ecliptic from north to south side, is also very near to 
the same orbit. It is these two marks, aphelion and node, 
which by their position identify Uranus as the planet in- 
strumental in capturing the meteor swarm, and the date of 
the capture is found by working back with their respective 
periodic times to an epoch at which planet and comet were 
simultaneously near this node. 

Jupiter, by reason of his great mass, is an especially effi- 
cient capturer of comets, and Fig. 116 shows his group of 


captives, his family of comets as they are sometimes called. 
The several orbits are marked with the names commonly 
given to the comets. Frequently this is the name of their 
discoverer, but often a different system is followed e. g., 

FIG. 116. Jupiter's family of comets. 

the name 1886, IV, means the fourth comet to pass through 
perihelion in the year 1886. The other great planets 
Saturn, Uranus, Neptune have also their families of cap- 
tured comets, and according to Schulhof, who does not 
entirely agree with the common opinion about captured 
comets, the earth has caught no less than nine of these 

1 77. Comet groups. But there is another kind of comet 
family, or comet group as it is called, which deserves some 
notice, and which is best exemplified by the Great Comet of 
1882 and its relatives. No less than four other comets are 
known to be traveling in substantially the same orbit with 


this one, the group consisting of comets 1668, I ; 1843, I ; 
1880, I ; 1882, II ; 1887, I. The orbit itself is not quite a 
parabola, but a very elongated ellipse, whose major axis 
and corresponding periodic time can not be very accu- 
rately determined from the available data, but it certainly 
extends far beyond the orbit of Neptune, and requires not 
less than 500 years for the comet to complete a revolution 
in it. It was for a time supposed that some one of the 
recent comets of this group of five might be a return of 
the comet of 1668 brought back ahead of time by unknown 
perturbations. There is still a possibility of this, but it is 
quite out of the question to suppose that the last four 
members of the group are anything other than separate 
and distinct comets moving in practically the same orbit. 
This common orbit suggests a common origin for the 
comets, but leaves us to conjecture how they became sep- 

The observed orbits of these five comets present some 
slight discordances among themselves, but if we suppose 
each comet to move in the average of the observed paths it 
is a simple matter to fix their several positions at the pres- 
ent time. They have all receded from the sun nearly on 
line toward the bright star Sirius, and were all of them, at 
the beginning of the year 1900, standing nearly motionless 
inside of a space not bigger than the sun and distant from 
the sun about 150 radii of the earth's orbit. The great 
rapidity with which they swept through that part of their 
orbit near the sun (see 162) is being compensated by 
the present extreme slowness of their motions, so that 
the comets of 1668 and 1882, whose passages through the 
solar system were separated by an interval of more than 
two centuries, now stand together near the aphelion of their 
orbits, separated by a distance only 50 per cent greater than 
the diameter of the moon's orbit, and they will continue 
substantially in this position for some two or three centu- 
ries to come. 


The slowness with which these bodies move when far 
from the sun is strikingly illustrated by an equation of 
celestial mechanics which for parabolic orbits takes the 
place of Kepler's Third Law viz. : 

where T is the time, in years, required for the comet to 
move from its perihelion to any remote part of the orbit, 
whose distance from the sun is represented, in radii of the 
earth's orbit, by r. If the comet of 1668 had moved in a 
parabola instead of the ellipse supposed above, how many 
years would have been required to reach its present dis- 
tance from the sun ? 

178. Relation of comets to the solar system. The orbits 
of these comets illustrate a tendency which is becoming 
ever more strongly marked. Because comet orbits are 
nearly parabolas, it used to be assumed that they were 
exactly parabolic, and this carried with it the conclusion 
that comets have their origin outside the solar system. It 
may be so, and this view is in some degree supported by 
the fact that these nearly parabolic orbits of both comets 
and meteors are tipped at all possible angles to the plane 
of the ecliptic instead of lying near it as do the orbits of 
the planets ; and by the further fact that, unlike the planets, 
the comets show no marked tendency to move around their 
orbits in the direction in which the sun rotates upon his 
axis. There is, in fact, the utmost confusion among them 
in this respect, some going one way and some another. 
The law of bhe solar system (gravitation) is impressed upon 
their movements, but its order is not. 

But as observations grow more numerous and more 
precise, and comet orbits are determined with increasing 
accuracy, there is a steady gain in the number of elliptic 
orbits at the expense of the parabolic ones, and if comets 
are of extraneous origin we must admit that a very con- 


siderable percentage of them have their velocities slowed 
down within the solar system, perhaps not so much by the 
attraction of the planets as by the resistance offered to their 
motion by meteor particles and swarms along their paths. 
A striking instance of what may befall a comet in this way 
is shown in Fig. 117, where the tail of a comet appears 

FIG. 117. Brooks's comet, October 21, 1893. BARNARD. 

sadly distorted and broken by what is presumed to have 
been a collision with a meteor swarm. A more famous case 
of impeded motion is oifered by the comet which bears the 
name of Encke. This has a periodic time less than that of 
any other known comet, and at intervals of forty months 
comes back to perihelion, each time moving in a little 
smaller orbit than before, unquestionably on account of 
some resistance which it has suffered. 

179. The development of a comet, "We saw in 174 
that the sun's action upon a meteor swarm tends to 
break it up into a long stream, and the same tendency to 


break up is true of comets whose attenuated substance pre- 
sents scant resistance to this force. According to the 
mathematical analysis of Eoche, if the comet stood still 
the sun's tidal force would tend first to draw it out on line 
with the sun, just as the earth's tidal force pulled the- 
moon out of shape ( 42), and then it would cause the 
lighter part of the comet's substance to flow away from 
both ends of this long diameter. This destructive action 
of the sun is not limited to comets and meteor streams, 
for it tends to tear the earth and moon to pieces as well ; 
but the densities and the resulting mutual attractions of 
their parts are far too great to permit this to be accom- 

As a curiosity of mathematical analysis we may note 
that a spherical cloud of meteors, or dust particles weigh- 
ing a gramme each, and placed at the earth's distance from 
the sun, will be broken up and dissipated by the sun's tidal 
action if the average distance between the particles exceeds 
two yards. Now, the earth is far more dense than such a 
cloud, whose extreme tenuity, however, suggests what we 
have already learned of the small density of comets, and 
prepares us in their case for an outflow of particles at both 
ends of the diameter directed toward the sun. Some- 
thing of this kind actually occurs, for the tail of a comet 
streams out on the side opposite to the sun, and in general 
points away from the sun, as is shown in Fig. 109, and the 
envelopes and jets rise up toward the sun ; but an inspec- 
tion of Fig. 106 will show that the tail and the envelope 
are too unlike to be produced by one and the same set of 

It was long ago suggested that the sun possibly exerts 
upon a comet's substance a repelling force in addition to 
the attracting force which we call gravity. We think nat- 
urally in this connection of the repelling force which a 
charge of electricity exerts upon a similar charge placed 
on a neighboring body, and we note that if both sun and 


comet carried a considerable store of electricity upon their 
surfaces this would furnish just such a repelling force as 
seems indicated by the phenomena of comets' tails ; for the 
force of gravity would operate between the substance of 
sun and comet, and on the whole would be the controlling 
force, while the electric charges would produce a repulsion, 
relatively feeble for the big particles and strong for the 
little ones, since an electric charge lies wholly on the sur- 
face, while gravity permeates the whole mass of a body, 
and the ratio of volume (gravity) to surface (electric 
charge) increases rapidly with increasing size. The repel- 
ling force would thrust back toward the comet those parti- 
cles which flowed out toward the sun, while it would urge 
forward those which flowed away from it, thus producing 
the difference in appearance between tail and envelopes, 
the latter being regarded from this standpoint as stunted 
tails strongly curved backward. In recent years the Eus- 
sian astronomer Bredichin has made a careful study of the 
shape and positions of comets' tails and finds that they fit 
with mathematical precision to the theories of electric 

180. Comet tails. According to Bredichin, a comet's 
tail is formed by something like the following process : In 
the head of the comet itself a certain part of its matter is 
broken up into fine bits, single molecules perhaps, which, 
as they no longer cling together, may be described as in 
the condition of vapor. By the repellent action of both 
sun and comet these molecules are cast out from the head 
of the comet and stream away in the direction opposite to 
the sun with different velocities, the heavy ones slowly and 
the light ones faster, much as particles of smoke stream 
away from a smokestack, making for the comet a tail 
which like a trail of smoke is composed of constantly 
changing particles. The result of this process is shown 
in Fig. 118, where the positions of the comet in its orbit 
on successive days are marked by the Roman numerals, and 



the broken lines represent the paths of molecules m 1 , m 11 , 
m m , etc., expelled from it on their several dates and travel- 
ing thereafter in 
orbits determined 
by the combined 
effect of the sun's 
attraction, the 
sun's repulsion, 
and the comet's 
repulsion. The 
comet's attrac- 
tion (gravity) is 
too small to be 
taken into ac- 
count. The line 
drawn upward 
from VI repre- 
sents the posi- 
tions of these 
molecules on the 
sixth day, and 
shows that all of 
them are arranged 
in a tail pointing 

nearly away from the sun. A similar construction for the 
other dates gives the corresponding positions of the tail, 
always pointing away from the sun. 

Only the lightest kind of molecules e. g., hydrogen 
could drift away from the comet so rapidly as is here shown. 
The heavier ones, such as carbon and iron, would be re- 
pelled as strongly by the electric forces, but they would be 
more strongly pulled back by the gravitative forces, thus 
producing a much slower separation between them and the 
head of the comet. Construct a figure such as the above, 
in which the molecules shall recede from the comet only 
one eighth as fast as in Fig. 118, and note what a different 

FIG. 118. Formation of a comet's tail. 


position it gives to the comet's tail. Instead of pointing 
directly away from the sun, it will be bent strongly to one 
side, as is the large plume-shaped tail of the Donati comet 
shown in Fig. 101. But observe that this comet has also a 
nearly straight tail, like the theoretical one of Fig. 118. 
We have here two distinct types of comet tails, and accord- 
ing to Bredichin there is still another but unusual type, 
even more strongly bent to one side of the line joining 
comet and sun, and appearing quite short and stubby. 
The existence of these three types, and their peculiarities 
of shape and position, are all satisfactorily accounted for 
by the supposition that they are made of different mate- 
rials. The relative molecular weights of hydrogen, some of 
the hydrocarbons, and iron, are such that tails composed 
of these molecules would behave just as do the actual tails 
observed and classified . into these three types. The spec- 
troscope shows that these materials hydrogen, hydrocar- 
bons, and iron are present in comets, and leaves little 
room for doubt of the essential soundness of Bredichin's 

181. Disintegration of comets. We must regard the tail 
as waste matter cast off from the comet's head, and although 
the amount of this matter is very small, it must in some 
measure diminish the comet's mass. This process is, of 
course, most active at the time of perihelion passage, and 
if the comet returns to perihelion time after time, as the 
periodic ones which move in elliptic orbits must do, this 
waste of material may become a serious matter, leading 
ultimately to the comet's destruction. It is significant in 
this connection that the periodic comets are all small and 
inconspicuous, not one of them showing a tail of any con- 
siderable dimensions, and it appears probable that they are 
far advanced along the road which, in the case of Biela's 
comet, led to its disintegration. Their fragments are in 
part strewn through the solar system, making some small 
fraction of its cloud of cosmic dust, and in part they have 


been carried away from the sun and scattered throughout 
the universe along hyperbolic orbits impressed upon them 
at the time they left the comet. 

But it is not through the tail only that the disinte- 
grating process is worked out. While Biela's comet is per- 
haps the most striking instance in which the head has 
broken up, it is by no means the only one. The Great 
Comet of 1882 cast off a considerable number of fragments 
which moved away as independent though small comets 
and other more recent comets have been seen to do the 
same. An even more striking phenomenon was the grad- 
ual breaking up of the nucleus of the same comet, 1882, 
II, into a half dozen nuclei arranged in line like beads 
upon a string, and pointing along the axis of the tail. See 
Fig. 119, which shows the series of changes observed in 
the head of this comet. 

182. Comets and the spectroscope. The spectrum pre- 
sented by comets was long a puzzle, and still retains some- 
thing of that character, although much progress has been 
made toward an understanding of it. In general it con- 
sists of two quite distinct parts first, a faint background 
of continuous spectrum due to ordinary sunlight reflected 
from the comet ; and, second, superposed upon this, three 
bright bands like the carbon band shown at the middle of 
Fig. 48, only not so sharply defined. These bands make a 
discontinuous spectrum quite similar to that given off by 
compounds of hydrogen and carbon, and of course indicate 
that a part of the comet's light originates in the body 
itself, which must therefore be incandescent, or at least 
must contain some incandescent portions. 

By heating hydrocarbons in our laboratories until they 
become incandescent, something like the comet spectrum 
may be artificially produced, but the best approximation 
to it is obtained by passing a disruptive electrical dis- 
charge through a tube in which fragments of meteors 
have been placed. A flash of lightning is a disruptive 

October 9, 1882. 

November 21, 1882. 

February 1, 1883. March 3, 1883. 

FIG. 119. The head of the Great Comet of 1882. WINLOCK. 


electrical discharge upon a grand scale. Now, meteors 
and electric phenomena have been independently brought 
to our notice in connection with comets, and with this 
suggestion it is easy to frame a general idea of the phys- 
ical condition of these objects for example, a cloud of 
meteors of different sizes so loosely clustered that the 
average density of the swarm is very low indeed ; the sev- 
eral particles in motion relative to each other, as well as to 
the sun, and disturbed in that motion by the sun's tidal 
action. Each particle carries its own electric charge, 
which may be of higher or lower tension than that of its 
neighbor, and is ready to leap across the intervening gap 
whenever two particles approach each other. To these 
conditions add the inductive effect of the sun's electric 
charge, which tends to produce a particular and artificial 
distribution of electricity among the comet's particles, and 
we may expect to find an endless succession of sparks, tiny 
lightning flashes, springing from one particle to another, 
most frequent and most vivid when the comet is near the 
sun, but never strong enough to be separately visible. 
Their number is, however, great enough to make the comet 
in part self-luminous with three kinds of light i. e., the three 
bright bands of its spectrum, whose wave lengths show in 
the comet the same elements and compounds of the ele- 
ments carbon, hydrogen, and oxygen which chemical 
analysis finds in the fallen meteor. It is not to be sup- 
posed that these are the only chemical elements in the 
comet, as they certainly are not the only ones in the me- 
teor. They are the easy ones to detect under ordinary cir- 
cumstances, but in special cases, like that of the Great 
Comet of 1882, whose near approach to the sun rendered 
its whole substance incandescent, the spectrum glows with 
additional bright lines of sodium, iron, etc. 

183. Collisions. A question sometimes asked, What 
would be the effect of a collision between the earth and a 
comet ? finds its answer in the results reached in the pre- 


ceding sections. There would be a star shower, more or 
less brilliant according to the number and size of the pieces 
which made up the comet's head. If these were like the 
remains of the Biela comet, the shower might even be a 
very tame one ; but a collision with a great comet would 
certainly produce a brilliant meteoric display if its head 
came in contact with the earth. If the comet were built of 
small pieces whose individual weights did not exceed a few 
ounces or pounds, the earth's atmosphere would prove a 
perfect shield against their attacks, reducing the pieces to 
harmless dust before they could reach the ground, and 
leaving the earth uninjured by the encounter, although the 
comet might suffer sadly from it. But big stones in the 
comet, meteors too massive to be consumed in their flight 
through the air, might work a very different effect, and by 
their bombardment play sad havoc with parts of the earth's 
surface, although any such result as the wrecking of the 
earth, or the destruction of all life upon it, does not seem 
probable. The 40 meteors of 169 may stand for a colli- 
sion with a small comet. Consult the Bible (Joshua x, 11) 
for an example of what might happen with a larger one. 



184. The constellations. In the earlier chapters the stu- 
dent has learned to distinguish between wandering stars 
(planets) and those fixed luminaries which remain year after 
year in the same constellation, shining for the most part 
with unvarying brilliancy, and presenting the most perfect 
known image of immutability. Homer and Job and pre- 
historic man saw Orion and the Pleiades much as we see 
them to-day, although the precession, by changing their 
relation to the pole of the heavens, has altered their risings 
and settings, and it may be that their luster has changed 
in some degree as they grew old with the passing centuries. 

The division of the sky into constellations dates back to 
the most primitive times, long before the Christian era, 
and the crooked and irregular boundaries of these con- 
stellations as shown by the dotted lines in Fig. 120, such 
as no modern astronomer would devise, are an inher- 
itance from antiquity, confounded and made worse in its 
descent to our day. The boundaries assigned to constella- 
tions near the south pole are much more smooth and regu- 
lar, since this part of the sky, invisible to the peoples from 
whom we inherit, was not studied and mapped until more 
modern times. The old traditions associated with each 
constellation a figure, often drawn from classical mythol- 
ogy, which was supposed to be suggested by the grouping 
of the stars : thus Ursa Major is a great bear, stalking across 
the sky, with the handle of the Dipper for his tail ; Leo is a 
lion ; Cassiopeia, a lady in a chair ; Andromeda, a maiden 



chained to a rock, etc. ; but for the most part the resem- 
blances are far-fetched and quite too fanciful to be followed 
by the ordinary eye. 

185. The number of stars. " As numerous as the stars 
of heaven " is a familiar figure of speech for expressing the 
idea of countless number, but as applied to the visible 
stars of the sky the words convey quite a wrong impression, 
for, under ordinary circumstances, in a clear sky every star 
to be seen may be counted in the course of a few hours, 
since they do not exceed 3,000 or 4,000, the exact number 
depending upon atmospheric conditions and the keenness 
of the individual eye. Test your own vision by counting 
the stars of the Pleiades. Six are easily seen, and you may 
possibly find as many as ten or twelve ; but however many 
are seen, there will be a vague impression of more just be- 
yond the limit of visibility, and doubtless this impression is 
partly responsible for the popular exaggeration of the num- 
ber of the stars. In fact, much more than half of what we 
call starlight comes from stars which are separately too 
small to be seen, but whose number is so great as to more 
than make up for their individual faintness. 

The Milky Way is just such a cloud of faint stars, and 
the student who can obtain access to a small telescope, or 
even an opera glass, should not fail to turn it toward the 
Milky Way and see for himself how that vague stream of 
light breaks up into shining points, each an independent 
star. These faint stars, which are found in every part of 
the sky as well as in the Milky Way, are usually called 
telescopic, in recognition of the fact that they can be seen 
only in the telescope, while the other brighter ones are 
known as lucid stars. 

186. Magnitudes, The telescopic stars show among them- 
selves an even greater range of brightness than do the lucid 
ones, and the system of magnitudes ( 9) has accordingly 
been extended to include them, the faintest star visible in 
the greatest telescope of the present time being of the six- 


teenth or seventeenth magnitude, while, as we have already 
learned, stars on the dividing line between the telescopic and 
the lucid ones are of the sixth magnitude. To compare the 
amount of light received from the stars with that from the 
planets, and particularly from the sun and moon, it has 
been found necessary to prolong the scale of magnitudes 
backward into the negative numbers, and we speak of the 
sun as having a stellar magnitude represented by the num- 
ber 26.5. The full moon's stellar magnitude is 12, and 
the planets range from 3 (Venus) to -f- 8 (Neptune). 
Even a very few of the stars are so bright that negative 
magnitudes must be used to represent their true relation 
to the fainter ones. Sirius, for example, the brightest of 
the fixed stars, is of the 1 magnitude, and such stars as 
Arcturus and Vega are of the magnitude. 

The relation of these magnitudes to each other has been 
so chosen that a star of any one magnitude is very approxi- 
mately 2.5 times as bright as one of the next fainter mag- 
nitude, and this ratio furnishes a convenient method of 
comparing the amount of light received from different stars. 
Thus the brightness of Venus is 2.5 X 2-5 times that of 
Sirius. The full moon is (2.5) 9 times as bright as Venus, 
etc. ; only it should be observed that the number 2.5 is not 
exactly the value of the light ratio between two consecutive 
magnitudes. Strictly this ratio is the \/ 100 = 2.5119-f-, 
so that to be entirely accurate we must say that a difference 
of five magnitudes gives a hundredfold difference of bright- 
ness. In mathematical symbols, if B represents the ratio of 
brightness (quantity of light) of two stars whose magni- 
tudes are m and n, then 

B = (100) '"? L 

How much brighter is an ordinary first-magnitude star, 
such as Aldebaran or Spica, than a star just visible to the 
naked eye ? How many of the faintest stars visible in a 
great telescope would be required to make one star just 


visible to the unaided eye ? How many full moons must 
be put in the sky in order to give an illumination as bright 
as daylight ? How large a part of the visible hemisphere 
would they occupy ? 

187. Classification by magnitudes. The brightness of all 
the lucid stars has been carefully measured with an instru- 
ment (photometer) designed for that special purpose, and 
the following table shows, according to the Harvard Pho- 
tometry, the number of stars in the whole sky, from pole to 
pole, which are brighter than the several magnitudes 
named in the table : 

The number of stars brighter than magnitude 1.0 is 11 

2.0 " 39 

" " " " 3.0 " 142 

" " " " 4.0 " 463 

" " " " " 5.0 " 1,483 

6.0 " 4,326 

It must not be inferred from this table that there are 
in the whole sky only 4,326 stars visible to the naked eye. 
The actual number is probably 50 or 60 per cent greater 
than this, and the normal human eye sees stars as faint as 
the magnitude 6.4 or 6.5, the discordance between this num- 
ber and the previous statement, that the sixth magnitude is 
the limit of the naked-eye vision, having been introduced 
in the attempt to make precise and accurate a classification 
into magnitudes which was at first only rough and approxi- 
mate. This same striving after accuracy leads to the intro- 
duction of fractional numbers to represent gradations of 
brightness intermediate between whole magnitudes. Thus 
of the 2,843 stars included between the fifth and sixth 
magnitudes a certain proportion are said to be of the 5.1 
magnitude, 5.2 magnitude, and so on to the 5.9 magnitude, 
even hundredths of a magnitude being sometimes employed. 

We have found the number of stars included between 
the fifth and sixth magnitudes by subtracting from the 
last number of the preceding table the number immedi- 


ately preceding it, and similarly we may find the number 
included between each other pair of consecutive magni- 
tudes, as follows : 

Magnitude 01234 5 6 

Number of stars. ... 11 28 103 321 1,020 2,843 
4 x 3 m 12 36 108 324 972 2,916 

In the last line each number after the first is found by 
multiplying the preceding one by 3, and the approximate 
agreement of each such number with that printed above it 
shows that on the whole, as far as the table goes, the fainter 
stars are approximately three times as numerous as those 
a magnitude brighter. 

The magnitudes of the telescopic stars have not yet 
been measured completely, and their exact number is un- 
known ; but if we apply our principle of a threefold increase 
for each successive magnitude, we shall find for the fainter 
stars those of the tenth and twelfth magnitudes prodi- 
gious numbers which run up into the millions, and even these 
are probably too small, since down to the ninth or tenth 
magnitude it is certain that the number of the telescopic 
stars increases from magnitude to magnitude in more than 
a threefold ratio. This is balanced in some degree by the 
less rapid increase which is known to exist in magnitudes 
still fainter ; and applying our formula without regard to 
these variations in the rate of increase, we obtain as a rude 
approximation to the total number of stars down to the 
fifteenth magnitude, 86,000,000. The Herschels, father 
and son, actually counted the number of stars visible in 
nearly 8,000 sample regions of the sky, and, inferring the 
character of the whole sky from these samples, we find it 
to contain 58,500,000 stars ; but the magnitude of the faint- 
est star visible in their telescope, and included in their 
count, is rather uncertain. 

How many first-magnitude stars would be needed to 
give as much light as do the 2,843 stars of magnitude 5.0 


to 6.0 ? How many tenth-magnitude stars are required to 
give the same amount of light ? 

To the modern man it seems natural to ascribe the dif- 
ferent brilliancies of the stars to their different distances 
from us ; but such was not the case 2,000 years ago, when 
each fixed star was commonly thought to be fastened to 
a " crystal sphere," which carried them with it, all at the 
same distance from us, as it turned about the earth. In 
breaking away from this erroneous idea and learning to 
think of the sky itself as only an atmospheric illusion 
through which we look to stars at very different distances 
beyond, it was easy to fall into the opposite error and to 
think of the stars as being much alike one with another, 
and, like pebbles on the beach, scattered throughout space 
with some rough degree of uniformity, so that in every 
direction there should be found in equal measure stars 
near at hand and stars far off, each shining with a luster 
proportioned to its remoteness. 

188. Distances of the stars, Now, in order to separate 
the true from the false in this last mode of thinking about 
the stars, we need some knowledge of their real distances 
from the earth, and in seeking it we encounter what is 
perhaps the most delicate and difficult problem in the 
whole range of observational astronomy. As shown in 
Fig. 121, the principles involved in determining these dis- 
tances are not fundamentally different from those em- 
ployed in determining the moon's distance from the earth. 
Thus, the ellipse at the left of the figure represents the 
earth's orbit and the position of the earth at different 
times of the year. The direction of the star A at these 
several times is shown by lines drawn through A and pro- 
longed to the background apparently furnished by the sky. 
A similar construction is made for the star B, and it is 
readily seen that owing to the changing position of the 
observer as he moves around the earth's orbit, both A and 
B will appear to move upon the background in orbits 


shaped like that of the earth as seen from the star, but 
having their size dependent upon the star's distance, the 
apparent orbit of A being larger than that of B, because A 
is nearer the earth. By measuring the angular distance 


FIG. 121. Determining a star's parallax. 

between A and B at opposite seasons of the year (e. g., the 
angles A Jan. B, and A July B) the astronomer 
determines from the change in this angle how much larger 
is the one path than the other, and thus concludes how 
much nearer is A than B. Strictly, the difference between 
the January and July angles is equal to the difference be- 
tween the angles subtended at A and B by the diameter of 
the earth's orbit, and if B were so far away that the angle 
Jan. B July were nothing at all we should get imme- 
diately from the observations the angle Jan. A July, 
which would suffice to determine the stars' distance. Sup- 
posing the diameter of the earth's orbit and the angle at A 
to be known, can you make a graphical construction that 
will determine the distance of A from the earth ? 

The angle subtended at A by the radius of the earth's 
orbit i. e., -J- (Jan. A July) is called the star's paral- 
lax, and this is commonly used by astronomers as a meas- 
ure of the star's distance instead of expressing it in linear 
units such as miles or radii of the earth's orbit. The dis- 


tance of a star is equal to the radius of the earth's orbit 
divided by the parallax, in seconds of arc, and multiplied 
by the number 206265. 

A weak point of this method of measuring stellar dis- 
tances is that it always gives what is called a relative paral- 
lax i. e., the difference between the parallaxes of A and 
B ; and while it is customary to select for B a star or stars 
supposed to be much farther off than A, it may happen, 
and sometimes does happen, that these comparison stars 
as they are called are as near or nearer than A, and give 
a negative parallax i. e., the difference between the angles 
at A and B proves to be negative, as it must whenever the 
star B is nearer than A. 

The first really successful determinations of stellar 
parallax were made by Struve and Bessel a little prior to 
1840, and since that time the distances of perhaps 100 stars 
have been measured with some degree of reliability, al- 
though the parallaxes themselves are so small never as 
great as 1" that it is extremely difficult to avoid falling 
into error, since even for the nearest star the problem of 
its distance is equivalent to finding the distance of an ob- 
ject more than 5 miles away by looking at it first with one 
eye and then with the other. Too short a base line. 

189. The sun and his neighbors. The distances of the 
sun's nearer neighbors among the stars are shown in Fig. 
123, where the two circles having the sun at their center 
represent distances from it equal respectively to 1,000,000 
and 2,000,000 times the distance between earth and sun. 
In the figure the direction of each star from the sun cor- 
responds to its right ascension, as shown by the Eoman 
numerals about the outer circle ; the true direction of the 
star from the sun can not, of course, be shown upon the 
flat surface of the paper, but it may be found by elevat- 
ing or depressing the star from the surface of the paper 
through an angle, as seen from the sun, equal to its declina- 
tion, as shown in the fifth column of the following table, 



The Surfs Nearest Neighbors 




R. A. 





a Centauri . 


14. 5h. 





LI. 21,185 



+ 37 




61 Cve-ni 



+ 38 




ft Herculis . . 



+ 39 











2 2 398 



+ 59 







+ 5 




y Draconis 


17 5 

+ 55 




Gr 34 







Lac 9 352 .... 







ff Draconis 
A. 0. 17,415-6 .... 
i\ Cassiopeias 



+ 69 

+ 68 

+ 57 






19 8 

+ 9 











Gr. 1,618 



+ 50 




10 Ursae Majoris. . 





+ 42 
+ 32 




LI. 21,258 



+ 44 




o^ Eridani 







A 11 677 


11 2 

+ 66 




LI. 18,115 
B. D. 36, 3,883 . . . 
Gr. 1,618 



+ 53 
+ 36 
+ 50 




ft Cassiopeias 



+ 59 




70 Ophiuchi 



+ 2 




Gr 1 830 



+ 74 
+ 39 




fi Cassiopeia) 



+ 54 




e Eridani 







t Qrsae Majoris 
ft Hydri 



+ 48 












Br. 3,077 
e Cvffni . . 




+ 57 
+ 33 




ft Comae 



+ 28 




dp AurigaB 



+ 44 




if Herculis 



+ 37 







+ 16 







+ 46 




B. D. 35, 4,003 . . . 
Gr. 1 646 



+ 35 

+ 49 




y Cysrni. . 



+ 40 







+ 12 







+ 39 





in which the numbers in the first column are those placed 
adjacent to the stars in the diagram to identify them. 

190. Light years. The radius of the inner circle in Fig. 
122, 1,000,000 times the earth's distance from the sun, is a 
convenient unit in which to express the stellar distances, 





FIG. 122. Stellar neighbors of the sun. 

and in the preceding table the distances of the stars from 
the sun are expressed in terms of this unit. To express 
them in miles the numbers in the table must be multi- 
plied by 93,000,000,000,000. The nearest star, a Centauri, 
is 25,000,000,000,000 miles away. But there is another 
unit in more common use i. e., the distance traveled over 


by light in the period of one year. We have already found 
( 141) that it requires light 8m. 18s. to come from the sun 
to the earth, and it is a simple matter to find from this 
datum that in a year light moves over a space equal to 
63,368 radii of the earth's orbit. This distance is called a 
light year, and the distance of the same star, a Centauri, 
expressed in terms of this unit, is 4.26 years i. e., it takes 
light that long to come from the star to the earth. 

In Fig. 122 the stellar magnitudes of the stars are indi- 
cated by the size of the dots the bigger the dot the brighter 
the star and a mere inspection of the figure will serve to 
show that within a radius of 30 light years from the sun 
bright stars and faint ones are mixed up together, and that, 
so far as distance is concerned, the sun is only a member 
of this swarm of stars, whose distances apart, each from its 
nearest neighbor, are of the same order of magnitude as 
those which separate the sun from the three or four stars 
nearest it. 

Fig. 122 is not to be supposed complete. Doubtless 
other stars will be found whose distance from the sun is less 
than 2,000,000 radii of the earth's orbit, but it is not prob- 
able that they will ever suffice to more than double or per- 
haps treble the number here shown. The vast majority of 
the stars lie far beyond the limits of the figure. 

191. Proper motions. It is evident that these stars are too 
far apart for their mutual attractions to have much influ- 
ence one upon another, and that we have here a case in which, 
according to 34, each star is free to keep unchanged its 
state of rest or motion with unvarying velocity along a 
straight line. Their very name, fixed stars, implies that 
they are at rest, and so astronomers long believed. Hippar- 
chus (125 B. c.) and Ptolemy (130 A. D.) observed and re- 
corded many allineations among the stars, in order to give 
to future generations a means of settling this very question 
of a possible motion of the stars and a resulting change in 
their relative positions upon the sky. For example, they 


found at the beginning of the Christian era that the four 
stars, Capella, e Persei, a and (3 Arietis, stood in a straight 
line i. e., upon a great circle of the sky. Verify this by 
direct reference to the sky, and see how nearly these stars 
have kept the same position for nearly twenty centuries. 
Three of them may be identified from the star maps, and the 
fourth, e Persei, is a third-magnitude star between Capella 
and the other two. 

Other allineations given by Ptolemy are : Spica, Arc- 
turus and ft Bootis ; Spica, 8 Corvi and y Corvi ; a Librse, 
Arcturus and Ursas Majoris. Arcturus does not now fit 
very well to these alignments, and nearly two centuries 
ago it, together with Aldebaran and Sirius, was on other 
grounds suspected to have changed its place in the sky 
since the days of Ptolemy. This discovery, long since 
fully confirmed, gave a great impetus to observing with all 
possible accuracy the right ascensions and declinations of the 
stars, with a view to finding other cases of what was called 
proper motion i. e., a motion peculiar to the individual 
star as contrasted with the change of right ascension and 
declination produced for all stars by the precession. 

Since the middle of the eighteenth century there have 
been made many thousands of observations of this kind, 
whose results have gone into star charts and star cata- 
logues, and which are now being supplemented by a photo- 
graphic survey of the sky that is intended to record per- 
manently upon photographic plates the position and mag- 
nitude of every star in the heavens down to the fourteenth 
magnitude, with a view to ultimately determining all their 
proper motions. 

The complete achievement of this result is, of course, a 
thing of the remote future, but sufficient progress in deter- 
mining these motions has been made during the past cen- 
tury and a half to show that nearly every lucid star pos- 
sesses some proper motion, although in most cases it is very 
small, there being less than 100 known stars in which it 


amounts to so much as 1" per annum i. e., a rate of mo- 
tion across the sky which would require nearly the whole 
Christian era to alter a star's direction from us by so much 
as the moon's angular diameter. The most rapid known 
proper motion is that of a telescopic star midway between 
the equator and the south pole, which changes its position 
at the rate of nearly 9" per annum, and the next greatest is 
that of another telescopic star, in the northern sky, No. 28 
of Fig. 122. It is not until we reach the tenth place in a 
list of large proper motions that we find a bright lucid 
star, No. 1 of Fig. 122. It is a significant fact that for the 
most part the stars with large proper motions are precisely 
the ones shown in Fig. 122, which is designed to show stars 
near the earth. This connection between nearness and 
rapidity of proper motions is indeed what we should expect 
to find, since a given amount of real motion of the star 
along its orbit will produce a larger angular displacement, 
proper motion, the nearer the star is to the earth, and this 
fact has guided astronomers in selecting the stars to be 
observed for parallax, the proper motion being determined 
first and the parallax afterward. 

192. The paths of the stars. We have already seen rea- 
son for thinking that the orbit along which a star moves is 
practically a straight line, and from a study of proper mo- 
tions, particularly their directions across the sky, it appears 
that these orbits point in all possible ways north, south, 
east, and west so that some of them are doubtless directed 
nearly toward or from the sun ; others are square to the 
line joining sun and star; while the vast majority occupy 
some position intermediate between these two. Now, our 
relation to these real motions of the stars is well illus- 
trated in Fig. 112, where the observer finds in some of the 
shooting stars a tremendous proper motion across the sky, 
but sees nothing of their rapid approach to him, while 
others appear to stand motionless, although, in fact, they 
are moving quite as rapidly as are their fellows. The fixed 


star resembles the shooting star in this respect, that its 
proper motion is only that part of its real motion which 
lies at right angles to the line of sight, and this needs to 
he supplemented by that other part of the motion which 
lies parallel to the line of sight, in order to give us any 
knowledge of the star's real orbit. 

193. Motion in the line of sight. It is only within the 
last 25 years that anything whatever has been accomplished 
in determining these stellar motions of approach or reces- 
sion, but within that time much progress has been made by 
applying the Doppler principle ( 89) to the study of stel- 
lar spectra, and at the present time nearly every great tele- 
scope in the world is engaged upon work of this kind. The 
shifting of the lines of the spectrum toward the violet or 

4450 4500 4550 

FIG. 123. Motion of Polaris in the line of sight as determined by the spectroscope. 


toward the red end of the spectrum indicates with cer- 
tainty the approach or recession of the star, but this shift- 
ing, which must be determined by comparing the star's 
spectrum with that of some artificial light showing corre- 
sponding lines, is so small in amount that its accurate meas- 
urement is a matter or extreme difficulty, as may be seen 
from Fig. 123. This cut shows along its central line a part 
of the spectrum of Polaris, between wave lengths 4,450 and 
4,600 tenth meters, while above and below are the corre- 
sponding parts of the spectrum of an electric spark whose 
light passed through the same spectroscope and was photo- 
graphed upon the same plate with that of Polaris. This 
comparison spectrum is, as it should be, a discontinuous or 
bright-line one, while the spectrum of the star is a con- 


tinuous one, broken only by dark gaps or lines, many of 
which have no corresponding lines in the comparison spec- 
trum. But a certain number of lines in the two spectra 
do correspond, save that the dark line is always pushed a 
very little toward the direction of shorter wave lengths, 

111 I I 

FIG. 124. Spectrum of /3 Aurigae. PICKERING. 

showing that this star is approaching the earth. This spec- 
trum was photographed for the express purpose of deter- 
mining the star's motion in the line of sight, and with it 
there should be compared Figs. 124 and 125, which show 
in the upper part of each a photograph obtained without 
comparison spectra by allowing the star's light to pass 
through some prisms placed just in front of the telescope. 
The lower section of each figure shows an enlargement of 
the original photograph, bringing out its details in a way 
not visible to the unaided eye. In the enlarged spectrum 
of /? Aurigas a rate of motion equal to that of the earth in 
its orbit would be represented by a shifting of 0.03 of a 
millimeter in the position of the broad, hazy lines. 

Despite the difficulty of dealing with such small quanti- 
ties as the above, very satisfactory results are now obtained, 
and from them it is known that the velocities of stars in 
the line of sight are of the same order of magnitude as the 
velocities of the planets in their orbits, ranging all the way 
from to 60 miles per second more than 200,000 miles per 
hour which latter velocity, according to Campbell, is the 
rate at which ^ Cassiopeise is approaching the sun. 


The student should not fail to note one important 
difference between proper motions and the motions deter- 
mined spectroscopically : the latter are given directly in 
miles per second, or per hour, while the former are ex- 
pressed in angular measure, seconds of arc, and there can 
be no direct comparison between the two until by means 
of the known distances of the stars their proper motions 
are converted from angular into linear measure. We are 
brought thus to the very heart of the matter ; parallax, 
proper motion, and motion in the line of sight are inti- 

; t lii 1 i i.HitllHil! Ill I 11 i II ' 

HI III I i i 


FIG. 125. Spectrum of Pollux. PICKERING. 

mately related quantities, all of which are essential to a 
knowledge of the real motions of the stars. 

194. Star drift. An illustration of how they may be 
made to work together is furnished by some of the stars 
which make up the Great Dipper /3, y, , and Ursae Ma- 
joris, whose proper motions have long been known to point 
in nearly the same direction across the sky and to be nearly 
equal in amount. More recently it has been found that 
these stars are all moving toward the sun with approxi- 
mately the same velocity 18 miles per second. One other 
star of the Dipper, 8 Ursae Majoris, shares in the common 
proper motion, but its velocity in the line of sight has not 
yet been determined with the spectroscope. These similar 
motions make it probable that the stars are really traveling 
together through space along parallel lines; and on the 



supposition that such is the case it is quite possible to 
write out a set of equations which shall involve their 
known proper motions and motions in the line of sight, 
together with their unknown distances and the unknown 
direction and velocity of their real motion along their 
orbits. Solving these equations for the values of the un- 
known quantities, it is found that the five stars probably 
lie in a plane which is turned nearly edgewise toward us, 
and that in this plane they are moving about twice as fast 
as the earth moves around the sun, and are at a distance 
from us represented by a parallax of less than 0.02" i. e., 
six times as great as the outermost circle in Fig. 122. A 
most extraordinary system of stars which, although sepa- 
rated from each oth- 
er by distances as 
great as the whole 
breadth of Fig. 122, 
yet move along in 
parallel paths which 
it is difficult to re- 
gard as the result 
of chance, and for 
which it is equally 
difficult to frame an 

The stars a and 
rj of the Great Dip- 
per do not share 
in this motion, and 
must ultimately part 
company with the 
other five, to the 
complete destruction 

of the Dipper's shape. Fig. 126 illustrates this change of 
shape, the upper part of the figure (a) showing these seven 
stars as they were grouped at a remote epoch in the past, 

FIG. 126. The Great Dipper, past, present, and 


while the lower section (c) shows their position for an 
equally remote epoch in the future. There is no resem- 
blance to a dipper in either of these configurations, but it 
should be observed that in each of them the stars a and 17 
keep their relative position unaltered, and the other five 
stars also keep /together, the entire change of appearance 
being due to/the changing positions of these two groups 
with respect to each other. 

This phenomenon of groups of stars moving together is 
called star drift, and quite a number of cases of it are 
found in different parts of the sky. The Pleiades are per- 
haps the most conspicuous one, for here some sixty or 
more stars are found traveling together along similar paths. 
Eepeated careful measurements of the relative positions of 
stars in this cluster show that one of the lucid stars and 
four or five of the telescopic ones do not share in this 
motion, and therefore are not to be considered as members 
of the group, but rather as isolated stars which, for a time, 
chance to be nearly on line with the Pleiades, and prob- 
ably farther off, since their proper motions are smaller. 

To rightly appreciate the extreme slowness with which 
proper motions alter the constellations, the student should 
bear in mind that the changes shown in passing from one 
section of Fig. 126 to the next represent the effect of the 
present proper motions of the stars accumulated for a pe- 
riod of 200,000 years. Will the stars continue to move in 
straight paths for so long a time ? 

195. The sun's way. Another and even more interest- 
ing application of proper motions and motions in the line 
of sight is the determination from them of the sun's orbit 
among the stars. The principle involved is simple enough. 
If the sun moves with respect to the stars and carries the 
earth and the other planets year after year into new regions 
of space, our changing point of view must displace in some 
measure every star in the sky save those which happen to 
be exactly on the line of the sun's motion, and even these 


will show its effect by their apparent motion of approach 
or recession along the line of sight. So far as their own 
orbital motions are concerned, there is no reason to sup- 
pose that more stars move north than south, or that more 
go east than west ; and when we find in their proper mo- 
tions a distinct tendency to radiate from a point some- 
where near the bright star Vega and to converge toward 
a point on the opposite side of the sky, we infer that this 
does not come from any general drift of the stars in that 
direction, but that it marks the course of the sun among 
them. That it is moving along a straight line pointing 
toward Vega, and that at least a part of the velocities 
which the spectroscope shows in the line of sight, comes 
from the motion of the sun and earth. Working along 
these lines, Kapteyn finds that the sun is moving through 
space with a velocity of 11 miles per second, which is de- 
cidedly below the average rate of stellar motion 19 miles 
per second. 

196. Distance of Sirian and solar stars, By combining 
this rate of motion of the sun with the average proper mo- 
tions of the stars of different magnitudes, it is possible to 
obtain some idea of the average distance from us of a first- 
magnitude star or a sixth-magnitude star, which, while it 
gives no information about the actual distance of any par- 
ticular star, does show that on the whole the fainter stars 
are more remote. But here a broad distinction must be 
drawn. By far the larger part of the stars belong to one of 
two well-marked classes, called respectively Sirian and solar 
stars, which are readily distinguished from each other by 
the kind of -spectrum they furnish. Thus ft Aurigse belongs 
to the Sirian class, as does every other star which has a spec- 
trum like that of Fig. 124, while Pollux is a solar star pre- 
senting in Fig. 125 a spectrum like that of the sun, as do 
the other stars of this class. 

Two thirds of the sun's near neighbors, shown in Fig. 
122, have spectra of the solar type, and in general stars of 


this class are nearer to us than are the stars with spectra 
unlike that of the sun. The average distance of a solar 
star of the first magnitude is very approximately repre- 
sented hy the outer circle in Fig. 122, 2,000,000 times the 
distance of the sun from the earth ; while the correspond- 
ing distance for a Sirian star of the first magnitude is rep- 
resented by the number 4,600,000. 

A third-magnitude star is on the average twice as far 
away as one of the first magnitude, a fifth-magnitude star 
four times as far off, etc., each additional two magnitudes 
doubling the average distance of the stars, at least down to 
the eighth magnitude and possibly farther, although be- 
yond this limit we have no certain knowledge. Put in 
another way, the naked eye sees many Sirian stars which 
may have " gone out " and ceased to shine centuries ago, 
for the light by which we now see them left those stars 
before the discovery of America by Columbus. For the 
student of mathematical tastes we note that the results of 
Kapteyn's investigation of the mean distances (D) of the 
stars of magnitude (m) may be put into two equations : 


For Solar Stars, D = 23 X 2 


For Sirian Stars, D = 52 X 2* 

where the coefficients 23 and 52 are expressed in light 
years. How long a time is required for light to come from 
an average solar star of the sixth magnitude ? 

197. Consequences of stellar distance. The amount of 
light which comes to us from any luminous body varies 
inversely as the square of its distance, and since many of 
the stars are changing their distance from us quite rapidly, 
it must be that with the lapse of time they will grow 
brighter or fainter by reason of this altered distance. 
But the distances themselves are so great that the most 
rapid known motion in the line of sight would require 
more than 1,000 years (probably several thousand) to pro- 
duce any perceptible change in brilliancy. 


The law in accordance with which this change of bril- 
liancy takes place is that the distance must be increased or 
diminished tenfold in order to produce a change of five 
magnitudes in the brightness of the object, and we may 
apply this law to determine the sun's rank among the stars. 
If it were removed to the distance of an average first-, or 
second-, or third-magnitude star, how would its light com- 
pare with that of the stars ? The average distance of a 
third-magnitude star of the solar type is, as we have seen 
above, 4,000,000 times the sun's distance from the earth, 
and since 4,000,000 = 10 6 - 6 , we find that at this distance the 
sun's stellar magnitude would be altered by 6.6 X 5 magni- 
tudes, and would therefore be 26.5 + 33.0 = 6.5 i. e., the 
sun if removed to the average distance of the third-magni- 
tude stars of its type would be reduced to the very limit 
of naked-eye visibility. It must therefore be relatively 
small and feeble as compared with the brightness of the 
average star. It is only its close proximity to us which 
makes the sun look brighter than the stars. 

The fixed stars may have planets circling around them, 
but an application of the same principles will show how 
hopeless is the prospect of ever seeing them in a telescope. 
If the sun's nearest neighbor, a Centauri, were attended by 
a planet like Jupiter, this planet would furnish to us no 
more light than does a star of the twenty-second magni- 
tude i. e., it would be absolutely invisible, and would re- 
main invisible in the most powerful telescope yet built, 
even though its bulk were increased to equal that of the 
sun. Let the student make the computation leading to 
this result, assuming the stellar magnitude of Jupiter to 
be -1.7. 

198. Double stars, In the constellation Taurus, not far 
from Aldebaran, is the fourth-magnitude star 6 Tauri, 
which can readily be seen to consist of two stars close 
together. The star a Capricorni is plainly double, and a 
sharp eye can detect that one of the faint stars which with 


Vega make a small equilateral triangle, is also a double 
star. Look for them in the sky. 

In the strict language of astronomy the term double 
star would not be applied to the first two of these objects, 
since it is usually restricted to those stars whose angular 
distance from each other is so small that in the telescope 
they appear much as do the stars named above to the naked 
eye i. e., their angular separation is measured by a few 
seconds or fractions of a single second, instead of the six 
minutes which separate the component stars of Tauri or 
a Capricorni. There are found in the sky many thousands 
of these close double stars, of which some are only optic- 
ally double i. e., two stars nearly on line with the earth 
but at very different distances from it while more of them 
are really what they seem, stars near each other, and in 
many cases near enough to influence each other's motion. 
These are called binary systems, and in cases of this kind 
the principles of celestial mechanics set forth in Chapter 
IV hold true, and we may expect to find each component 
of a double star moving in a conic section of some kind, 
having its focus at the common center of gravity of the 
two stars. We are thus presented with problems of orbital 
motion quite similar to those which occur in the solar sys- 
tem, and careful telescopic observations are required year 
after year to fix the relative positions of the two stars i. e., 
their angular separation, which it is customary to call their 
distance, and their direction one from the other, which is 
called position angle. 

199. Orbits of double stars. The sun's nearest neighbor, 
a Centauri, is such a double star, whose position angle and 
distance have been measured by successive generations of 
astronomers for more than a century, and Fig. 127 shows 
the result of plotting their observations. Each black dot 
that lies on or near the circumference of the long ellipse 
stands for an observed direction and distance of the fainter 
of the two stars from the brighter one, which is represented 



by the small circle at the intersection of the lines inside 
the ellipse. It appears from the figure that during this 

time the one star has 
gone completely around 
the other, as a planet 
goes around the sun, 
and the true orbit must 
therefore be an ellipse 
having one of its foci 
at the center of gravity 
of the two stars. The 
other star moves in an 
ellipse of precisely simi- 
lar shape, but probably 
smaller size, since the 
dimensions of the two 
FIG. is?. The orbit of a Centauri. SEE. orbits are inversely pro- 

portional to the masses 

of the two bodies, but it is customary to neglect this motion 
of the larger star and to give to the smaller one an orbit 
whose diameter is equal to the sum of the diameters of the 
two real orbits. This practice, which has been followed in 
Fig. 127, gives correctly the relative positions of the two 
stars, and makes one orbit do the work of two. 

In Fig. 127 the bright star does not fall anywhere near 
the focus of the ellipse marked out by the smaller one, and 
from this we infer that the figure does not show the true 
shape of the orbit, which is certainly distorted, foreshort- 
ened, by the fact that we look obliquely down upon its 
plane. It is possible, however, by mathematical analysis, 
to find just how much and in what direction that plane 
should be turned in order to bring the focus of the 
ellipse up to the position of the principal star, and thus 
give the true shape and size of the orbit. See Fig. 128 
for a case in which the true orbit is turned exactly edge- 
wise toward the earth, and the small star, which really 



moves in an ellipse like that shown in the figure, appears 
to oscillate to and fro along a straight line drawn through 
the principal star, as shown at the left of the figure. 

In the case of a 
Centauri the true orbit 
proves to have a major 
axis 47 times, and a 
minor axis 40 times, 
as great as the distance 
of the earth from the 
sun. The orbit, in 
fact, is intermediate 
in size between the 
orbits of Uranus and 
Xeptune, and the pe- 
riodic time of the star 
in this orbit is 81 
years, a little less than 
the period of Uranus. 

200. Masses of double stars. If we apply to this orbit 
Kepler's Third Law in the form given it at page 179, we 
shall find 

FIG. 128. Apparent orbit and real orbit of the 
double star 42 Comse Berenicis. SEE. 

where M and m represent the masses of the two stars. We 
have already seen that &, the gravitation constant, is equal 
to 1 when the masses are measured in terms of the sun's 
mass taken as unity, and when T and a are expressed in 
years and radii of the earth's orbit respectively, and with 
this value of Ic we may readily find from the above equa- 
tion, M-\-m = 2.5 i. e., the combined mass of the two com- 
ponents of a Centauri is equal to rather more than twice 
the mass of the sun. It is not every double star to which 
this process of weighing can be applied. The major axis 
of the orbit, #, is found from the observations in angular 
measure, 35" in this case, and it is only when the parallax 



of the star is known that this can be converted into the 
required linear units, radii of the earth's orbit, by dividing 
the angular major axis by the parallax ; 47 = 35" -j- 0.75". 
Our list of distances ( 189) contains six double stars 
whose periodic times and major axes have been fairly well 
determined, and we find in the accompanying table the in- 
formation which they give about the masses of double stars 
and the size of the orbits in which they move : 


Major axis. 

Minor axis. 



t\ CassiopGisB 





o' 2 Eridani . ... 

i 63 




a Centauri 





70 Ophiuchi 

.... 56 





... 34 




Sirius . . . 

I 43 




The orbit of Uranus, diameter = 38, and Neptune, diam- 
eter = 60, are of much the same size as these double-star 
orbits ; but the planetary orbits are nearly circular, while 
in every case the double stars show a substantial difference 
between the long and short diameters of their orbits. This 
is a characteristic feature of most double-star orbits, and 
seems to stand in some relation to their periodic times, for, 
on the average, the longer the time required by a star to 
make its orbital revolution the more eccentric is its orbit 
likely to prove. 

Another element of the orbits of double stars, which 
stands in even closer relation to the periodic time, is the 
major axis ; the smaller the long diameter of the orbit the 
more rapid is the motion and the shorter the periodic time, 
so that astronomers in search of interesting double-star 
orbits devote themselves by preference to those stars whose 
distance apart is so small that they can barely be distin- 
guished one from the other in the telescope. 

Although the half-dozen stars contained in the table 
all have orbits of much the same size and with much the 


same periodic time as those in which Uranus and Neptune 
move, this is by no means true of all the double stars, many 
of which have periods running up into the hundreds if not 
thousands of years, while a few complete their orbital revo- 
lutions in periods comparable with, or even shorter than, 
that of Jupiter. 

201. Dark stars. Procyon, the next to the last star of 
the preceding table, calls for some special mention, as the 
determination of its mass and orbit stands upon a rather 
different basis from that of the other stars. More than 
half a century ago it was discovered that its proper motion 
was not straight and uniform after the fashion of ordinary 
stars, but presented a series of loops like those marked out 
by a bright point on the rim of a swiftly running bicycle 
wheel. The hub may move straight forward with uniform 
velocity, but the point near the tire goes up and down, and, 
while sharing in the forward motion of the hub, runs some- 
times ahead of it, sometimes behind, and such seemed to 
be the motion of Procyon and of Sirius as well. Bessel, 
who discovered it, did not hesitate to apply the laws of mo- 
tion, and to affirm that this visible change of the star's 
motion pointed to the presence of an unseen companion, 
which produced upon the motions of Sirius and Procyon 
just such effects as the visible companions produce in the 
motions of double stars. A new kind of star, dark instead 
of bright, was added to the astronomer's domain, and its 
discoverer boldly suggested the possible existence of many 
more. " That countless stars are visible is clearly no argu- 
ment againsu the existence of as many more invisible ones." 
" There is no reason to think radiance a necessary property 
of celestial bodies." But most astronomers were incredu- 
lous, and it was not until 1862 that, in the testing of a new 
and powerful telescope just built, a dark star was brought 
to light and the companion of Sirius actually seen. The 
visual discovery of the dark companion of Procyon is 
of still more recent date (November, 1896), when it was 


detected with the great telescope of the Lick Observatory. 
This discovery is so recent that the orbit is still very uncer- 
tain, being based almost wholly upon the variations in the 
proper motion of the star, and while the periodic time must 
be very nearly correct, the mass of the stars and dimensions 
of the orbit may require considerable correction. 

The companion of Sirius is about ten magnitudes and 
that of Procyon about twelve magnitudes fainter than the 
star itself. How much more light does the bright star give 
than its faint companion ? Despite the tremendous differ- 
ence of brightness represented by the answer to this ques- 
tion, the mass of Sirius is only about twice as great as 
that of its companion, and for Procyon the ratio does not 
exceed five or six. / 

The visual discovery of the companions to Sirius and 
Procyon removes them from the list of dark stars, but 
others still remain unseen, although their/existence is in- 
dicated by variable proper motions oi^Jtfy variable orbital 
motion, as in the case of Cancri, where one of the compo- 
nents of a triple star moves around the other two in a series 
of loops whose presence indicates a disturbing body which 
has never yet been seen. 

202. Multiple stars. Combinations of three, four, or 
more stars close to each other, like Cancri, are called mul- 
tiple stars, and while they are far from being as common as 
are double stars, there is a considerable number of them in 
the sky, 100 or more as against the more than 10,000 dou- 
ble stars that are known. That their relative motions are 
subject to the law of gravitation admits of no serious doubt, 
but mathematical analysis breaks down in face of the diffi- 
culties here presented, and no astronomer has ever been 
able to determine what will be the general character of 
the motions in such a system. 

203. Spectroscopic binaries. In the year 1890 Professor 
Pickering, of the Harvard Observatory, announced the dis- 
covery of a new class of double stars, invisible as such in 


even the most powerful telescope, and producing no per- 
turbations such as have been considered above, but show- 
ing in their spectrum that two or more bodies must be 
present in the source of light which to the eye is indistin- 
guishable from a single star. In Fig. 129 we suppose A 
and B to be the two components of a double star, each 
moving in its own orbit about their common center of 

To the Earth 

FIG. 129. Illustrating the motion of a spectroscopic binary. 

gravity, C\ whose distance from the earth is several million 
times greater than the distance between the stars them- 
selves. Under such circumstances no telescope could dis- 
tinguish between the two stars, which would appear fused 
into one ; but the smaller the orbit the more rapid would 
be their motion in it, and if this orbit were turned edgewise 
toward the earth, as is supposed in the figure, whenever 
the stars were in the relative position there shown, A would 
be rapidly approaching the earth by reason of its orbital 
motion, while B would move away from it, so that in 
accordance with the Doppler principle the lines composing 
their respective spectra would be shifted in opposite direc- 
tions, thus producing a doubling of the lines, each single 
line breaking up into two, like the double-sodium line Z>, 
only not spaced so far apart. When the stars have moved 
a quarter way round their orbit to the points A 1 , B', their 
velocities are turned at right angles to the line of sight 


and the spectrum returns to the normal type with single 
lines, only to break up again when after another quarter 
revolution their velocities are again parallel with the line 
of sight. The interval of time between consecutive dou- 
blings of the lines in the spectrum thus furnishes half 
the time of a revolution in the orbit. The distance be- 
tween the components of a double line shows by means of 
the Doppler principle how fast the stars are traveling, and 
this in connection with the periodic times fixes the size 
of the orbit, provided we assume that it is turned exactly 
edgewise to the earth. This assumption may not be quite 
true, but even though the orbit should deviate consider- 
ably from this position, it will still present the phenomenon 
of the double lines whose displacement will now show some- 
thing less than the true velocities of the stars in their or- 
bits, since the spectroscope measures only that component 
of the whole velocity which is directed toward the earth, 
and it is important to note that the real orbits and masses 
of these spectroscopic binaries, as they are called, will usu- 
ally be somewhat larger than those indicated by the spec- 
troscope, since it is only in exceptional cases that the orbit 
will be turned exactly edgewise to us. 

The bright star Capella is an excellent illustration of 
these spectroscopic binaries. At intervals of a little less 
than a month the lines of its spectrum are alternately 
single and double, their maximum separation correspond- 
ing to a velocity in the line of sight amounting to 37 miles 
per second. Each component of a doubled line appears to 
be shifted an equal amount from the position occupied by 
the line when it is single, thus indicating equal velocities 
and equal masses for the two component stars whose peri- 
odic time in their orbit is 104 days. From this periodic 
time, together with the velocity of the star's motion, let the 
student show that the diameter of the orbit i. e., the dis- 
tance of the stars from each other is approximately 53,000,- 
000 miles, and that their combined mass is a little less than 


that of a Centauri, provided that their orbit plane is turned 
exactly edgewise toward the earth. 

There are at the present time (1901) 34 spectroscopic 
binaries known, including among them such stars as Pola- 
ris, Capella, Algol, Spica, (3 Aurigae, Ursae Majoris, etc., 
and their number is rapidly increasing, about one star out of 
every nine whose motion in the line of sight is determined 
proving to be a binary or, as in the case of Polaris, possibly 
triple. On account of smaller distance apart their periodic 
times are much shorter than those of the ordinary double 
stars, and range from a few days up to several months 
more than two years in the case of y Pegasi, which has the 
longest known period of any star of this class. 

Spectroscopic binaries agree with ordinary double stars 
in having masses rather greater than that of the sun, but 
there is as yet no assured case of a mass ten times as great 
as that of the sun. 

204. Variable stars. Attention has already been drawn 
(23) to the fact that some stars shine with a changing 
brightness e. g., Algol, the most famous of these variable 
stars, at its maximum of brightness furnishes three times 
as much light as when at its minimum, and other variable 
stars show an even greater range. The star o Ceti has been 
named Mira (Latin, the wonderful), from its extraordinary 
range of brightness, more than six-hundred-fold. For the 
greater part of the time this star is invisible to the naked 
eye, but during some three months in every year it bright- 
ens up sufficiently to be seen, rising quite rapidly to its 
maximum brilliancy, which is sometimes that of a second- 
magnitude star, but more frequently only third or even 
fourth magnitude, and, after shining for a few weeks with 
nearly maximum brilliancy, falling off to become invisi- 
ble for a time and then return to its maximum bright- 
ness after an interval of eleven months from the preceding 
maximum. In 1901 it should reach its greatest brilliancy 
about midsummer, and a month earlier than this for each 


succeeding year. Find it by means of the star map, and 
by comparing its brightness from night to night with 
neighboring stars of about the same magnitude see how it 
changes with respect to them. 

The interval of time from maximum to maximum of 
brightness 331.6 days for Mira is called the star's pe- 
riod, and within its period a star regularly variable runs 
through all its changes of brilliancy, much as the weather 
runs through its cycle of changes in the period of a year. 
But, as there are wet years and dry ones, hot years and cold, 
so also with variable stars, many of them show differences 
more or less pronounced between different periods, and 
one such difference has already been noted in the case of 
Mira ; its maximum brilliancy is different in different years. 
So, too, the length of the period fluctuates in many cases, 
as does every other circumstance connected with it, and 
predictions of what such a variable star will do are notori- 
ously unreliable. 

205. The Algol variables. On the other hand, some vari- 
able stars present an almost perfect regularity, repeating 
their changes time after time with a precision like that of 
clockwork. Algol is one type of these regular variables, 
having a period of 68.8154 hours, during six sevenths of 
which time it shines with unchanging luster as a star of 
the 2.3 magnitude, but during the remaining 9 hours of 
each period it runs down to the 3.5 magnitude, and comes 
back again, as is shown by a curve in Fig. 130. The horizon- 
tal scale here represents hours, reckoned from the time of 
the star's minimum brightness, and the vertical scale shows 
stellar magnitudes. Such a diagram is called the star's 
light curve, and we may read from it that at any time be- 
tween 5h. and 32h. after the time of minimum the star's 
magnitude is 2.32; at 2h. after a minimum the magni- 
tude is 2.88, etc. What is the magnitude an hour and a 
half before the time of minimum ? What is the magnitude 
43 days after a minimum ? 



The arrows shown in Fig. 130 are a feature not usually 
found with light curves, but in this case each one repre- 
sents a spectroscopic determination of the motion of Algol 
in the line of sight. These observations extended over a 

FIG. 130. The light curve of Algol. 

period of more than two years, but they are plotted in the 
figure with reference to the number of hours each one pre- 
ceded or followed a minimum of the star's light, and each 
arrow shows not only the direction of the star's motion 
along the line of sight, the arrows pointing down denoting 
approach of the star toward the earth, but also its velocity, 
each square of the ruling corresponding to 10 kilometers 
(6.2 miles per second). The differences of velocity shown 
by adjacent arrows come mainly from errors of observation 
and furnish some idea of how consistent among themselves 
such observations are, but there can be no doubt that before 
minimum the star is moving away from the earth, and after 
minimum is approaching it. It is evident from these ob- 
servations that in Algol we have to do with a spectroscopic 
binary, one of whose components is a dark star which, once 
in each revolution, partially eclipses the bright star and 
produces thus the variations in its light. By combining 
the spectroscopic observations with the variations in the 
star's light, Vogel finds that the bright star, Algol, itself 
has a diameter somewhat greater than that of the sun, but 



is of low density, so that its mass is less than half that of 
the sun, while the dark star is a very little smaller than the 
sun and has about a quarter of its mass. The distance be- 
tween the two stars, dark and bright, is 3,200,000 miles. 
Fig. 129, which is drawn to scale, shows the relative posi- 
tions and sizes of these stars as well as the orbits in which 
they move. 

The mere fact already noted that close binary systems 
exist in considerable numbers is sufficient to make it 
probable that a certain proportion of these stars would 
have their orbit planes turned so nearly edgewise toward 
the earth as to produce eclipses, and corresponding to this 
probability there are already known no less than 15 stars of 
the Algol type of eclipse variables, and only a beginning 
has been made in the search for them. 

206. Variables of the (3 Lyrse type. In addition to these 
there is a certain further number of binary variables in 
which both components are bright and where the varia- 
tion of brightness follows a very different course. Capella 


FIG. 131. The light curve of Lyrse. 

would be such a variable if its orbit plane were directed 
exactly toward the earth, and the fact that its light is not 
variable shows conclusively that such is not the position of 
the orbit. Fig. 131 represents the light curve of one of the 


best-known variable systems of this second type, that of 
/? Lyrse, whose period is 12 days 21.8 hours, and the student 
should read from the curve the magnitude of the star for 
different times during this interval. According to Myers, 
this light curve and the spectroscopic observations of the 
star point to the existence of a binary star of very remark- 
able character, such as is shown, together with its orbit and 
a scale of miles, in Fig. 132. Note the tide which each of 

To the Earth 

10,000,000 miles 

FIG. 132. The system of /3 Lyrae. MYERS. 

these stars raises in the other, thus changing their shapes 
from spheres into ellipsoids. The astonishing dimensions 
of these stars are in part compensated by their very low 
density, which is less than that of air, so that their masses 
are respectively only 10 times and 21 times that of the 
sun ! But these dimensions and masses perhaps require 
confirmation, since they depend upon spectroscopic obser- 
vations of doubtful interpretation. In Fig. 132 what rela- 
tive positions must the stars occupy in their orbit in order 
that their combined light should give ft Lyrae its maxi- 
mum brightness ? What position will furnish a minimum 
brightness ? 

207. Variables of long and short periods, It must not be 
supposed that all variable stars are binaries which eclipse 
each other. By far the larger part of them, like Mira, are 
not to be accounted for in this way, and a distinction which 


is pretty well marked in the length of their periods is sig- 
nificant in this connection. There is a considerable num- 
ber of variable stars with periods shorter than a month, and 
there are many having periods longer than 6 months, but 
there are very few having periods longer than 18 months, 
or intermediate between 1 month and 6 months, so that it 
is quite customary to divide variable stars into two classes 
those of long period, 6 months or more, and those of 
short period less than 6 months, and that this distinction 
corresponds to some real difference in the stars themselves 
is further marked by the fact that the long-period variables 
are prevailingly red in color, while the short-period stars 
are almost without exception white or very pale yellow. 
In fact, the longer the period the redder the star, although 
it is not to be inferred that all red stars are variable ; a 
considerable percentage of them shine with constant light. 
The eclipse explanation of variability holds good only for 
short-period variables, and possibly not for all of them, 
while for the long-period variables there is no explanation 
which commands the general assent of astronomers, al- 
though unverified hypotheses are plenty. 

The number of stars known to be variable is about 400, 
while a considerable number of others are "suspected," 
and it would not be surprising if a large fraction of all the 
stars should be found to fluctuate a little in brightness. 
The sun's spots may suffice to make it a variable star with 
a period of 11 years. 

The discovery of new variables is of frequent occur- 
rence, and may be expected to become more frequent when 
the sky is systematically explored for them by the ingen- 
ious device suggested by Pickering and illustrated in Fig. 
133. A given region of the sky e. g., the Northern Crown 
is photographed repeatedly upon the same plate, which is 
shifted a little at each new exposure, so that the stars shall 
fall at new places upon it. The finally developed plate 
shows a row of images corresponding to each star, and if 



the star's light is constant the images in any given row will 
all be of the same size, as are most of those in Fig. 133 ; 
but a variable star such as is shown by the arrowhead 
reveals its presence by the broken aspect of its row of 


FIG. 133. Discovery of a variable star by means of photography. PICKERING. 

dots, a minimum brilliancy being shown by smaller and a 
maximum by larger ones. In this particular case, at two 
exposures the star was too faint to print its image upon 
the plate. 

208. New stars. Next to the variable stars of very long 
or very irregular period stand the so-called new or tempo- 
rary stars, which appear for the most part suddenly, and 
after a brief time either vanish altogether or sink to com- 
parative insignificance. These were formerly thought to 
be very remarkable and unusual occurrences " the birth 
of a new world " and it is noteworthy that no new star 
is recorded to have been seen from 1670 to 1848 A. D., for 
since that time there have been no less than four of them 


visible to the naked eye and others telescopic. In so far 
as these new stars are not ordinary variables (Mira, first 
seen in 1596, was long counted as a new star), they are com- 
monly supposed due to chance encounters between stars 
or other cosmic bodies moving with considerable velocities 
along orbits which approach very close to each other. The 
actual collision of two dark bodies moving with high ve- 
locities is clearly sufficient to produce a luminous star 
e. g., meteors and even the close approach of two cooled- 
off stars, might result in tidal actions which would rend 
open their crusts and pour out the glowing matter from 
within so as to produce temporarily a very great accession 
of brightness. 

The most famous of all new stars is that which, accord- 
ing to Tycho Brahe's report, appeared in the year 1572, and 
was so bright when at its best as to be seen with the naked 
eye in broad daylight. It continued visible, though with 
fading light, for about 16 months, and finally disappeared 
to the naked eye, although there is some reason to suppose 
that it can be identified with a ruddy star of the eleventh 
magnitude in the constellation Cassiopeia, whose light still 
shows traces of variability. 

No modern temporary star approaches that of Tycho 
in splendor, but in some respects the recent ones surpass 
it in interest, since it has been possible to apply the spec- 
troscope to the analysis of their light and to find thereby 
a much more complex set of conditions in the star than 
would have been suspected from its light changes alone. 
The temporary star which appeared in the constellation 
Auriga in December, 1891, disappeared in April, 1892, and 
three months later reappeared for another season, is the 
most remarkable of recent temporary stars, and presents 
many anomalies for which no entirely satisfactory expla- 
nation has yet been found. Its spectrum contained both 
dark and bright lines, apparently due to the same chemical 
substances, but displaced toward opposite ends of the spec- 


trum, as if they came from different bodies moving past 
each other with velocities to be measured in hundreds of 
miles per second. In character the lines, chiefly those of 
hydrogen and iron, suggested at one time the sun's chro- 
mosphere, at another the conditions which obtain in neb- 
ulas (Chapter XI V), and the only conclusion regarding it 
upon which there seems to be a substantial agreement is 
that in producing and reviving the temporary brightness 
of this star at least two and possibly several independent 
bodies were involved, although even this is not altogether 



209. Stellar colors, We have already seen that one star 
differs from another in respect of color as well as bright- 
ness, and the diligent student of the sky will not fail to 
observe for himself how the luster of Sirius and Rigel is 
more nearly a pure white than is that of any other stars in 
the heavens, while at the other end of the scale a Orionis 
and Aldebaran are strongly ruddy, and Antares presents an 
even deeper tone of red. Between these extremes the 
light of every star shows a mixture of the rainbow hues, in 
which a very pale yellow is the predominant color, shading 
off, as we have seen, to white at one end of the scale and 
red at the other. There are no green stars, or blue stars, 
or violet stars, save in one exceptional class of cases viz., 
where the two components of a double star are of very dif- 
ferent brightness, it is quite the usual thing for them to 
have different colors, and then, almost without exception, 
the color of the fainter star lies nearer to the violet end 
of the spectrum than does the color of the bright one, 
and sometimes shows a distinctly blue or green hue. A 
fine type of such double star is ft Cygni, in which the 
components are respectively yellow and blue, and the yel- 
low star furnishes eight times as much light as the blue 

The exception which double stars thus make to the gen- 
eral rule of stellar colors, yellow and red, but no color of 
shorter wave length, has never been satisfactorily explained, 


but the rule itself presents no difficulties. Each star is an 
incandescent body, giving off radiant energy of every wave 
length within the limits of the visible spectrum, and, in- 
deed, far beyond these limits. If this radiant energy could 
come unhindered to our eyes every star would appear white, 
but they are all surrounded by atmospheres analogous to 
the chromosphere and reversing layer of the sun which 
absorb a portion of their radiant energy and, like the earth's 
atmosphere, take a heavier toll from the violet than from 
the red end of the spectrum. The greater the absorption 
in the star's atmosphere, therefore, the feebler and the rud- 
dier will be its light, and corresponding to this the red stars 
are as a class fainter than the white ones. 

210. Chemistry of the stars, The spectroscope is pre-em- 
inently the instrument to deal with this absorption of light 
in the stellar atmospheres, just as it deals with that absorp- 
tion in the sun's atmosphere to which are due the dark lines 
of the solar spectrum, although the faiiitness of starlight, 
compared with that of the sun, presents a serious obstacle 
to its use. Despite this difficulty most of the lucid stars 
and many of the telescopic ones have been studied with 
the spectroscope and found to be similar to the sun and 
the earth as respects the material of which they are made. 
Such familiar chemical elements as hydrogen and iron, car- 
bon, sodium, and calcium are scattered broadcast through- 
out the visible universe, and while it would be unwarranted 
by the present state of knowledge to say that the stars con- 
tain nothing not found in the earth and the sun, it is evi- 
dent that in a broad way their substance is like rather than 
unlike that composing the solar system, and is subject to 
the same physical and chemical laws which obtain here. 
Galileo and Kewton extended to the heavens the terrestrial 
sciences of mathematics and mechanics, but it remained to 
the nineteenth century to show that the physics and chem- 
istry of the sky are like the physics and chemistry of the 


211. Stellar spectra, When the spectra of great numbers 
of stars are compared one with another, it is found that 
they bear some relation to the colors of the stars, as, indeed, 
we should expect, since spectrum and color are both pro- 
duced by the stellar atmospheres, and it is found useful to 
classify these spectra into three types, as follows : 

Type I. Sirian stars. Speaking generally, the stars 
which are white or very faintly tinged with yellow, furnish 
spectra like that of Sirius, from which they take their 
name, or that of (3 Aurigse (Fig. 124), which is a continuous 
spectrum, especially rich in energy of short wave length 
i. e., violet and ultra-violet light, and is crossed by a rela- 
tively small number of heavy dark lines corresponding to 
the spectrum of hydrogen. Sometimes, however, these lines 
are much fainter than is here shown, and we find associated 
with them still other faint ones pointing to the presence of 
other metallic substances in the star's atmosphere. These 
metallic lines are not always present, and sometimes even 
the hydrogen lines themselves are lacking, but the spectrum 
is always rich in violet and ultra-violet light. 

Since with increasing temperature a body emits a con- 
tinually increasing proportion of energy of short wave 
length ( 118), the richness of these spectra in such energy 
points to a very high temperature in these stars, probably 
surpassing in some considerable measure that of the sun. 
Stars with this type of spectrum are more numerous than 
all others combined, but next to them in point of numbers 

Type II. Solar stars. To this type of spectrum belong 
the yellow stars, which show spectra like that of the sun, 
or of Pollux (Fig. 125). These are not so rich in violet 
light as are those of Type I, but in complexity of spectrum 
and in the number of their absorption lines they far sur- 
pass the Sirian stars. They are supposed to be at a lower 
temperature than the Sirian stars, and a much larger num- 
ber of chemical elements seems present and active in the 


reversing layer of their atmospheres. The strong resem- 
blance which these spectra bear to that of the sun, together 
with the fact that most of the sun's stellar neighbors have 
spectra of this type, justify us in ranking both them and it 
as members of one class, called solar stars. 

Type III. Red stars. A small number of stars show 
spectra comparable with that of a Herculis (Fig. 134), in 
which the blue and the violet part of the spectrum is al- 
most obliterated, and the remaining yellow and red parts 

FIG. 134. The spectrum of a Herculis. ESPIN. 

show not only dark lines, but also numerous broad dark 
bands, sharp at one edge, and gradually fading out at the 
other. It is this selective absorption, extinguishing the blue 
and leaving the red end of the spectrum, which produces 
the ruddy color of these stars, while the bands in their 
spectra " are characteristic of chemical combinations, and 
their presence . . . proves that at certain elevations in the 
atmospheres of these stars the temperature has sunk so low 
that chemical combinations can be formed and maintained " 
(Scheiner-Frost). One of the chemical compounds here in- 
dicated is a hydrocarbon similar to that found in comets. 
In the white and yellow stars the temperatures are so high 
that the same chemical elements, although present, can not 
unite one with another to form compound substances. 

Most of the variable stars are red and have spectra of 
the third type ; but this does not hold true for the eclipse 
variables like Algol, all of which are white stars with spec- 
tra of the first type. The ordinary variable star is there- 
fore one with a dense atmosphere of relatively low tempera- 
ture and complex structure, which produces the prevailing 
red color of these stars by absorbing the major part of 


their radiant energy of short wave length while allowing 
the longer, red waves to escape. Although their exact 
nature is not understood, there can be little doubt that the 
fluctuation in the light of these stars is due to processes 
taking place within the star itself, but whether above or 
below its photosphere is still uncertain. 

212. Classes of stars, There is no hard-and-fast dividing 
line between these types of stellar spectra, but the change 
from one to another is by insensible gradations, like the 
transition from youth to manhood and from manhood to 
old age, and along the line of transition are to be found 
numberless peculiarities and varieties of spectra not enu- 
merated above e. g., a few stars show not only dark absorp- 
tion lines in their spectra but bright lines as well, which, 
like those in Fig. 48, point to the presence of incandescent 
vapors, even in the outer parts of their atmospheres. Among 
the lucid stars about 75 per cent have spectra of the first 
type, 23 per cent are of the second type, 1 per cent of the 
third type, and the remaining 1 per cent are peculiar or of 
doubtful classification. Among the telescopic stars it is 
probable that much the same distribution holds, but in the 
present state of knowledge it is not prudent to speak with 
entire confidence upon this point. 

That the great number of stars whose spectra have been 
studied should admit of a classification so simple as the 
above, is an impressive fact which, when supplemented by 
the further fact of a gradual transition from one type of 
spectrum to the next, leaves little room for doubt that in 
the stars we have an innumerable throng of individuals be- 
longing to the same species but in different stages of devel- 
opment, and that the sun is only one of these individuals, 
of something less than medium size and in a stage of de- 
velopment which is not at all peculiar, since it is shared by 
nearly a fourth of all the stars. 

213. Star clusters. In previous chapters we have noted 
the Pleiades and Prsesepe as star clusters visible to the 



FIG. 135. Star cluster in Hercules. 

naked eye, and to them we may add the Hyades, near Aldeb- 
aran, and the little constellation Coma Berenices. But 
more impressive than any of these, although visible only 
in a telescope, is the splendid cluster in Hercules, whose 
appearance in a tele- 
scope of moderate size 
is shown in Fig. 135, 
while Fig. 136 is a pho- 
tograph of the same 
cluster taken with a 
very large reflecting 
telescope. This is only 
a type of many tele- 
scopic clusters which 
are scattered over the 
sky, and which are made 
up of stars packed so 
closely together as to become indistinguishable, one from 
another, at the center of the cluster. Within an area 
which could be covered by a third of the full moon's face 
are crowded in this cluster more than five thousand stars 
which are unquestionably close neighbors, but whose ap- 
parent nearness to each other is doubtless due to their 
great distance from us. It is quite probable that even at 
the center of this cluster, where more than a thousand stars 
are included within a radius of 160", the actual distances 
separating adjoining stars are much greater than that sepa- 
rating earth and sun, but far less than that separating the 
sun from its nearest stellar neighbor. 

An interesting discovery of recent date, made by Pro- 
fessor Bailey in photographing star clusters, is that some 
few of them, which are especially rich in stars, contain an 
extraordinary number of variable stars, mostly very faint 
and of short period. Two clusters, one in the northern and 
one in the southern hemisphere, contain each more than a 
hundred variables, and an even more extraordinary case is 


presented by a cluster, called Messier 5, not far from the 
star a Serpentis, which contains no less than sixty-three 
variables, all about of the fourteenth magnitude, all having 
light periods which differ, but little from half a day, all 

FIG. 136. Star cluster in Hercules. KEELER. 

having light curves of about the same shape, and all having 
a range of brightness from maximum to minimum of about 
one magnitude. An extraordinary set of coincidences 
which "points unmistakably to a common origin and cause 
of variability." 


214. Nebulae, Returning to Fig. 136, we note that its 
background has a hazy appearance, and that at its center 

FIG. 137. The Andromeda nebula as seen in a very small telescope. 

the stars can no longer be distinguished, but blend one 
with another so as to appear like a bright cloud. The 

FIG. 138. The Andromeda nebula and Holmes's comet. 
Photographed by BARNARD. 


outer part of the cluster is resolved into stars, while in the 
picture the inner portion is not so resolved, although in 

FIG. 139. A drawing of the Andromeda nebula. 

the original photographic plate the individual stars can be 
distinguished to the very center of the cluster. In many 

FIG. 140. A photograph of the Andromeda nebula. ROBERTS. 



cases, however, this is not possible, and we have an irre- 
solvable duster which it is customary to call a nebula 
(Latin, little cloud). 

The most conspicuous example of this in the northern 
heavens is the great nebula in Andromeda (R. A. O h 37 m , 
Dec. + 41), which may be seen with the naked eye as a 
faint patch of foggy light. Look for it. This appears in 
an opera glass or very small telescope not unlike Fig. 137, 
which is reproduced from a sketch. Fig. 138 is from a 
photograph of the same object showing essentially the same 
shape as in the preceding figure, but bringing out more 
detail. Note the two small nebulae adjoining the large 
one, and at the bottom of the picture an object which might 
easily be taken for another nebula but which is in fact 
a tailless comet that chanced to be passing that part of 
the sky when the picture was taken. Fig. 139 is from an- 
other drawing of this nebula, 
although it is hardly to be 
recognized as a representa- 
tion of the same thing; but 
its characteristic feature, the 
two dark streaks near the cen- 
ter of the picture, is justified 
in part by Fig. 140, which is 
from a photograph made with 
a large reflecting telescope. 

A comparison of these sev- 
eral representations of the 
same thing will serve to illus- 
trate the vagueness of its out- 
lines, and how much the im- 
pressions to be derived from 
nebulae depend upon the tele- 
scopes employed and upon the 

observer's own prepossessions. The differences among the 
pictures can not be due to any change in the nebula itself, 

FIG. 141. Types of nebulae. 


for half a century ago it was sketched much as shown in 
the latest of them (Fig. 140). 

215. Typical nebulae. Some of the fantastic forms which 
nebulae present in the telescope are shown on a small scale 
in Fig. 141, but in recent years astronomers have learned to 

FIG. 142. The Trifld nebula. KEELER. 

place little reliance upon drawings such as these, which are 
now almost entirely supplanted by photographs made with 
long exposures in powerful telescopes. One of the most 
exquisite of these modern photographs is that of the Trifid 



nebula in Sagittarius (Fig. 142). Note especially the dark 
lanes that give to this nebula its name, Trifid, and which run 
through its brightest parts, breaking it into seemingly inde- 
pendent sections. The area of the sky shown in this cut is 
about 15 per cent less than that covered by the full moon. 

FIG. 143. A nebula in Cygnus. KEELER. 

Fig. 143 shows a very different type of nebula, found in 
the constellation Cygnus, which appears made up of fila- 
ments closely intertwined, and stretches across the sky for 
a distance considerably greater than the moon's diameter. 



A much smaller but equally striking nebula is that in 
the constellation Canes Venatici (Fig. 144), which shows a 
most extraordinary spiral structure, as if the stars compos- 
ing it were flowing in along curved lines toward a center of 
condensation. The diameter of the circular part of this 

FIG. 144. Spiral nebula in Canes Venatici. KEELER. 

nebula, omitting the "projection toward the bottom of the 
picture, is about five minutes of arc, a sixth part of the 
diameter of the moon, and its thickness is probably very 
small compared with its breadth, perhaps not much exceed- 


ing the width of the spiral streams which compose it. Note 
how the bright stars that appear within the area of this 
nebula fall on the streams of nebulous matter as if they 
were part of them. This characteristic grouping of the 
stars, which is followed in many other nebulas, shows that 

FIG. 145. Great nebula about the e tar p Ophiuchi. BARNARD. 

they are really part and parcel of the nebula and not merely 
on line with it. Fig. 145 shows how a great nebula is asso- 
ciated with the star p Ophiuchi. 

Probably the most impressive of all nebulae is the great 
one in Orion (Fig. 146), whose position is shown on the 
star map between Eigel and Orionis. Look for it with 
an opera glass or even with the unaided eye. This is some- 
times called an amorphous i. e., shapeless nebula, because 
it presents no definite form which the eye can grasp and 
little trace of structure or organization. It is "without 
form and void " at least in its central portions, although on 
its edges curved filaments may be traced streaming away 


from the brighter parts of the central region. This nebula, 
as shown in Fig. 146, covers an area about equal to that of 
the full moon, without counting as any part of this the 
companion nebula shown at one side, but photographs 
made with suitable exposures show that faint outlying parts 
of the nebula extend in curved lines over the larger part of 

FIG. 146. The Orion nebula. 

the constellation Orion. Indeed, over a large part of the 
entire sky the background is faintly covered with nebulous 
light whose brighter portions, if each were counted as a 
separate nebula, would carry the total number of such ob- 
jects well into the hundreds of thousands. 

The Pleiades (Plate IV) present a case of a resolvable 
star cluster projected against such a nebulous background 
whose varying intensity should be noted in the figure. A 
part of this nebulous matter is shown in wisps extending 
from one star to the next, after the fashion of a bridge, and 
leaving little doubt that the nebula is actually a part of the 
cluster and not merely a background for it. 

Fig. 147 shows a series of so-called double nebulae per- 
haps comparable with double stars, although the most 
recent photographic work seems to indicate that they are 



really faint spiral nebulae in which only the brightest parts 
are shown by the telescope. 

According to Keeler, the spiral is the prevailing type 
of nebulae, and while Fig. 144 presents the most perfect ex- 
ample of such a nebula, the 
student should not fail to 
note that the Andromeda neb- 
ula (Fig. 140) shows distinct 
traces of a spiral structure, 
only here we do not see its 
true shape, the nebula being 
turned nearly edgewise toward 
us so that its presumably cir- 
cular outline is foreshortened 
into a narrow ellipse. 

Another type of nebula of 
some consequence presents in 
the telescope round disks like 
those of Uranus or Xeptune, 
and this appearance has given 
them the name planetary neb- 

iilce. The comet in Fig. 138, if smaller, would represent 
fairly well the nebulae of this type. Sometimes a planetary 
nebula has a star at its center, arid sometimes it appears 
hollow, like a smoke ring, and is then called a ring nebula. 
The most famous of these is in the constellation Lyra, not 
far from Vega. 

216. Spectra of nebulae. A star cluster, like the one in 
Hercules, shows, of course, stellar spectra, and even when 
irresolvable the spectrum is a continuous one, testifying to 
the presence of stars, although they stand too close to- 
gether to be separately seen. But in a certain, number of 
nebulae the spectrum is altogether different, a discontinu- 
ous one containing only a few bright lines, showing that 
here the nebular light comes from glowing gases which 
are subject to no considerable pressure. The planetary 

FIG. 147. Double nebulae. 


nebulae all have spectra of this kind and make up about 
half of all the known gaseous nebulae. It is worthy of 
note that a century ago Sir William Herschel had observed 
a green shimmer in the light of certain nebulae which led 
him to believe that they were " not of a starry nature," a 
conclusion which has been abundantly confirmed by the 
spectroscope. The green shimmer is, in fact, caused by a 
line in the green part of the spectrum that is always pres- 
ent and is always the brightest part of the spectrum of 
gaseous nebulae. 

In faint nebulae this line constitutes the whole of their 
visible spectrum, but in brighter ones two or three other 
and fainter lines are usually associated with it, and a very 
bright nebula, like that in Orion, may show a considerable 
number of extra lines, but for the most part they can not 
be identified in the spectrum of any terrestrial substances. 
An exception to this is found in the hydrogen lines, which 
are well marked in most spectra of gaseous nebulae, and 
there are indications of one or two other known sub- 

217. Density of nebulae. It is known from laboratory 
experiments that diminishing the pressure to which an in- 
candescent gas is subject, diminishes the number of lines 
contained in its spectrum, and we may surmise from the 
very simple character and few lines of these nebular spec- 
tra that the gas which produces them has a very small 
density. But this is far from showing that the nebula 
itself is correspondingly attenuated, for we must not as- 
sume that this shining gas is all that exists in the nebula ; 
so far as telescope or camera are concerned, there may be 
associated with it any amount of dark matter which can 
not be seen because it sends to us no light. It is easy 
to think in this connection of meteoric dust or the stuff of 
which comets are made, for these seem to be scattered 
broadcast on every side of the solar system and may, per- 
chance, extend out to the region of the nebulae. 


But, whatever may be associated in the nebula with the 
glowing gas which we see, the total amount of matter, in- 
visible as well as visible, must be very small, or rather its 
average density must be very small, for the space occupied 
by such a nebula as that of Orion is so great that if the 
average density of its matter were equal to that of air the 
resulting mass by its attraction would exert a sensible effect 
upon the motion of the sun through space. The brighter 
parts of this nebula as seen from the earth subtend an angle 
of about half a degree, and while we know nothing of its 
distance from us, it is easy to see that the farther it is away 
the greater must be its real dimensions, and that this in- 
crease of bulk and mass with increasing distance will just 
compensate the diminishing intensity of gravity at great 
distances, so that for a given angular diameter e. g., half 
a degree the force with which this nebula attracts the sun 
depends upon its density but not at all upon its distance. 
Now, the nebula must attract the sun in some degree, and 
must tend to move it and the planets in an orbit about 
the attracting center so that year after year we should see 
the nebula from slightly different points of view, and this 
changed point of view should produce a change in the ap- 
parent direction of the nebula from us i. e., a proper mo- 
tion, whose amount would depend upon the attracting force, 
and therefore upon the density of the attracting matter. 
Observations of the Orion nebula show that its proper 
motion is wholly inappreciable, certainly far less than half 
a second of arc per year, and corresponding to this amount 
of proper motion the mean density of the nebula must be 
some millions of times (10 10 according to Eanyard) less than 
that of air at sea level i. e., the average density throughout 
the nebula is comparable with that of those upper parts 
of the earth's atmosphere in which meteors first become 

218. Motion of nebulae. The extreme minuteness of 
their proper motions is a characteristic feature of all 


nebulae. Indeed, there is hardly a known case of sensible 
proper motion of one of these bodies, although a dozen or 
more of them show velocities in the line of sight ranging 
in amount from -f-30 to 40 miles per second, the plus 
sign indicating an increasing distance. While a part of 
these velocities may be only apparent and due to the mo- 
tion of earth and sun through space, a part at least is real 
motion of the nebulas themselves. These seem to move 
through the celestial spaces in much the same way and 

FIG. 148. A part of the Milky Way. 

with the same velocities as do the stars, and their smaller 
proper motions across the line of sight (angular motions) 
are an index of their great distance from us. No one has 
ever succeeded in measuring the parallax of a nebula or 
star cluster. 

The law of gravitation presumably holds sway within 
these bodies, and the fact that their several parts and the 
stars which are involved within them, although attracted 
by each other, have shown little or no change of position 



during the past century, is further evidence of their low 
density and feeble attraction. In a few cases, however, 
there seem to be in progress within a nebula changes of 
brightness, so that what was formerly a faint part has be- 
come a brighter one, or vice versa ; but, on the whole, even 
these changes are very small. 

219. The Milky Way. Closely related to nebulae and 
star clusters is another feature of the sky, the galaxy or 
Milky Way, with whose appearance to the unaided eye the 

FIG. 149. The Milky Way near 6 Ophiuchi. BAUNARD. 

student should become familiar by direct study of the thing 
itself. Figs. 148 and 149 are from photographs of two 
small parts of it, and serve to bring out the small stars of 
which it is composed. Every star shown in these pictures 
is invisible to the naked eye, although their combined light 
is easily seen. The general course of the galaxy across the 
heavens is shown in the star maps, but these contain no 
indication of the wealth of detail which even the naked eye 
may detect in it. Bright and faint parts, dark rifts which 



cut it into segments, here and there a hole as if the ribbon 
of light had been shot away such are some of the features 
to be found by attentive examination. 

Speaking generally, the course of the Milky Way is a 
great circle completely girdling the sky and having its 
north pole in the constellation Coma Berenices. The 
width of this stream of light is very different in different 
parts of the heavens, amounting where it is widest, in Lyra 
and Cygnus, to something more than 30, although its 
boundaries are too vague and ill denned to permit much 
accuracy of measurement. Observe the very bright part 
between ft and y Cygni, nearly opposite Vega, and note 

FIG. 150. The Milky Way near /3 Cygni. BARNAKD. 

how even an opera glass will partially resolve the nebulous 
light into a great number of stars, which are here rather 
brighter than in other parts of its course. But the resolu- 
tion into stars is only partial, and there still remains a 
background of unresolved shimmer. Fig. 150 is a photo- 


graph of a small part of this region in which, although 
each fleck of light represents a separate star, the galaxy is 
not completely resolved. Compare with this region, rich 
in stars, the nearly empty space between the branches of 
the galaxy a little west of Altair. Another hole in the 
Milky Way may be found a little north and east of a Cygni, 
and between the extremes of abundance and poverty here 
noted there may be found every gradation of nebulous 

The Milky Way is not so simple in its structure as might 
at first be thought, but a clear and moonless night is 
required to bring out its details. The nature of these 
details, the structure of the galaxy, its shape and extent, 
the arrangement of its parts, and their relation to stars 
and nebulae in general, have been subjects of much specu- 
lation by astronomers and others who have sought to trace 
out in this way what is called the construction of the 

220. Distribution of the stars. How far out into space 
do the stars extend ? Are they limited or infinite in num- 
ber ? Do they form a system of mutually related parts, or 
are they bunched promiscuously, each for itself, without 
reference to the others ? Here is what has been well called 
"the most important problem of stellar astronomy, the 
acquisition of well-founded ideas about the distribution of 
the stars." While many of the ideas upon this subject 
which have been advanced by eminent astronomers and 
which are still current in the books are certainly wrong, 
and few of their speculations along this line are demon- 
strably true, the theme itself is of such grandeur and per- 
manent interest as to demand at least a brief considera- 
tion. But before proceeding to its speculative side we 
need to collect facts upon which to build, and these, how- 
ever inadequate, are in the main simple and not far to seek. 

Parallaxes, proper motions, motions in the line of sight, 
while pertinent to the problem of stellar distribution, are 


of small avail, since they are far too scanty in number and 
relate only to limited classes of stars, usually the very 
bright ones or those nearest to the sun. Almost the sole 
available data are contained in the brightness of the stars 
and the way in which they seem scattered in the sky. The 
most casual survey of the heavens is enough to show that 
the stars are not evenly sprinkled upon it. The lucid stars 
are abundant in some regions, few in others, and the labori- 
ous star gauges, actual counting of the stars in sample 
regions of the sky, which have been made by the Herschels, 
Celoria, and others, suffice to show that this lack of uni- 
formity in distribution is even more markedly true of the 
telescopic stars. 

The rate of increase in the number of stars from one 
magnitude to the next, as shown in 187, is proof of 
another kind of irregularity in their distribution. It is not 
difficult to show, mathematically, that if in distant regions 
of space the stars were on the average as numerous and as 
bright as they are in the regions nearer to the sun, then 
the stars of any particular magnitude ought to be four 
times as numerous as those of the next brighter magnitude 
e. g., four times as many sixth-magnitude stars as there 
are fifth-magnitude ones. But, as we have already seen in 
187, by actual count there are only three times as many, 
and from the discrepancy between these numbers, an actual 
threefold increase instead of a fourfold one, we must con- 
clude that on the whole the stars near the sun are either 
bigger or brighter or more numerous than in the remoter 
depths of space. 

221. The stellar system, But the arrangement of the 
stars is not altogether lawless and chaotic ; there are traces 
of order and system, and among these the Milky Way is the 
dominant feature. Telescope and photographic plate alike 
show that it is made up of stars which, although quite ir- 
regularly scattered along its course, are on the average 
some twenty times as numerous in the galaxy as at its 


poles, and which thin out as we recede from it on either 
side, at first rapidly and then more slowly. This tendency 
to cluster along the Milky Way is much more pronounced 
among the very faint telescopic stars than among the 
brighter ones, for the lucid stars and the telescopic ones 
down to the tenth or eleventh magnitude, while very 
plainly showing the clustering tendency, are not more than 
three times as numerous in the galaxy as in the constella- 
tions most remote from it. It is remarkable as showing 
the condensation of the brightest stars that one half of all 
the stars in the sky which are brighter than the second 
magnitude are included within a belt extending 12 on 
either side of the center line of the galaxy. 

In addition to this general condensation of stars toward 
the Milky Way, there are peculiarities in the distribution of 
certain classes of stars which are worth attention. Planet- 
ary nebulae and new stars are seldom, if ever, found far 
from the Milky Way, and stars with bright lines in their 
spectra especially affect this region of the sky. Stars with 
spectra of the first type Sirian stars are much more 
strongly condensed toward the Milky Way than are stars 
of the solar type, and in consequence of this the Milky 
Way is peculiarly rich in light of short wave lengths. Ee- 
solvable star clusters are so much more numerous in the 
galaxy than elsewhere, that its course across the sky would 
be plainly indicated by their grouping upon a map showing 
nothing but clusters of this kind. 

On the other hand, nebulae as a class show a distinct 
aversion for the galaxy, and are found most abundantly in 
those parts of the sky farthest from it, much as if they 
represented raw material which was lacking along the 
Milky Way, because already worked up to make the stars 
which are there so numerous. 

222. Relation of the sun to the Milky Way. The fact 
that the galaxy is a great circle of the sky, but only of mod- 
erate width, shows that it is a widely extended and com- 


paratively thin stratum of stars within which the solar sys- 
tem lies, a member of the galactic system, and probably not 
very far from its center. This position, however, is not to 
be looked upon as a permanent one, since the sun's motion, 
which lies nearly in the plane of the Milky Way, is cease- 
lessly altering its relation to the center of that system, and 
may ultimately carry us outside its limits. 

The Milky Way itself is commonly thought to be a 
ring, or series of rings, like the coils of the great spiral 
nebula in Andromeda, and separated from us by a space far 
greater than the thickness of the ring itself. Note in Figs. 
149 and 150 how the background is made up of bright and 
dark parts curiously interlaced, and presenting much the 
appearance of a thin sheet of cloud through which we look 
to barren space beyond. While, mathematically, this ap- 
pearance can not be considered as proof that the galaxy 
is in fact a distant ring, rather than a sheet of starry 
matter stretching continuously from the nearer stellar 
neighbors of the sun into the remotest depths of space, 
nevertheless, most students of the question hold it to be 
such a ring of stars, which are relatively close together 
while its center is comparativeljjyag^i. although even 
here are 1^01116 liuiiTIreds'ol 1 Ln'ousanos of stars which on the 
whole have a tendency to cluster near its plane and to 
crowd together a little more densely than elsewhere in the 
region where the sun is placed. 

223. Dimensions of the galaxy, The dimensions of this 
stellar system are wholly unknown, but there can be no 
doubt that it extends farther in the plane of the Milky 
Way than at right angles to that plane, for stars of the fif- 
teenth and sixteenth magnitudes are common in the galaxy, 
and testify by their feeble light to their great distance 
from the earth, while near the poles of the Milky Way there 
seem to be few stars fainter than the twelfth magnitude. 
Herschel, with his telescope of 18 inches aperture, could 
count in the Milky Way more than a dozen times as many 


stars per square degree as could Celoria with a telescope of 
4 inches aperture ; but around the poles of the galaxy the 
two telescopes showed practically the same number of stars, 
indicating that here even the smaller telescope reached to 
the limits of the stellar system. Very recently, indeed, the . 
telescope with which Fig. 140 was photographed seems to 
have reached the farthest limit of the Milky Way, for on a 
photographic plate of one of its richest regions Roberts 
finds it completely resolved into stars which stand out upon 
a black background with no trace of nebulous light between 

224,. Beyond the Milky Way. Each additional step into 
the depths of space brings us into a region of which less is 
known, and what lies beyond the Milky Way is largely a 
matter of conjecture. We shrink from thinking it an in- 
finite void, endless emptiness, and our intellectual sympa- 
thies go out to Lambert's speculation of a universe filled 
with stellar systems, of which ours, bounded by the galaxy, 
is only one. There is, indeed, little direct evidence that 
other such systems exist, but the Andromeda nebula is not 
altogether unlike a galaxy with a central cloud of stars, 
and in the southern hemisphere, invisible in our latitudes, 
are two remarkable stellar bodies like the Milky Way in 
appearance, but cut off from all apparent connection with 
it, much as we might expect to find independent stellar 
systems, if such there be. 

These two bodies are known as the Magellanic clouds, 
and individually bear the names of Major and Minor Xubec- 
ula. According to Sir John Herschel, " the Xubecula 
Major, like the Minor, consists partly of large tracts and 
ill-defined patches of irresolvable nebula, and of nebulosity 
in every stage of resolution up to perfectly resolved stars 
like the Milky Way, as also of regular and irregular nebulae 
... of globular clusters in every stage of resolvability, and 
of clustering groups sufficiently insulated and condensed to 
come under the designation of clusters of stars." Its out- 


lines are vague and somewhat uncertain, but surely include 
an area of more than 40 square degrees i. e., as much as 
the bowl of the Big Dipper and within this area Herschel 
counted several hundred nebulse and clusters " which far 
exceeds anything that is to be met with in any other region 
of the heavens." Although its excessive complexity of de- 
tail baffled Herschel's attempts at artistic delineation, it 
has yielded to the modern photographic processes, which 
show the Nubecula Major to be an enormous spiral nebula 
made up of subordinate stars, nebula?, and clusters, as is 
the Milky Way. 

Compared with the Andromeda nebula, its greater angu- 
lar extent suggests a smaller distance, although for the 
present all efforts at determining the parallax of either 
seem hopeless. But the spiral form which is common to 
both suggests that the Milky Way itself may be a gigantic 
spiral nebula near whose center lies the sun, a humble 
member of a great cluster of stars which is roughly globu- 
lar in shape, but flattened at the poles of the galaxy 
and completely encircled by its coils. However plausible 
such a view may appear, it is for the present, at least, pure 
hypothesis, although vigorously advocated by Easton, who 
bases his argument upon the appearance of the galaxy 

225. Absorption of starlight. We have had abundant 
occasion to learn that at least within the confines of the 
solar system meteoric matter, cosmic dust, is profusely scat- 
tered, and it appears not improbable that the same is true, 
although in smaller degree, in even the remoter parts of 
space. In this case the light which comes from the farther 
stars over a path requiring many centuries to travel, must 
be in some measure absorbed and enfeebled by the obstacles 
which it encounters on the way. Unless celestial space is 
transparent to an improbable degree the remoter stars do 
not show their true brightness ; there is a certain limit 
beyond which no star is able to send its light, and beyond 


which the universe must be to us a blank. A lighthouse 
throws into the fog its beams only to have them extin- 
guished before a single mile is passed, and though the 
celestial lights shine farther, a limit to their reach is none 
the less certain if meteoric dust exists outside the solar 
system. If there is such an absorption of light in space, 
as seems plausible, the universe may well be limitless and 
the number of stellar systems infinite, although the most 
attenuated of dust clouds suffices to conceal from us and 
to shut off from our investigation all save a minor fraction 
of it and them. 



226. Nature of the problem. To use a common figure of 
speech, the universe is alive. We have found it filled with 
an activity that manifests itself not only in the motions of 
the heavenly bodies along their orbits, but which extends 
to their minutest parts, the molecules and atoms, whose 
vibrations furnish the radiant energy given off by sun and 
stars. Some of these activities, such as the motions of the 
heavenly bodies in their orbits, seem fitted to be of endless 
duration ; while others, like the radiation of light and heat, 
are surely temporary, and sooner or later must come to an 
end and be replaced by something different. The study of 
things as they are thus leads inevitably to questions of 
what has been and what is to be. A sound science should 
furnish some account of the universe of yesterday and 
to-morrow as well as of to-day, and we need not shrink 
from such questions, although answers to them must be 
vague and in great measure speculative. 

The historian of America finds little difficulty with events 
of the nineteenth century or even the eighteenth, but the 
sources of information about America in the fifteenth cen- 
tury are much less definite ; the tenth century presents 
almost a blank, and the history of American mankind in 
the first century of the Christian era is wholly unknown. 
So, as we attempt to look into the past or the future of the 
heavens, we must expect to find the mists of obscurity grow 
denser with remoter periods until even the vaguest outlines 
of its development are lost, and we are compelled to say, 


beyond this lies the unknown. Our account of growth and 
decay in the universe, therefore, can not aspire to cover the 
whole duration of things, but must be limited in its scope 
to certain chapters whose epochs lie near to the time in 
which we live, and even for these we need to bear con- 
stantly in mind the logical bases of such an inquiry and 
the limitations which they impose upon us. 

227. Logical bases and limitations. The first of these 
bases is : An adequate knowledge of the present universe. 
Our only hope of reading the past and future lies in an 
understanding of the present; not necessarily a complete 
knowledge of it, but one which is sound so far as it goes. 
Our position is like that of a detective who is called upon 
to unravel a mystery or crime, and who must commence 
with the traces that have been left behind in its commis- 
sion. The foot print, the blood stain, the broken glass must 
be examined and compared, and fashioned into a theory of 
how they came to be ; and as a wrong understanding of 
these elements is sure to vitiate the theories based upon 
them, so a false science of the universe as it now is, will 
surely give a false account of what it has been; while a 
correct but incomplete knowledge of the present does not 
wholly bar an understanding of the past, but only puts us 
in the position of the detective who correctly understands 
what he sees but fails to take note of other facts which 
might greatly aid him. 

The second basis of our inquiry is : The assumed per- 
manence of natural laws. The law of gravitation certainly 
held true a century ago as well as a year ago, and for aught 
we know to the contrary it may have been a law of the uni- 
verse for untold millions of years ; but that it has prevailed 
for so long a time is a pure assumption, although a neces- 
sary one for our purpose. So with those other laws of 
mathematics and mechanics and physics and chemistry to 
which we must appeal ; if there was ever a time or place 
in which they did not hold true, that time and place lie 


beyond the scope of our inquiry, and are in the domain 
inaccessible to scientific research. It is for this reason 
that science knows nothing and can know nothing of a 
creation or an end of the universe, but considers only its 
orderly development within limited periods of time. What 
kind of a past universe would, under the operation of 
known laws, develop into the present one, is the question 
with which we have to deal, and of it we may say with 
Helmholtz : " From the standpoint of science this is no 
idle speculation but an inquiry concerning the limitations 
of its methods and the scope of its known laws." 

To ferret out the processes by which the heavenly bodies 
have been brought to their present condition we seek first 
of all for lines of development now in progress which tend 
to change the existing order of things into something dif- 
ferent, and, having found these, to trace their effects into 
both past and future. Any force, however small, or any 
process, however slow, may produce great results if it works 
always and ceaselessly in the same direction, and it is in 
these processes, whose trend is never reversed, that we find 
a partial clew to both past and future. 

228. The sun's development. The first of these to claim 
our attention is the shrinking of the sun's diameter which, 
as we have seen in Chapter X, is the means by which the 
solar output of radiant energy is maintained from year to 
year. Its amount, only a few feet per annum, is far too 
small to be measured with any telescope ; but it is cumula- 
tive, working century after century in the same direction, 
and, given time enough, it will produce in the future, and 
must have produced in the past, enormous transformations 
in the sun's bulk and equally significant changes in its 
physical condition. 

Thus, as we attempt to trace the sun's history into the 
past, the farther back we go the greater shall we expect to 
find its diameter and the greater the space (volume) 
through which its molecules are spread. By reason of this 


expansion its density must have been less then than now, 
and by going far enough back we may even reach a time at 
which the density was comparable with what we find in the 
nebulae of to-day. If our ideas of the sun's present mechan- 
ism are sound, then, as a necessary consequence of these,, 
its past career must have been a process of condensation in 
which its component particles were year by year packed 
closer together by their own attraction for each other. As 
we have seen in 126, this condensation necessarily devel- 
oped heat, a part of which was radiated away as fast as pro- 
duced, while the remainder was stored up, and served to 
raise the temperature of the sun to what we find it now. 
At the present time this temperature is a chief obstacle to 
further shrinkage, and so powerfully opposes the gravita- 
tive forces as to maintain nearly an equilibrium with them, 
thus causing a very slow rate of further condensation. But 
it is not probable that this was always so. In the early 
stages of the sun's history, when the temperature was low, 
contraction of its bulk must have been more rapid, and 
attempts have been made by the mathematicians to measure 
its rate of progress and to determine how long a time has 
been consumed in the development of the present sun from 
a primitive nebulous condition in which it filled a space of 
greater diameter than Xeptune's orbit. Of course, numer- 
ical precision is not to be expected in results of this kind, 
but, from a consideration of the greatest amount of heat 
that could be furnished by the shrinkage of a mass equal to 
that of the sun, it seems that the period of this develop- 
ment is to be measured in tens of millions or possibly hun- 
dreds of millions of years, but almost certainly does not 
reach a thousand millions. 

229. The sun's future, The future duration of the sun 
as a source of radiant energy is surely to be measured in 
far smaller numbers than these. Its career as a dispenser 
of light and heat is much more than half spent, for the 
shrinkage results in an ever-increasing density, which 


makes its gaseous substance approximate more and more 
toward the behavior of a liquid or solid, and we recall that 
these forms of matter can not by any further condensation 
restore the heat whose loss through radiation caused them 
to contract. They may continue to shrink, but their tem- 
perature must fall, and when the sun's substance becomes 
too dense to obey the laws of gaseous matter its surface 
must cool rapidly as a consequence of the radiation into 
surrounding space, and must congeal into a crust which, 
although at first incandescent, will speedily become dark 
and opaque, cutting off the light of the central portions, 
save as it may be rent from time to time by volcanic 
outbursts of the still incandescent mass beneath. But 
such outbursts can be of short duration only, and its final 
.condition must be that of a dark body, like the earth or 
moon, no longer available as a source of radiant energy. 
Even before the formation of a solid crust it is quite pos- 
sible that the output of light and heat may be seriously 
diminished by the formation of dense vapors completely 
enshrouding it, as is now the case with Jupiter and Saturn. 
It is believed that these planets were formerly incandescent, 
and at the present time are in a state of development 
through which the earth has passed and toward which the 
sun is moving. According to Kewcomb, the future during 
which the sun can continue to furnish light and heat at its 
present rate is not likely to exceed 10,000,000 years. 

This idea of the sun as a developing body whose pres- 
ent state is only temporary, furnishes a clew to some of the 
vexing problems of solar physics. Thus the sun-spot period, 
the distribution of the spots in latitude, and the peculiar 
law of rotation of the sun in different latitudes, may be, 
and very probably are, results not of anything now operat- 
ing beneath its photosphere, but of something which hap- 
pened to it in the remote past e. g., an unsymmetrical 
shrinkage or possibly a collision with some other body. At 
sea the waves continue to toss long after the storm which 


produced them has disappeared, and, according to the 
mathematical researches of Wilsing, a profound agitation 
of the sun's mass might well require tens of thousands, or 
even hundreds of thousands of years to subside, and during 
this time its effects would be visible, like the waves, as phe- 
nomena for which the actual condition of things furnishes 
no apparent cause. 

230. The nebular hypothesis. The theory of the sun's 
progressive contraction as a necessary result of its radiation 
of energy is comparatively modern, but more than a cen- 
tury ago philosophic students of Nature had been led in 
quite a different way to the belief that in the earlier stages 
of its career the sun must have been an enormously ex- 
tended body whose outer portions reached even beyond the 
orbit of the remotest planet. Laplace, whose speculations 
upon this subject have had a dominant influence during 
the nineteenth century, has left, in a popular treatise upon 
astronomy, an admirable statement of the phenomena of 
planetary motion, which suggest and lead up to the nebular 
theory of the sun's development, and in presenting this 
theory we shall follow substantially his line of thought, 
but with some freedom of translation and many omissions. 

He says : " To trace out the primitive source of the plan- 
etary movements, we have the following five phenomena : 
(1) These movements all take place in the same direction 
and nearly in the same plane. (2) The movements of the 
satellites are in the same direction as those of the planets. 
(3) The rotations of the planets and the sun are in the 
same direction as the orbital motions and nearly in the same 
plane. (4) Planets and satellites alike have nearly circular 
orbits. (5) The orbits of comets are wholly unlike these by 
reason of their great eccentricities and inclinations to the 
ecliptic." That these coincidences should be purely the 
result of chance seemed to Laplace incredible, and, seeking 
a cause for them, he continues : " Whatever its nature may 
be, since it has produced or controlled the motions of the 


planets, it must have reached out to all these bodies, and, in 
view of the prodigious distances which separate them, the 
cause can have been nothing else than a fluid of great ex- 
tent which must have enveloped the sun like an atmosphere. 
A consideration of the planetary motions leads us to think 
that . . . the sun's atmosphere formerly extended far be- 
yond the orbits of all the planets and has shrunk by degrees 
to its present dimensions." This is not very different from 
the idea developed in 228 from a consideration of the 
sun's radiant energy ; but in Laplace's day the possibility 
of generating the sun's heat by contraction of its bulk was 
unknown, and he was compelled to assume a very high tem- 
perature for the primitive nebulous sun, while we now know 
that this is unnecessary. Whether the primitive nebula 
was hot or cold the shrinkage would take place in much 
the same way, and would finally result in a star or sun of 
very high temperature, but its development would be slower 
if it were hot in the beginning than if it were cold. 

But again Laplace : " How did the sun's atmosphere 
determine the rotations and revolutions of planets and 
satellites ? If these bodies had been deeply immersed in 
this atmosphere its resistance to their motion would have 
made them fall into the sun, and we may therefore conjec- 
ture that the planets were formed, one by one, at the outer 
limits of the solar atmosphere by the condensation of zones 
of vapor which were cast off in the plane of the sun's equa- 
tor." Here he proceeds to show by an appeal to dynamical 
principles that something of this kind must happen, and 
that the matter sloughed off by the nebula in the form of a 
ring, perhaps comparable to the rings of Saturn or the 
asteroid zone, would ultimately condense into a planet, 
which in its turn might shrink and cast off rings to pro- 
duce satellites. 

Planets and satellites would then all have similar mo- 
tions, as noted at the beginning of this section, since in 
every case this motion is an inheritance from a common 



source, the rotation of the primitive nebula about its own 
axis. " All the bodies which circle around a planet having 
been thus formed from rings which its atmosphere succes- 
sively abandoned as rotation became more and more rapid, 
this rotation should take place in less time than is required 
for the orbital revolution of any of the bodies which have 
been cast off, and this holds true for the sun as compared 
with the planets." 

231. Objections to the nebular hypothesis. In Laplace's 
time this slower rate of motion was also supposed to hold 
true for Saturn's rings as compared with the rotation of 
Saturn itself, but, as we have seen in Chapter XI, this ring is 
made up of a great number of independent particles which 
move at different rates of speed, and comparing, through 
Kepler's Third Law, the motion of the inner edge of the 
ring with the known periodic time of the satellites, we may 
find that these particles must rotate about Saturn more 
rapidly than the planet turns upon its axis. Similarly the 
inner satellite of Mars completes its revolution in about 
one third of a Martian day, and we find in cases like this 
grounds for objection to the nebular theory. Compare also 
Laplace's argument with the peculiar rotations of Uranus, 
Neptune; and their satellites (Chapter XI). Do these for- 
tify or weaken his case ? 

Despite these objections and others equally serious that 
have been raised, the nebular theory agrees with the facts 
of Nature at so many points that astronomers upon the 
whole are strongly inclined to accept its major outlines as 
being at least an approximation to the course of develop- 
ment actually followed by the solar system ; but at some 
points e. g., the formation of planets and satellites through 
the casting off of nebulous rings the objections are so 
many and strong as to call for revision and possibly serious 
modification of the theory. 

One proposed modification, much discussed in recent 
years, consists in substituting for the primitive gaseous 


nebula imagined by Laplace, a very diffuse cloud of mete- 
oric matter which in the course of its development would 
become transformed into the gaseous state by rising tem- 
perature. From this point of view much of the meteoric 
dust still scattered throughout the solar system may be 
only the fragments left over in fashioning the sun and 
planets. Chamberlin and Moulton, who have recently 
given much attention to this subject, in dissenting from 
some of Laplace's views, consider that the primitive nebu- 
lous condition must have been one in which the matter of 
the system was " so brought together as to give low mass, 
high momentum, and irregular distribution to the outer 
part, and high mass, low momentum, and sphericity to the 
central part," and they suggest a possible oblique collision 
of a small nebula with the outer parts of a large one. 

232. Bode's law. We should not leave the theory of 
Laplace without noting the light it casts upon one point 
otherwise obscure the meaning of Bode's law ( 134). 
This law, stated in mathematical form, makes a geomet- 
rical series, and similar geometrical series apply to the 
distances of the satellites of Jupiter and Saturn from 
these planets. Now, Eoche has shown by the application 
of physical laws to the shrinkage of a gaseous body that 
its radius at any time may be expressed by means of a 
certain mathematical formula very similar to Bode's law, 
save that it involves the amount of time that has elapsed 
since the beginning of the shrinking process. By compar- 
ing this formula with the one corresponding to Bode's law 
he reaches the conclusion that the peculiar spacing of the 
planets expressed by that law means that they were formed 
at successive equal intervals of time i. e., that Mars is as 
much older than the earth as the earth is older than 
Venus, etc. The failure of Bode's law in the case of 
Neptune would then imply that the interval of time be- 
tween the formation of Neptune and Uranus was shorter 
than that which has prevailed for the other planets. But 


too much stress should not be placed upon this conclusion. 
So long as the manner in which the planets came into being 
continues an open question, conclusions about their time 
of birth must remain of doubtful validity. 

233. Tidal friction between earth and moon. An impor- 
tant addition to theories of development within the solar 
system has been worked out by Prof. G. H. Darwin, who, 
starting with certain very simple assumptions as to the 
present condition of things in earth and moon, derives 
from these, by a strict process of mathematical reasoning, 
far-reaching conclusions of great interest and importance. 
The key to these conclusions lies in recognition of the fact 
that through the influence of the tides ( 42) there is now 
in progress and has been in progress for a very long time, a 
gradual transfer of motion (moment of momentum) from 
the earth to the moon. The earth's motion of rotation is 
being slowly destroyed by the friction of the tides, as the 
motion of a bicycle is destroyed by the friction of a brake, 
and, in consequence of this slowing down, the moon is 
pushed farther and farther away from the earth, so that 
it now moves in a larger orbit than it had some millions 
of years ago. 

Fig. 24 has been used to illustrate the action of the 
moon in raising tides upon the earth, but in accordance 
with the third law of motion ( 36) this action must be 
accompanied by an equal and contrary reaction whose 
nature may readily be seen from the same figure. The 
moon moves about its orbit from west to east and the 
earth rotates about its axis in the same direction, as 
shown by the curved arrow in the figure. The tidal wave, 
/, therefore points a little in advance of the moon's posi- 
tion in its orbit and by its attraction must tend to pull the 
moon ahead in its orbital motion a little faster than it 
would move if the whole substance of the earth were 
placed inside the sphere represented by the broken circle 
in the figure. It is true that the tidal wave at I" pulls 


back and tends to neutralize the effect of the wave at /, 
but on the whole the tidal wave nearer the moon has the 
stronger influence, and the moon on the whole moves a 
very little faster, and by virtue of this added impetus 
draws continually a little farther away from the earth 
than it would if there were no tides. 

234. Consequences of tidal friction upon the earth. This 
process of moving the moon away from the earth is a 
cumulative one, going on century after century, and with 
reference to it the moon's orbit must be described not as 
a circle or ellipse, or any other curve which returns into 
itself, but as a spiral, like the balance spring of a watch, 
each of whose coils is a little larger than the preceding 
one, although this excess is, to be sure, very small, be- 
cause the tides themselves are small and the tidal in- 
fluence feeble when compared with the whole attrac- 
tion of the earth for the moon. But^ given time enough, 
even this small force may accomplish great results, and 
something like 100,000,000 years of past opportunity 
would have sufficed for the tidal forces to move the moon 
from close proximity with the earth out to its present po- 

For millions of years to come, if moon and earth endure 
so long, the distance between them must go on increasing, 
although at an ever slower rate, since the farther away the 
moon goes the smaller will be the tides and the slower the 
working out of their results. On the other hand, when 
the moon was nearer the earth than now, tidal influences 
must have been greater and their effects more rapidly 
produced than at the present time, particularly if, as 
seems probable, at some past epoch the earth was hot and 
plastic like Jupiter and Saturn. Then, instead of tides in 
the water of the sea, such as we now have, the whole sub- 
stance of the earth would respond to the moon's attraction 
in bodily tides of semi-fluid matter not only higher, but with 
greater internal friction of their molecules one upon an- 


other, and correspondingly greater effect in checking the 
earth's rotation. 

But, whether the tide be a bodily one or confined to the 
waters of the sea, so long as the moon causes it to flow 
there will be a certain amount of friction which will affect 
the earth much as a brake affects a revolving wheel, slow- 
ing down its motion, and producing thus a longer day as 
well as a longer month on account of the moon's increased 
distance. Slowing down the earth's rotation is the direct 
action of the moon upon the earth. Pushing the moon 
away is the form in which the earth's equal and contrary 
reaction manifests itself. 

235. Consequences of tidal friction upon the moon. When 
the moon was plastic the earth must have raised in it a 
bodily tide manifold greater than the lunar tides upon the 
earth, and, as we have seen in Chapter IX, this tide has 
long since worn out the greater part of the moon's rotation 
and brought our satellite to the condition in which it pre- 
sents always the same face toward the earth. 

These two processes, slowing down the rotation and 
pushing away the disturbing body, are inseparable one 
requires the other ; and it is worth noting in this connec- 
tion that when for any reason the tide ceases to flow, and 
the tidal wave takes up a permanent position, as it has in 
the moon ( 99), its work is ended, for when there is no 
motion of the wave there can be no friction to further 
reduce the rate of rotation of the one body, and no reaction 
to that friction to push away the other. But this perma- 
nent and stationary tidal wave in the moon, or elsewhere, 
means that the satellite presents always the same face 
toward its planet, moving once about its orbit in the time 
required for one revolution upon its axis, and the tide 
raised by the moon upon the earth tends to produce here 
the result long since achieved in our satellite, to make our 
day and month of equal length, and to make the earth 
turn always the same side toward the moon. But the 


moon's tidal force is small compared with that of the earth, 
and has a vastly greater momentum to overcome, so that 
its work upon the earth is not yet complete. According 
to Thomson and Tait, the moon must be pushed off an- 
other hundred thousand miles, and the day lengthened out 
by tidal influence to seven of our present weeks before the 
day and the lunar month are made of equal length, and 
the moon thereby permanently hidden from one hemisphere 
of the earth. 

236. The earth-moon system, Eetracing into the past 
the course of development of the earth and moon, it is pos- 
sible to reach back by means of the mathematical theory 
of tidal friction to a time at which these bodies were much 
nearer to each other than now, but it has not been found 
possible to trace out the mode of their separation from one 
body into two, as is supposed in the nebular theory. In 
the earliest part of their history accessible to mathematical 
analysis they are distinct bodies at some considerable dis- 
tance from each other, with the earth rotating about an 
axis more nearly perpendicular to the moon's orbit and to 
the ecliptic than is now the case. Starting from such a 
condition, the lunar tides, according to Darwin, have been 
instrumental in tipping the earth's rotation axis into its 
present oblique position, and in determining the eccen- 
tricity of the moon's orbit and its position with respect to 
the ecliptic as well as the present length of day and month. 

337. Tidal friction upon the planets. The satellites of the 
outer planets are equally subject to influences of this kind, 
and there appears to be independent evidence that some of 
them, at least, turn always the same face toward their 
respective planets, indicating that the work of tidal friction 
has here been accomplished. We saw in Chapter XI that 
it is at present an open question whether the inner planets, 
Venus and Mercury, do not always turn the same face 
toward the sun, their day and year being of equal length. 
In addition to the direct observational evidence upon this 


point, Schiaparelli has sought to show by an appeal to tidal 
theory that such is probably the case, at least for Mercury, 
since the tidal forces which tend to bring about this result 
in that planet are about as great as the forces which have 
certainly produced it in the case of the moon and Saturn's 
satellite, Japetus. The same line of reasoning would show 
that every satellite in the solar system, save possibly the 
newly discovered ninth satellite of Saturn, must, as a con- 
sequence of tidal friction, turn always the same face toward 
its planet. 

238. The solar tide, The sun also raises tides in the 
earth, and their influence must be similar in character to 
that of the lunar tides, checking the rotation of the earth 
and thrusting earth and sun apart, although quantitatively 
these effects are small compared with those of the moon. 
They must, however, continue so long as the solar tide 
lasts, possibly until the day and year are made of equal 
length i. e., they may continue long after the lunar tidal 
influence has ceased to push earth and moon apart. Should 
this be the case, a curious inverse effect will be produced. 
The day being then longer than the month, the moon will 
again raise a tide in the earth which will run around it 
from west to east, opposite to the course of the present tide, 
thus tending to accelerate the earth's rotation, and by its 
reaction to bring the moon back toward the earth again, 
and ultimately to fall upon it. 

We may note that an effect of this kind must be in 
progress now between Mars and its inner satellite, Phobos, 
whose time of orbital revolution is only one third of a Mar- 
tian day. It seems probable that this satellite is in the last 
stages of its existence as an independent body, and must 
ultimately fall into Mars. 

239. Roche's limit In looking forward to such a catas- 
trophe, however, due regard must be paid to a dynamical 
principle of a different character. The moon can never be 
precipitated upon the earth entire, since before it reaches 


us it will have been torn asunder by the excess of the 
earth's attraction for the near side of its satellite over that 
which it exerts upon the far side. As the result of Eoche's 
mathematical analysis we are able to assign a limiting dis- 
tance between any planet and its satellite within which the 
satellite, if it turns always the same face toward the planet, 
can not come without being broken into fragments. If we 
represent the radius of the planet by r, and the quotient 
obtained by dividing the density of the 'planet by the den- 
sity of the satellite by <?, then 

Eoche's limit = 2.44 r l/q. 

Thus in the case of earth and moon we find from the den- 
sities given in 95, q = 1.65, and with r = 3,963 miles we 
obtain 11,400 miles as the nearest approach which the moon 
could make to the earth without being broken up by the 
difference of the earth's attractions for its opposite sides. 

We must observe, however, that Eoche's limit takes no 
account of molecular forces, the adhesion of one molecule 
to another, by virtue of which a stick or stone resists frac- 
ture, but is concerned only with the gravitative forces by 
which the molecules are attracted toward the moon's center 
and toward the earth. Within a stone or rock of moderate 
size these gravitative forces are insignificant, and cohesion 
is the chief factor in preserving its integrity, but in a large 
body like the moon, the case is just reversed, cohesion plays 
a small part and gravitation a large one in holding the 
body together. We may conclude, therefore, that at a 
proper distance these forces are capable of breaking up the 
moon, or any other large body, into fragments of a size 
such that molecular cohesion instead of gravitation is the 
chief agent in preserving them from further disintegration. 

240. Saturn's rings. Saturn's rings are of peculiar in- 
terest in this connection. The outer edge of the ring sys- 
tem lies just inside of Eoche's limit for this planet, and we 
have already seen that the rings are composed of small frag- 


ments independent of each other. Whatever may have 
been the process by which the nine satellites of Saturn 
came into existence, we have in Eoche's limit the explana- 
tion why the material of the ring was not worked up into 
satellites ; the forces exerted by Saturn would tear into 
pieces any considerable satellite thus formed and equally 
would prevent the formation of one from raw material. 

Saturn's rings present the only case within the solar 
system where matter is known to be revolving about a 
planet at a distance less than Roche's limit, and it is an 
interesting question whether these rings can remain as a 
permanent part of the planet's system or are only a tempo- 
rary feature. The drawings of Saturn made two centuries 
ago agree among themselves in representing the rings as 
larger than they now appear, and there is some reason to 
suppose that as a consequence of mutual disturbances col- 
lisions their momentum is being slowly wasted so that 
ultimately they must be precipitated into the planet. But 
the direct evidence of such a progress that can be drawn 
from present data is too scanty to justify positive conclu- 
sions in the matter. On the other hand, Xolan suggests 
that in the outer parts of the ring small satellites might be 
formed whose tidal influence upon Saturn would suffice to 
push them away from the ring beyond Roche's limit, and 
that the very small inner satellites of Saturn may have 
been thus formed at the expense of the ring. 

The inner satellite of Mars is very close to Roche's limit 
for that planet, and, as we have seen above, must be approach- 
ing still nearer to the danger line. 

241. The moon's development The fine series of photo- 
graphs of the moon obtained within the last few years at 
Paris, have been used by the astronomers of that observa- 
tory for a minute study of the lunar formations, much as 
geologists study the surface of the earth to determine some- 
thing about the manner in which it was formed. Their 
conclusions are, in general, that at some past time the moon 


was a hot and fluid body which, as it cooled and condensed, 
formed a solid crust whose further shrinkage compressed 
the liquid nucleus and led to a long series of fractures in 
the crust and outbursts of liquid matter, whose latest and 
feeblest stages produced the lunar craters, while traces of 
the earlier ones, connected with a general settling of the 
crust, although nearly obliterated, are still preserved in cer- 
tain large but vague features of the lunar topography, such 
as the distribution of the seas, etc. They find also in cer- 
tain markings of the surface what they consider convincing 
evidence of the existence in past times of a lunar atmos- 
phere. But this seems doubtful, since the force of gravity 
at the moon's surface is so small that an atmosphere similar 
to that of the earth, even though placed upon the moon, 
could not permanently endure, but would be lost by the 
gradual escape of its molecules into the surrounding space. 
The molecules of a gas are quite independent one of 
another, and are in a state of ceaseless agitation, each one 
darting to and fro, colliding with its neighbors or with 
whatever else opposes its forward motion, and traveling 
with velocities which, on the average, amount to a good 
many hundreds of feet per second, although in the case of 
any individual molecule they may be much less or much 
greater than the average value, an occasional molecule hav- 
ing possibly a velocity several times as great as the average. 
In the upper regions of our own atmosphere, if one of these 
swiftly moving particles of oxygen or nitrogen were headed 
away from the earth with a velocity of seven miles per sec- 
ond, the whole attractive power of the earth would be 
insufficient to check its motion, and it would therefore, 
unless stopped by some collision, escape from the earth and 
return no more. But, since this velocity of seven miles per 
second is more than thirty times as great as the average 
velocity of the molecules of air, it must be very seldom in- 
deed that one is found to move so swiftly, and the loss of 
the earth's atmosphere by leakage of this sort is insignifi- 


cant. But upon the moon, or any other body where the 
force of gravity is small, conditions are quite different, and 
in our satellite a velocity of little more than one mile per 
second would suffice to carry a molecule away from the 
outer limits of its atmosphere. This velocity, only five times 
the average, would be frequently attained, particularly in 
former times when the moon's temperature was high, for 
then the average velocity of all the molecules would be con- 
siderably increased, and the amount of leakage might be- 
come, and probably would become, a serious matter, steadi- 
ly depleting the moon's atmosphere and leading finally to 
its present state of exhaustion. It is possible that the 
moon may at one time have had an atmosphere, but if so it 
could have been only a temporary possession, and the same 
line of reasoning may be applied to the asteroids and to 
most of the satellites of the solar system, and also, though 
in less degree, to the smaller planets, Mercury and Mars. 

242. Stellar development. We have already considered 
in this chapter the line of development followed by one 
star, the sun, and treating this as a typical case, it is com- 
monly believed that the life history of a star, in so far as it 
lies within our reach, begins with a condition in which its 
matter is widely diffused, and presumably at a low tempera- 
ture. Contracting in bulk under the influence of its own 
gravitative forces, the star's temperature rises to a maxi- 
mum, and then falls off in later stages until the body ceases 
to shine and passes over to the list of dark stars whose 
existence can only be detected in exceptional cases, such 
as are noted in Chapter XIII. The most systematic devel- 
opment of this idea is due to Lockyer, who looks upon all 
the celestial bodies sun, moon and planets, stars, nebulae, 
and comets as being only collections of meteoric matter in 
different stages of development, and who has sought by 
means of their spectra to classify these bodies and to deter- 
mine their stage of advancement. While the fundamental 
ideas involved in this " meteoritic hypothesis " are not seri- 


ously controverted, the detailed application of its principles 
is open to more question, and for the most part those 
astronomers who hold that in the present state of knowl- 
edge stellar spectra furnish a key to a star's age or degree 
of advancement do not venture beyond broad general state- 

24:3. Stellar spectra. Thus the types of stellar spectra 
shown in Fig. 151 are supposed to illustrate successive 
stages in the development of an average star. Type I cor- 

FIG. 151. Types of stellar spectra substantially according to SECCHT. 

responds to the period in which its temperature is near the 
maximum ; Type II belongs to a later stage in which the 
temperature has commenced to fall ; and Type III to the 
period immediately preceding extinction. 

While human life, or even the duration of the human 
race, is too short to permit a single star to be followed 
through all the stages of its career, an adequate picture of 
that development might be obtained by examining many 
stars, each at a different stage of progress, and, following 


this idea, numerous subdivisions of the types of stellar 
spectra shown in Fig. 151 have been proposed in order to 
represent with more detail the process of stellar growth 
and decay ; but for the most part these subdivisions and 
their interpretation are accepted by astronomers with much 

It is significant that there are comparatively few stars 
with spectra of Type III, for this is what we should expect 
to find if the development of a star through the last stages 
of its visible career occupied but a small fraction of its 
total life. From the same point of view the great number 
of stars with spectra of the first type would point to a long 
duration of this stage of life. The period in which the 
sun belongs, represented by Tj T pe II, probably has a dura- 
tion intermediate between the others. Since most of the 
variable stars, save those of the Algol class, have spectra of 
the third type, we conclude that variability, with its associ- 
ated ruddy color and great atmospheric absorption of light, 
is a sign of old age and approaching extinction. The Algol 
or eclipse variables, on the other hand, having spectra of the 
first type, are comparatively young stars, and, as we shall 
see a little later, the shortness of their light periods in some 
measure confirms this conclusion drawn from their spectra. 

We have noted in 196 that the sun's near neighbors 
are prevailingly stars with spectra of the second type, 
while the Milky Way is mainly composed of first-type stars, 
and from this we may now conclude that in our particular 
part of the entire celestial space the stars are, as a rule, 
somewhat further developed than is the case elsewhere. 

244. Double stars. The double stars present special 
problems of development growing out of the effects of tidal 
friction, which must operate in them much as it does be- 
tween earth and moon, tending steadily to increase the dis- 
tance between the components of such a star. So, too, 
in such a system as is shown in Fig. 133, gravity must 
tend to make each component of the double star shrink to 


smaller dimensions, and this shrinkage must result in 
faster rotation and increased tidal friction, which in turn 
must push the components apart, so that in view of the 
small density and close proximity of those particular stars 
we may fairly regard a star like {3 Lyrae as in the early stages 
of its career and destined with increasing age to lose its 
variability of light, since the eclipses which now take place 
must cease with increasing distance between the compo- 
nents unless the orbit is turned exactly edgewise toward the 
earth. Close proximity and the resulting shortness of pe- 
riodic time in a double star seem, therefore, to be evidence 
of its youth, and since this shortness of periodic time is 
characteristic of both Algol variables and spectroscopic 
binaries as a class, we may set them down as being, upon 
the whole, stars in the early stages of their career. On 
the other hand, it is generally true that the larger the or- 
bit, and the greater the periodic time in the orbit, the 
farther is the star advanced in its development. 

In his theory of tidal friction, Darwin has pointed out 
that whenever the periodic time in the orbit is more than 
twice as long as the time required for rotation about the 
axis, the effect of the tides is to increase the eccentricity of 
the orbit, and, following this indication, See has urged that 
with increasing distance between the components of a 
double star their orbits about the common center of grav- 
ity must grow more and more eccentric, so that we have in 
the shape of such orbits a new index of stellar develop- 
ment ; the more eccentric the orbit, the farther advanced 
are the stars. It is important to note in this connection 
that among the double stars whose orbits have been com- 
puted there seems to run a general rule the larger the 
orbit the greater is its eccentricity a relation which must 
hold true if tidal friction operates as above supposed, and 
which, being found to hold true, confirms in some degree 
the criteria of stellar age which are furnished by the theory 
of tidal friction. 


245. Nebulae, The nebular hypothesis of Laplace has 
inclined astronomers to look upon nebulae in general as 
material destined to be worked up into stars, but which is 
now in a very crude and undeveloped stage. Their great 
bulk and small density seem also to indicate that gravitation 
has not yet produced in them results at all comparable with 
what we see in sun and stars. But even among nebulae 
there are to be found very different stages of development. 
The irregular nebula, shapeless and void like that of 
Orion ; the spiral, ring, and planetary nebulas and the star 
cluster, clearly differ in amount of progress toward their 
final goal. But it is by no means sure that these several 
types are different stages in one line of development ; for 
example, the primitive nebula which grows into a spiral 
may never become a ring or planetary nebula, and vice 
versa. So too there is no reason to suppose that a star 
cluster will ever break up into isolated stars such as those 
whose relation to each other is shown in Fig. 122. 

246. Classification. Considering the heavenly bodies 
with respect to their stage of development, and arranging 
them in due order, we should probably find lowest down in 
the scale of progress the irregular nebula of chaotic ap- 
pearance such as that represented in Fig. 146. Above 
these in point of development stand the spiral, ring, and 
planetary nebulae, although the exact sequence in which 
they should be arranged remains a matter of doubt. Still 
higher, up in the scale are star clusters whose individual 
members, as well as isolated stars, are to be classified by 
means of their spectra, as shown in Fig. 151, where the 
order of development of each star is probably from Type I, 
through II, into III and beyond, to extinction of its light 
and the cutting off of most of its radiant energy. Jupiter 
and Saturn are to be regarded as stars which have recently 
entered this dark stage. The earth is further developed 
than these, but it is not so far along as are Mars and Mer- 
cury ; while the moon is to be looked upon as the most 


advanced heavenly body accessible to our research, having 
reached a state of decrepitude which may almost be called 
death a stage typical of that toward which all the others 
are moving. 

Meteors and comets are to be regarded as fragments of 
celestial matter, chips, too small to achieve by themselves 
much progress along the normal lines of development, but 
destined sooner or later, by collision with some larger body, 
to share thenceforth in its fortunes. 

247. Stability of the universe, It was considered a great 
achievement in the mathematical astronomy of a century 
ago when Laplace showed that the mutual attractions of 
sun and planets might indeed produce endless perturba- 
tions in the motions and positions of these bodies, but 
could never bring about collisions among them or greatly 
alter their existing orbits. But in the proof of this great 
theorem two influences were neglected, either of which is 
fatal to its validity. One of these tidal friction as we 
have already seen, tends to wreck the systems of satellites, 
and the same effect must be produced upon the planets by 
any other influence which tends to impede their orbital 
motion. It is the inertia of the planet in its forward move- 
ment that balances the sun's attraction, and any diminu- 
tion of the planet's velocity will give this attraction the 
upper hand and must ultimately precipitate the planet 
into the sun. The meteoric matter with which the earth 
comes ceaselessly into collision must have just this influ- 
ence, although its effects are very small, and some- 
thing of the same kind may come from the medium 
which transmits radiant energy through the interstellar 

It seems incredible that the luminiferous ether, which 
is supposed to pervade all space, should present absolutely 
no resistance to the motion of stars and planets rushing 
through it with velocities which in many cases exceed 
50,000 miles per hour. If there is a resistance to this mo- 


tion, however small, we may extend to the whole visible 
universe the words of Thomson and Tait, who say in their 
great Treatise on Katural Philosophy, " We have no data in 
the present state of science for estimating the relative im- 
portance of tidal friction and of the resistance of the resist- 
ing medium through which the earth and moon move ; 
but, whatever it may be, there can be but one ultimate 
result for such a system as that of the sun and planets, 
if continuing long enough under existing laws and not 
disturbed by meeting with other moving masses in 
space. That result is the falling together of all into 
one mass, which, although rotating for a time, must in 
the end come to rest relatively to the surrounding me- 

Compare with this the words of a great poet who in 
The Tempest puts into the mouth of Prospero the lines : 

" The cloud-capp'd towers, the gorgeous palaces, 
The solemn temples, the great globe itself, 
Yea, all which it inherit, shall dissolve ; 
And, like this insubstantial pageant faded, 
Leave not a rack behind." 

248. The future. In spite of statements like these, it 
lies beyond the scope of scientific research to affirm that 
the visible order of things will ever come to naught, and 
the outcome of present tendencies, as sketched above, may 
be profoundly modified in ages to come, by influences of 
which we are now ignorant. We have already noted that 
the farther our speculation extends into either past or 
future, the more insecure are its conclusions, and the re- 
moter consequences of present laws are to be accepted with 
a corresponding reserve. But the one great fact which 
stands out clear in this connection is that of change. The 
old concept of a universe created in finished form and des- 
tined so to abide until its final dissolution, has passed away 
from scientific thought and is replaced by the idea of slow 


development. A universe which is ever becoming some- 
thing else and is never finished, as shadowed forth by 
Goethe in the lines : 

" Thus work I at the roaring loom of Time, 
And weave for Deity a living robe sublime " 



THE Greek letters are so much used by astronomers in 
connection with the names of the stars, and for other pur- 
poses, that the Greek alphabet is printed below not neces- 
sarily to be learned, but for convenient reference : 

A a 

B ft 

r 7 

A d 

E e or e 

Z f 

H T, 

e # or 6 

1 i 
K K 
A X 
M /A 
N v 
O o 

n TT 

p p 

2 a- or $ 
T T 

Y v 






















































THE following brief bibliography, while making no 
pretense at completeness, may serve as a useful guide to 
supplementary reading : 

General Treatises 

^ YOUNG. General Astronomy. An admirable general survey of the 
entire field. 

V NEWCOMB. Popular Astronomy. The second edition of a German 
translation of this work by Engelmann and Vogel is especially valuable. 

v BALL. Story of the Heavens. Somewhat easier reading than either 
of the preceding. 

v CHAMBERS. Descriptive Astronomy. An elaborate but elementary 
work in three volumes. 

vLANGLEY. The New Astronomy. Treats mainly of the physical 
condition of the celestial bodies. 

/PROCTOR and RANYARD. Old and New Astronomy. 

Special Treatises 

PROCTOR. The Noon. A general treatment of the subject. 
NASMYTH and CARPENTER. The Moon. An admirably illustrated 
but expensive work dealing mainly with the topography and physical 
conditions of the moon. There is a cheaper and very good edition in 

v YOUNG. The Sun. International Scientific Series. The most recent 
and authoritative treatise on this subject. 

" PROCTOR. Other Worlds than Ours. An account of planets, com- 
ets, etc. 

NEWTON. Meteor. Encyclopaedia Britannica. 
AIRY. Gravitation. A non-mathematical exposition of the laws 
of planetary motion. 

^ STOKES. On Light as a Means of Investigation. Burnett Lectures. 
II. The basis of spectrum analysis. 
^CHELLEN. Spectrum Analysis. 

V/THOMSON (Sir W., Lord KELVIN), Popular Lectures, etc. Lectures 
on the Tides, The Sun's Heat, etc. 


Time and Tide. An exposition of the researches of G. H. 
Darwin upon tidal friction. , 

GORE. The Visible Universe. Deals with a class of problems inad- 
equately treated in most popular astronomies. 
y DARWIN. The Tides. An admirable elementary exposition. 
^CLERKE. The System of the Stars. Stellar astronomy. 

NEWCOMB. Chapters on the Stars, in Popular Science Monthly for 

CLERKE. History of Astronomy during the Nineteenth Century. 
An admirable work. 

WOLF. Geschichte der Astronomic. Mlinchen, 1877. An excellent 
German work. 




See 8 20. 



Right Ascension. 




h. m. 



77 Ceti 


1 3.6 


a Ceti 


2 57.1 

+ 3.7 

y Eridani . 


3 53.4 

13 8 



4 30.2 

4 16.3 

Rig el 

5 9.7 


K Orioriis 


5 43.0 



6 18.3 




6 40 7 



7 34.1 

+ 5.5 

ct HvdrsB 


9 22.7 


Reoulus . 


10 3.0 

+ 12.5 

v HydraB 


10 44.7 



12 5.0 


y Corvi . . . 


12 10.7 




13 19.9 


(* Virsrinis , 


13 29.6 

- 0.1 

a Librae 


14 45.3 


)8 LibraB 


15 11.6 

- 9.0 

Antarcs . ... 


16 23.3 



17 30.3 

+ 12.6 

e Sagittarii 


18 17.5 



19 20.5 

+ 2.9 



19 45.9 

+ 8.6 

/8 Aquarii 


21 26.3 

- 6.0 


22 0.6 

- 0.8 

FoTtmlhciut . . 


22 52.1 



The references are to section numbers. 

Absorption of starlight, 225. 
Absorption spectra, 87. 
Accelerating force, 35. 
Adjustment of observations, 2. 
Albedo of moon, 97. 

of Venus, 148. 
Algol, 205. 
Altitudes, 4, 21. 
Andromeda nebula, 214. 
Angles, measurement of, 2. 
Angular diameter, 7. 
Annular eclipse, 64. 
Asteroids, 156. 
Atmosphere of the earth, 49. 

of the moon, 103. 

of Jupiter, 139. 

of Mars, 153. 
Aurora, 51. 
Azimuth, 5, 21. 

Biela's comet, 181. 
Bode's law, 134, 232. 
Bredichin's theory of comet tails, 

Calendar, 0. S. and N. S., 61. 
Capture of comets and meteors, 


Canals of Mars, 154. 
Celestial mechanics, 32. 
Changes upon the moon, 108. 

Chemical constitution of sun, 116. 

of stars, 210. 

Chromosphere, the sun's, 124. 
Chronology, 59. 
Classification of stars, 212. 
Clocks and watches, 74. 

sidereal clock, 12. 
Collisions with comets, 183. 
Colors of stars, 209. 
Comets, general characteristics, 

development of, 179, 181. 

groups, 177. 

orbits, 161. 

periodic, 176. 

spectra, 182. 

tails, 180. 
Comets and meteors, relation of, 


Conic sections, 38. 
Constellations, 184. 
Corona, the sun's, 123. 
Craters, lunar, 105. 

Dark stars, 201. 
Day, 52, 62. 
Declination, 21. 
Development of comet, 179. 

of moon, 241. 

of nebulae, 245. 

of stars, 242, 244. 



Development of sun, 228. 

of universe, 226. 
Distribution of stars and nebulae, 


Diurnal motion, 10, 15. 
Doppler principle, 89. 
Double nebulae, 215. 
Double stars, 198. 

development of, 244. 
Driving clock, 80. 

Earth, atmosphere, 48. 

mass, 45. 

size and shape, 44. 

warming of the earth, 47. 
Eclipses, nature of, 63. 

annular eclipse, 64. 

eclipse limits, 68. 

eclipse maps, 70, 71. 

number of, in a year, 69. 

partial eclipse, 64. 

prediction of, 70, 71. 

recurrence of, 72. 

shadow cone, 64, 66. 

total eclipse, 64. 

uses of, 73. 

Eclipses of Jupiter's satellites, 141. 
Eclipse theory of variable stars, 

Ecliptic, 26. 

obliquity of, 25. 
Ellipse, 33. 

Epochs for planetary motion, 30. 
Energy, radiant, 75. 

condensation of, 76. 
Epicycle, 32. 
Equation of time, 53. 
Equator, 16, 21. 
Equatorial mounting, 80. 
Equinoxes, 25. 
Ether, 75. 
Evening star, 31. 

Faculae, 122. 

Falling bodies, law of, 35. 
Finding the stars, 14. 
Fraunhofer lines, 87. 

Galaxy, 219. 

Geography of the sky, 16. 
Graphical representation, 6. 
Grating, diffraction, 84. 
Gravitation, law of, 37. 

Harvest moon, 93. 

Heat of the sun, 118, 126. 

Helmholtz, contraction theory of 

the sun, 126, 228. 
Horizon, 4, 21. 
Hour angle, 21. 
Hour circle, 21. 
Hyperbola, 38. 

Japetus, satellite of Saturn, 145. 
Jupiter, 136. 

atmosphere, 139. 

belts, 137. 

invisible from fixed stars, 197. 

orbit of, 29. 

physical condition, 139. 

rotation and flattening, 138. 

satellites, 140. 

surface markings, 137. 

Kepler's laws, 33, 111. 

Latitude, determination of, 18. 

Leap year, 61. 

Lenses, 77. 

Leonid meteor shower, 172. 

perturbations of, 174. 
Librations of moon, 98. 
Life upon the planets, 157. 
Light curves, 205. 
Light, nature of, 75. 



Light year, 190. 
Limits of eclipses, 68. 
Longitude, 56. 

determination of, 58. 
Lunation, 60. 

Magnifying power of telescope, 


Magnitude, stellar, 9, 186. 
Mars, atmosphere, temperature, 

canals, 154. 

orbit, 30. 

polar caps, 152. 

rotation, 151. 

satellites, 155. 

surface markings, 150. 
Mass, determination of, 37. 

of .comets, 164. 

of double stars, 200. 

of moon, 94. 

of planets, 40, 133. 
Measurements, accurate, 1. 
Mercury, 149. 

motion of its perihelion, 43. 

orbit of, 30. 
Meridian, 19, 21. 
Meteors, nature of, 165, 169. 

number of, 167. 

velocity, 170. 
Meteors and comets, relation of, 

Meteor showers, radiant, 171. 

Leonids, capture of, 172, 173. 

perturbations, 174. 
Milky Way, 219. 
Mira, o Ceti, 204. 
Mirrors, 77. 
Month, 60. 
Moon, 91. 

albedo, 97. 

atmosphere, 103. 

Moon, changes in, 108. 

density, surface gravity, 95. 

development of, 241. 

harvest moon, 93. 

influence upon the earth, 109, 

librations, 98. 

map of, 101. 

mass and size, 94. 

motion, 24, 92. 

mountains and craters, 104. 

phases, 91, 92. 

physical condition, 100, 107. 
Month, 60. 
Morning star, 31. 
Motion in line of sight, 89, 193. 
Multiple stars, 202. 

Names of stars. 8. 
Nebulae, 214. 

density, 217. 

development of, 245. 

motion, 218. 

spectra, 216. 

types and classes of, 215. 
Nebular hypothesis, 230. 

objections to, 231. 
Neptune, 146. 

discovery of, 41. 
Newton's laws of motion, 34. 

law of gravitation, 37, 43. 
Nodes, 39. 

relation to eclipses, 67, 71. 
Nucleus, of comet, 160. 

Objective, of telescope, 78. 
Obliquity of ecliptic, 25. 
Observations, of stars, 10. 
Occultation of stars, 103. 
Orbits, of comets, 161. 

of double stars, 199. 

of moon, 92. 



Orbits, of planets, 38. 
Orion nebula, 215. 

Parabola, 35, 38, 161. 
Parabolic velocity, 38. 
Parallax, 114, 188. 
Penumbra, 64, 121. 
Perihelion, 38. 
Periodic comets, 176. 
Personal equation, 82. 
Perturbations, 39. 

of meteors, 174. 
Phases, of the moon, 91, 92. 
Photography, 81. 

of stars, 13. 

Photosphere, of sun, 121. 
Planets, 26, 133. 

distances from the sun, 134. 

how to find, 29. 

mass, density, size, 133. 

motion of, 27, 38. 

periodic times of, 30. 
Planetary nebulas, 215. 
Pleiades, 16, 215. 
Plumb-line apparatus, 11, 18. 
Poles, 21. 
Precession, 46. 
Prisms, 84. 

Problem of three bodies, 39. 
Prominences, solar, 125. 
Proper motions, 191. 
Protractor, 2. 
Ptolemaic system, 32. 

Radiant energy, 75. 

Radiant, of meteor shower, 171. 

Radius victor, 33. 

Reference lines and circles, 17. 

Refraction, 50. 

Right ascension, 16, 20, 21. 

Roche's limit, 239. 

Rotation, of earth, 55. 

Rotation, of Mars, 151. 
of moon, 99. 
of Jupiter, 138. 
of Saturn, 144. 
of sun, 120, 132. 

Saros, 72. 

Satellites, of Jupiter, 136, 140. 

of Mars, 155. 

of Saturn, 145. 
Saturn, 142. 

ball of, 144. 

orbit, 29. 

rings, 142. 

rotation, 144. 

satellites, 145. 
Seasons, on the earth, 47. 

on Mars, 151. 
Shadow cone, 64, 66. 
Sidereal time, 20, 54. 
Shooting stars, 158. (See Meteor.) 
Spectroscope, 84. 
Spectroscopic binaries, 203. 
Spectrum, 84, 87. 

of comets, 182. 

of nebulae, 216. 

of stars, 211. 

types of, 88. 
Spectrum analysis, 85. 
Spiral nebulae, 215. 
Standard time, 57. 
Stars, 8, 184. 

classes of, 212. 

clusters, 213. 

colors, 209. 

dark stars, 201. 

development of, 242. 

distances from the sun, 188, 196. 

distribution of, 220. 

double stars, 198, 203. 

drift, 194. 

magnitudes, 9, 196. 



Stars, number of, 185. 

spectra, 211. 

temporary, 208. 

variable, 204. 

Starlight, absorption of, 225. 
Star maps, construction of, 23. 
Stellar system, extent of, 223. 
Sun's apparent motion, 25. 

real motion, 195. 
Sun, 110. 

chemical composition, 116. 

chromosphere, 124. 

corona, 123. 

distance from the earth, 111. 

f acute, 119, 122. 

gaseous constitution, 127. 

heat of, 117. 

mechanism of, 126. 

physical properties, 115-120. 

prominences, 125. 

rotation, 120, 132. 

surface of, 119. 

temperature, 118. 
Sun spots, 119, 121. 

period, 129, 131. 

zones, 130. 

Telescopes, 78. 

equatorial mounting for, 80. 

magnifying power of, 79. 
Temperature of Jupiter, 139. 

of Mars, 152. 

of Mercury, 149. 

of moon, 107. 

of sun, 118. 
Temporary stars, 208. 

Terminator, 91. 
Tenth meter, 75. 
Tidal friction, 233-238. 
Tides, 42. 
Time, sidereal, 20, 54. 

solar, 52. 

determination of, 20. 

equation of, 53. 

standard, 57. 
Triangulation, 3. 
Trifid nebula, 215. 
Twilight, 51. 
Twinkling, of stars, 48. 

Universe, development of, 226. 

stability of, 247. 
Uranus, 146. 

Variable stars, 204. 

Velocity, its relation to orbital 

motion, 38. 
Venus, 148. 

orbit of, 30. 
Vernal equinox, 21, 25. 
Vertical circle, 21. 

Wave front, 76. 
Wave lengths, 75, 86. 

Year, 25. 
leap year, 61. 
sidereal year, 59. 
tropical year, 60. 

Zenith, 21. 
Zodiac, 26. 
Zodiacal light, 168. 







General Library . 
University of California 


VB 3598! 



544') 34 




This publication is due n the 1AST DATE 
and HOUR stamped below. 


(R3381slO)4188 A-32 




CC >- 

^ 1