QB
835
UC-NRLF
173 355
George Davidson
l RPB-1911
Professor of Geography
Uhiversity of California
A PLAN
FOU
SECURING OBSERVATIONS
OF THE
VARIABLE STARS.
EDWARD C. /PICKERING,
DIKKCTOK OF THE HARVAKD COLLEGE OBSEHVATORY.
CAMBRIDGE:
JOHN W I L S O N AND SON.
Sanitorrsttg ^ircss.
1882.
A PLAN
FOR
SECURING OBSERVATIONS
OF THE
VARIABLE STARS.
BY
EDWARD C. PICKERING,
DIRECTOR OF THE HARVARD COLLEGE OBSERVATORY.
CAMBRIDGE :
JOHN WILSON AND SON.
1882.
A PLAN FOR SECURING OBSERVATIONS
OF THE VARIABLE STARS.
FOR several reasons the investigations here proposed are es-
pecially suited to observers under very various conditions. The
work is capable of indefinite sub-division. Small as well as
large telescopes may be employed and many observations are
needed which can best be made with an opera-glass or field-glass,
or even with the naked eye. No attachment is needed to an
ordinary telescope, so that no additional expense on this account
is required. Useful observations may be made by an unskilled
observer provided that he is capable of identifying a star with
certainty. The work is quantitative, and the observer has,
therefore, a continual test of the increased accuracy he has ac-
quired by practice. As a portion of the investigation will
probably lead to the discovery of interesting objects, the obser-
vations will possess an interest often wanting in quantitative
research. The aid of the professional astronomer is earnestly
requested for this scheme. Suggestions by which it may be
modified and improved will be gratefully received. The profes-
sional astronomer, in consequence of his greater skill, instru-
mental appliances, and command of his own time, could fill gaps
in the work, and thus greatly increase its value as a whole.
Such observations could often be made in the intervals of other
work or at times unsuitable for the observations to which he was
especially devoting himself. It should be added that especial
care will be taken not to interfere with observations of variable
stars now in progress. Observers of these objects are particu-
larly requested to notify the writer what work they propose to
carry out, so that a needless repetition of it may be avoided.
It is on the amateur and student of astronomy that we must
depend largely for the success of the plan here proposed. Many
such persons spend evening after evening at their telescopes
without obtaining results of any permanent value. Either no
publication is made and the results are therefore valueless, or
time is spent on objects that can be much more usefully ex-
amined with a larger instrument. Most commonly the observer
has no special plan and spends many hours without result, while
the same time might have been employed with equal pleasure
to himself and results of great value collected. Those who have
not tried it do not realize the growing interest in a systematic
research and the satisfaction in feeling that by one's own labors
the sum of human knowledge has been increased.
Much valuable assistance might be rendered by a class whose
aid in such work has usually been overlooked. Many ladies
are interested in astronomy and own telescopes, but with two
or three noteworthy exceptions their contributions to the science
have been almost nothing. Many of them have the time and
inclination for such work, and especially among the graduates
of women's colleges are many who have had abundant training
to make excellent observers. As the work may be done at
hcme, even from an open window, provided the room has the
temperature of the outer air, there seems to be no reason why
they should not thus make an advantageous use of their skill.
It is believed that it is only necessary to point the way to
secure most valuable assistance. The criticism is often made by
the opponents of the higher education of women that, while they
are capable of following others as far as men can, they originate
almost nothing, so that human knowledge is not advanced by
their work. This reproach would be well answered could we
point to a long series of such observations as are detailed below,
made by women observers.
Variable stars may be defined as those which exhibit a vary-
ing degree of brightness at different times. The following classi-
fication of them is believed to be a natural one. (Proc. Amer.
Acad. xvi, 1, 257.)
I. Temporary stars, or those which shine out suddenly, some-
times with great brilliancy, and gradually fade away. Examples,
Tycho Brahe's star of 1572, new star in Corona, 1866.
II. Long period variables, or those undergoing great variations
of light, the changes recurring in periods of several months.
Examples o Ceti and % Ceti.
III. Stars undergoing slight changes according to laws as yet
unknown. Examples, a Orionis and a Cassiopeice.
IV. Short period variables, or stars whose light is continually
varying, but the changes are repeated with great regularity in a
period not exceeding a few days. Examples, y8 Lyrce and 8
Cephei.
V. Algol stars, or stars which for the greater portion of the
time undergo no change in light, but every few days suffer a
remarkable diminution in light for a few hours. This phenome-
non recurs with such regularity that the interval between suc-
cessive minima may be determined in some cases within a
fraction of a second. Examples /3 Persei (Algol) and S Cancri.
Stars belonging to the first of these classes are seen so rarely
that the apparent discovery of one is to be received with the
utmost caution. On the other hand, the importance of early
observations of such an object is so great that no pains should be
spared to secure an early announcement if one is really found.
On the best star charts many stars are omitted of the brightness
of the faintest objects given. But any star much brighter than
these should be measured by the method given below, and a
watch kept to see if any change takes place. If it proves to be
a temporary star an immediate announcement should be made.
If a telegram is sent to this Observatory the object will be at
once examined, and, if verified, notification will be made in this
country and in Europe with the name of the discoverer or sender
of the telegram. A similar notification may be sent of any sus-
6
pected objects, which will be examined in the same way, and
announced at once if they prove to be of interest. It is essen-
tial that the position of the object should be given with all the
precision practicable, and that a letter should be sent by the next
mail giving the observations in detail. This often proves of the
greatest value in case the object is not readily found. It also
serves to establish the claims of the first discoverer.
Nearly three quarters of the known variables belong to the
second class. Most of them undergo very large changes of light,
and may therefore be observed with comparative ease. Our
knowledge of their variations is however very defective. Hither-
to the attention of observers has been directed principally to
determining the times at which they attain their maximum light,
while their light at intermediate times has been neglected. It
is now proposed to secure observations of these objects once or
twice in every month, so that their light curves or variations
throughout their entire periods may be determined. Again, many
observers are accustomed to state their brightness in magnitudes
without giving any clue to the scale which they employ. In
most cases such observations have little value owing to the
uncertainty of the scale of the fainter magnitudes.
According to Dr. Gould and some other observers most of the
visible stars undergo slight changes of light and should there-
fore be assigned to the third class of variables. It is probable
that our Sun also belongs to this class, as it is not likely that
its light is the same during the maximum and minimum of the
sun spot period. At present we are unable to tell in which
case the light would be greatest. It by no means follows that
when the spots are most abundant the Sun's total light is least,
for the remaining portions of the Sun may then have an increased
brightness more than compensating for their diminished area.
As long as the suspected variations in light of the stars are
small, not exceeding half a magnitude for instance, they seem in
the present state of science to have comparatively little interest.
They are so liable to be affected, or even caused, by errors of
observation, that the observation of such objects does not seem
now to be advisable. Doubtless many such so-called variables
are really due to errors caused by moonlight, the proximity of
brighter stars, varying position of the images on the retina of the
observer, and other similar causes. They will not therefore be
considered further in this paper.
The stars of the fourth class as compared with the second are
relatively few in number, and the changes in light small. While
many of them need observation, especially to determine their
light curves more precisely, it is advised that this work be left
to those who have acquired a high degree of skill in these ob-
servations. That the work may be of value it is essential that
the errors should be extremely small. As, however, nearly all
are visible in an opera-glass, a skilful observer unprovided with
a telescope may secure valuable results by their observation.
This remark applies with especial force to many of those dis-
covered in the southern heavens by Dr. Gould.
The phenomena of the Algol stars are in many respects the
most striking of any. The rapidity of the changes, their sur-
prising regularity, and the comparative rarity of these objects,
combine to render the discovery of each new one a matter of
unusual interest. As in the case of stars of the fourth class,
however, the study of their light curves should be left to those
who have acquired especial skill in this work. This is particu-
larly desirable, when, as in- this case, the unaided eye enters into
competition with photometric apparatus, by which, as some think,
it should properly be altogether replaced.
An elaborate bibliographical work on the variable stars has
been undertaken at this Observatory by Mr. Chandler. It will
include the collection of all available published observations of
known or suspected variables. A catalogue of suspected vari-
ables has thus been prepared, doubtless containing many stars
which are really important variables. But it is also likely that
many objects have been introduced in the list by errors in the
original observations. Such stars often appear in one catalogue
after another of suspected variables, and it is difficult to prevent
the continued circulation of such an error. Of course if an
8
experienced observer at any time estimates a star as above or
below its normal brightness, it is impossible to prove that the
observation was not correct, and the star really variable. No
amount of subsequent observing could prove that it had not then,
and then only, an abnormal brightness. We can, however, prove
that in all probability it does not belong to one or more of the
above classes, and thus make it more and more probable that the
observation is due to an error. If the star varies in light by
one magnitude, what will be the chances that we shall get a
series of observations having a range of variation of one fifth of
a magnitude ? Evidently on the average, there will be only
one chance out of five that any observation shall fall in the same
fifth of a magnitude as another. The chances for three such
observations will be only ^ and for four T |-g-, etc. These ratios
expressed decimally are .2, .04, .008, 0016, .0003, etc. Since
the separate determinations of the light of a constant star by the
method given below should not differ more than two or three
tenths of a magnitude, it is obvious that if the variations of the
star are large, a few observations would generally establish this
fact. If the star belongs to class four, observations on half a
dozen evenings would hardly fail to show the variation. Con-
versely, if no such variation is detected we may be almost cer-
tain that the star is not a variable of that class, or at least that
the variation, if any, is not large. If the star belongs to class
two, it will change so slowly when near its maximum or mini-
mum that a variation might not be noted if the observations are
near together. An interval of several months should therefore
be allowed to take place, or perhaps it would be better to wait
until the star is again visible the following year. The total
variation in light is usually so great in these stars that the
change will often be visible at the first glance.
To prove that a star does not belong to the fifth class is a
matter of much greater difficulty. In fact it is almost impossi-
ble to prove that it may not be an Algol star with a long period
between the minima. Since these stars may have their full
brightness for nine tenths of the time, it is obvious that they
9
may be examined again and again without happening to be seen
at the time of a minimum.
On the other hand, during a considerable portion of the time
when it is varying, the light will be so much less than usual
that a careful measurement is not needed to detect the change.
Moreover, it will be useless to look for an increase of light, and
the observation may be so planned as to detect a diminution
only.
If we assume that only during one tenth of the time the
change in light will be sufficient to be perceptible, the chance on
any given evening will be 9 out of 10 or T 9 Q that the star will
have its full brightness. For two evenings the chance will
be (y 9 Q-) 2 for three (^), 3 etc. These quantities expressed decimally
are .9, .81, .73, .66, .59, .53, .48, etc. Even after seven nights'
observations, on which no change is noted, it will only be
about an even chance that the star may not still be of the
Algol type. A different method of observing is therefore recom-
mended when the star is supposed to belong to this class. Select
for comparison a star slightly fainter, so that a moment's glance
will satisfy the observer that the suspected variable is the
brighter. It is only necessary to repeat this observation night
after night. If the star is bright enough to be visible with a
field glass, a few seconds will be sufficient for this observation
after the observer has become familiar with the vicinity. The
fact that the light is normal, and the time to the nearest minute,
should be recorded after each observation. When convenient, it
is well to repeat the inspection two or more times during the
night, as in determining the period all the observations will
have a value, provided that they are separated by intervals of
more than two or three hours. If the star is ever found below
its normal brightness, comparisons should be made with the ad-
jacent stars, and continued as long as possible, or until it has
regained its usual brightness. The most complete proof that a
star was not of the Algol type would be for observers in the
polar regions to examine it at intervals of a few hours for sev-
eral days, or for observers in different longitudes to make the
10
same observations. If it could thus be watched for a week or
fortnight by enough observers to avoid interference by clouds, it
would be nearly certain that it is not an Algol star unless its
period is greater than that of any such object as yet discovered.
The problems to be undertaken may be defined as follows :
1. To observe all the long period variables once or twice every
month throughout their variations according to such a system
that all the observations may be reduced to the same absolute
scale of magnitudes.
2. To observe the stars whose variability is suspected and
prove either that they are really variable, or that in all proba-
bility they do not belong to the first, second, or fourth class. If
any are thought to belong to the fifth class, to watch them until
such a variation is proved, or is shown to be improbable.
All of .this work will depend on the possibility of readily
determining the brightness of a star according to such a method
that all the observations can ultimately be reduced to the same
system. Herschel and Argelander have independently invented
what appears to be the true method to be followed. If a star is
seen to be very nearly equal to several others, from their light
we can at any time define its brightness. It is essential that at
least one of the stars selected should be a little brighter, another
a little fainter, than the star to be observed. The range
within which its light is known is thus also defined. Such
observations will far exceed in value any direct estimate of
magnitude. When stars are to be compared many times, it is
convenient to designate them by letters for brevity. Let v repre-
sent a star which is suspected to be variable, and a an adjacent
star of nearly equal brightness. Owing to fluctuations in the
atmosphere, each star will appear to be constantly varying in
brightness. If the stars appear equal after a careful examina-
tion, or if one appears brighter as often as it appears fainter than
the other, we may denote this equality by av or va t these terms
having precisely the same meaning. If one of the stars is sus-
pected to be brighter, that is, if it appears sometimes brighter
and sometimes fainter, but more frequently brighter, the interval
11
may be designated as one grade. The observation may be written
u 1 v or v 1 a, the brightest star being named first. If one star is
certainly brighter than the other, the difference, however, being
very small,. so that they sometimes appear equal, the difference
will be two grades, and may be written a 2 v or v 2 a. Greater
intervals may be estimated as three or four grades, but such
observations have much less value. It is found in practice that
a grade thus estimated will slightly exceed a tenth of a magni-
tude. A useful exercise for an observer is to select two stars of
known magnitude and several others of intermediate brightness.
Arrange them in a series in the order of brightness, and estimate
the intervals in grades. The difference in magnitude of the first
stars divided by the total number of grades gives the value of
one grade. By using different intermediate stars, the same
standard stars may be employed repeatedly. The following
well-known polar stars will be convenient, since they are always
visible : a Ursce Minoris, 2.2 magn. ; 7 Ursce Minoris, 3.0
magn. ; S Ursce Minoris, 4.4 magn. ; 51 Cephi, 5.4 magn. ; X Ursce
Minoris, 6.5 magn. The above method is essentially that of
Argelander. Sir William Herschel had already employed a
method which differed mainly in his notation, a . , and
being equivalent to one, two, or three grades.
In all work of this kind the observer must look directly at
the star he is observing at the moment, and never try to
compare two stars by a simultaneous inspection of both.
After examining one star until he has a distinct impression
of its average brightness, freed from the momentary changes
due to atmospheric disturbance, he should observe the other in
the same manner. Alternate observations of the two stars,
each observation lasting for a few seconds, will give a truer
impression than can be derived from a simultaneous observa-
tion in which the two images must be differently placed on the
retina.
The principal objection to this method is the difficulty of
determining the value of a grade, as it is liable to vary with the
observer, the time, the condition of the air, and the brightness
12
of the stars. These difficulties are avoided by the follow-
ing method. Select two stars for comparison ; one, a, slightly-
brighter than the star to be measured, v, the other, b, slightly
fainter. The interval between a and b should never .exceed one
magnitude. Estimate the brightness of v in tenths of the inter-
val from a to b. Thus, if v is midway between a and b the
interval will be five tenths, and we may write a 5 b. If v is
nearly as bright as a, we may have a 1 b or a 2 b ; if v is not
much brighter than 6, we may have a 8 b or a 9 b. An advan-
tage of this method is that larger intervals in brightness may be
used between the comparison stars, and accordingly less distant
stars employed. An increase in distance of the stars always
renders the comparison more difficult. We can also obtain many
independent comparisons by using several comparison stars. If
we have m stars brighter and n fainter, we shall only have m -\- n
independent measures by the method of grades, while we may
have m n comparisons by estimating tenths, since estimates may
be made in terms of the intervals between each brighter and each
fainter star. On the other hand, especially when observing stars
not very near together, it is a decided advantage to have to com-
pare two stars rather than three. Each method has its advan-
tages, and that to be used should doubtless depend on the
temperament of the observer.
Several precautions are needed to secure the best results.
No observations should be made near the horizon ; and, when the
objects examined are at any considerable zenith distance, stars
differing several degrees in altitude should be avoided. If the
stars are bright and there is no choice, a correction may be made
for the error due to the varying absorption at these different
altitudes if the time of observation has been noted. When
using a telescope or opera-glass, the stars should be brought in
turn to the centre of the field, as when near the edge they will
not appear of their true brightness. This is found to be better
than placing them at equal distances from the centre. In select-
ing comparison stars, the proximity of a brighter star is very
objectionable, causing a large error, which varies with the mag-
13
nifying power used. Double stars should be avoided if the pow-
er used is sufficient to show the companion. Comparing stars
of different colors is also objectionable.
Any persons who desire to take part in these observations are
requested to communicate with the writer, and send answers to
the questions given below.
1. What is the location of your point of observation ? In
the city or in the country, on the ground, from a roof, or from a
window ? Is any part of your horizon obstructed, or can you
observe in all parts of the sky ?
2. What is the aperture, focal length, and name of maker of
your telescope ? also the lowest magnifying power and largest
field of view you can obtain with it ? Have you a field-glass or
opera-glass ?
3. Can you identify bright and faint stars from their designa-
tions or right ascensions and declinations ? Have you Heis'
Atlas Crelestis Novus, the Uranometria Argentina, the Durch-
musterung, or other maps and catalogues of the stars ?
4. Would you prefer to observe the known or the suspected
variables, or to divide your time between them ?
For convenience in making the reductions and for future refer-
ence, it is essential that all the observations should be made ac-
cording to the same system. Observers are accordingly requested
to adopt the following form. Use half-sheets of letter paper (eight
inches by ten), writing only on one side and leaving a margin
of half an inch for binding. Begin with a new sheet every
evening, and write the date and location (township and state) on
the first line. Each sheet when completed should be signed, and
all should be numbered consecutively. When several sheets
are used on the same night, the date should be entered on each.
The record should be made in pencil, and all subsequent remarks
or corrections added or interlined with ink, taking especial care
not to obliterate or render illegible the original record.
A general statement should be made each evening of the con-
dition of the sky, as " clear," " hazy," " passing clouds," etc. The
time of beginning and ending work should also be noted. One
14
line should be assigned to each comparison. The hour and
minute should be written to the left, and the comparison next
to it. The right-hand half of the line will be left blank for
reducing the observation.
Certain evenings or portions of evenings must also be devoted
to the selection of the comparison stars of suspected variables.
If they are contained in maps which are available, the letters
assigned to each star may be marked on the maps and lines
drawn to show with what suspected variable star they are asso-
ciated. If preferred, a sketch may be made of the neighboring
stars and the letters entered on them. This sketch with a
proper description should be entered on the observing sheets
described above, and a copy should be retained for reference.
Every month the observations will be interrupted by moonlight,
and accordingly, three or four days before the full moon, all the
sheets that have accumulated should be mailed, addressed Har-
vard College Observatory, Cambridge, Mass. An acknowledg-
ment will be sent at once, so that if this is not received a second
notification should be sent.
To attain success it is particularly important that the plan
should not be local or national. Observers in the southern
hemisphere are much needed, and for some purposes those in
various longitudes. It is hoped that among the many amateurs
of Europe, and especially of England, may be found some ready
to participate in this work. No restriction regarding the ob-
servations or publication is intended ; but it is hoped that a
large addition to our present knowledge of the variable stars
may be secured, without interfering with what would otherwise
be obtained. Copies of this pamphlet and further information
will be furnished on application. Any persons desiring to par-
ticipate are requested to address the writer, sending answers to
the questions given above. The details will differ with each
observer, and will be arranged by correspondence. Apart from
the value of the results attained, it is believed that many ama-
teurs will find it a benefit to accustom themselves to work in a
systematic manner, and that they will thus receive a training
15
in their work not otherwise easily obtained outside of a large
observatory. The lesson should be taught that time spent at a
telescope is nearly wasted, unless results are secured worthy of
publication and having a permanent value. Those who have
once accomplished such work are likely in the future to appre-
ciate its value, and will often continue to do useful work in
some other department of practical astronomy, if not in that of
variable stars. The education of a class of skilled observers
would be a work of no less value than the results anticipated
from the observation of the variable stars.
EDWARD C. PICKEEING.
HARVARD COLLEGE OBSERVATORY,
Cambridge, Mass.
Monufocturtd by
I 6AYLORD BROS. Inc.
I Syracuse, N. Y.
Stockton, Calif.
M287971
THE UNIVERSITY OF CALIFORNIA LIBRARY
