,a ,,plan                               
,,for                    ,,securing     
,,observations                          
,,of ,,the                              
,,variable ,,stars4                     
,,by                    ,,edward ,c4    
,,pickering1         ,,director ,,of    
,,the ,,harvard ,,college ,,observatory4
                                        
,,cambridge3                    ,,john  
,,wilson ,,and ,,son4                   
,university ,press                      
#ahhb4                      ,a ,,plan   
,,for ,,securing ,,observations         
,,of ,,the ,,variable ,,stars4          
,,for several reasons the investigations
 here proposed are especially suited to 
observers under very various conditions4
 ,the work is capable of indefinite     
sub-division4 ,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-glass1 or even with the naked eye4
 ,no attachment is needed to an ordinary

 telescope1 so that no additional       
expense on this account is required4    
,useful observations may be made by an  
unskilled observer provided that he is  
capable of identifying a star with      
certainty4 ,the work is quantitative1   
and the observer has1 therefore1 a      
continual test of the increased accuracy
 he has acquired by practice4 ,as a     
portion of the investigation will       
probably lead to the discovery of       
interesting objects1 the observations   
will possess an interest often wanting  
in quantitative research4 ,the aid of   
the professional astronomer is earnestly
 requested for this scheme4 ,suggestions
 by which it may be modified and        
improved will be gratefully received4   
,the professional astronomer1 in        
consequence of his greater skill1       
instrumental appliances1 and command of 
his own time1 could fill gaps in the    
work1 and thus greatly increase its     
value as a whole4 ,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 himself4 ,it should 
be added that especial care will be     
taken not to interfere with observations
 of variable stars now in progress4     
,observers of these objects are         
particularly requested to notify the    
writer what work they propose to carry  
out1 so that a needless repetition of it
 may be avoided4  ,it is on the amateur 
and student of astronomy that we must   
depend largely for the success of the   
plan here proposed4 ,many such persons  
spend evening after evening at their    
telescopes without obtaining results of 
any permanent value4 ,either no         
publication is made and the results are 
therefore valueless1 or time is spent on
 objects that can be much more usefully 
examined with a larger instrument4 ,most
 commonly the observer has no special   
plan and spends many hours without      
result1 while the same time might have  
been employed with equal pleasure to    

himself and results of great value      
collected4 ,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 increased4  ,much valuable     
assistance might be rendered by a class 
whose aid in such work has usually been 
overlooked4 ,many ladies are interested 
in astronomy and own telescopes1 but    
with two or three noteworthy exceptions 
their contributions to the science have 
been almost nothing4 ,many of them have 
the time and inclination for such work1 
and especially among the graduates of   
women's colleges are many who have had  
abundant training to make excellent     
observers4 ,as the work may be done at  
home1 even from an open window1 provided
 the room has the temperature of the    
outer air1 there seems to be no reason  
why they should not thus make an        
advantageous use of their skill4 ,it is 
believed that it is only necessary to   

point the way to secure most valuable   
assistance4 ,the criticism is often made
 by the opponents of the higher         
education of women that1 while they are 
capable of following others as far as   
men can1 they originate almost nothing1 
so that human knowledge is not advanced 
by their work4 ,this reproach would be  
well answered could we point to a long  
series of such observations as are      
detailed below1 made by women observers4
  ,variable stars may be defined as     
those which exhibit a varying degree of 
brightness at different times4 ,the     
following classification of them is     
believed to be a natural one4 7,proc4   
,amer4 ,acad4 xvi1 #a1 #beg47  ,i4      
,temporary stars1 or those which shine  
out suddenly1 sometimes with great      
brilliancy1 and gradually fade away4    
,examples1 ,tycho ,brahe's star of      
#aegb1 new star in ,corona1 #ahff4      
,,ii4 ,long period variables1 or those  
undergoing great variations of light1   
the changes recurring in periods of     

several months4 ,examples omicron ,ceti 
and chi ,ceti4  ,,iii4 ,stars undergoing
 slight changes according to laws as yet
 unknown4 ,examples1 alpha ,orionis and 
alpha ,cassiopeiae4  ,,iv4 ,short period
 variables1 or stars whose light is     
continually varying1 but the changes are
 repeated with great regularity in a    
period not exceeding a few days4        
,examples1 beta ,lyrae and delta        
,cephei4  ,v4 ,algol stars1 or stars    
which for the greater portion of the    
time undergo no change in light1 but    
every few days suffer a remarkable      
diminution in light for a few hours4    
,this phenomenon recurs with such       
regularity that the interval between    
successive minima may be determined in  
some cases within a fraction of a       
second4 ,examples beta ,persei 7,algol7 
and ,s ,cancri4  ,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   
caution4 ,on the other hand1 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 found4 ,on
 the best star charts many stars are    
omitted of the brightness of the        
faintest objects given4 ,but any star   
much brighter than these should be      
measured by the method given below1 and 
a watch kept to see if any change takes 
place4 ,if it proves to be a temporary  
star an immediate announcement should be
 made4 ,if a telegram is sent to this   
,observatory the object will be at once 
examined1 and1 if verified1 notification
 will be made in this country and in    
,europe with the name of the discoverer 
or sender of the telegram4 ,a similar   
notification may be sent of any         
suspected objects1 which will be        
examined in the same way1 and announced 
at once if they prove to be of interest4
 ,it is essential that the position of  
the object should be given with all the 
precision practicable1 and that a letter

 should be sent by the next mail giving 
the observations in detail4 ,this often 
proves of the greatest value in case the
 object is not readily found4 ,it also  
serves to establish the claims of the   
first discoverer4  ,nearly three        
quarters of the known variables belong  
to the second class4 ,most of them      
undergo very large changes of light1 and
 may therefore be observed with         
comparative ease4 ,our knowledge of     
their variations is however very        
defective4 ,hitherto the attention of   
observers has been directed principally 
to determining the times at which they  
attain their maximum light1 while their 
light at intermediate times has been    
neglected4 ,it is now proposed to secure
 observations of these objects once or  
twice in every month1 so that their     
light curves or variations throughout   
their entire periods may be determined4 
,again1 many observers are accustomed to
 state their brightness in magnitudes   
without giving any clue to the scale    

which they employ4 ,in most cases such  
observations have little value owing to 
the uncertainty of the scale of the     
fainter magnitudes4  ,according to ,dr4 
,gould and some other observers most of 
the visible stars undergo slight changes
 of light and should therefore be       
assigned to the third class of          
variables4 ,it is probable that our ,sun
 also belongs to this class1 as it is   
not likely that its light is the same   
during the maximum and minimum of the   
sun spot period4 ,at present we are     
unable to tell in which case the light  
would be greatest4 ,it by no means      
follows that when the spots are most    
abundant the ,sun's total light is      
least1 for the remaining portions of the
 ,sun may then have an increased        
brightness more than compensating for   
their diminished area4 ,as long as the  
suspected variations in light of the    
stars are small1 not exceeding half a   
magnitude for instance1 they seem in the
 present state of science to have       

comparatively little interest4 ,they are
 so liable to be affected1 or even      
caused1 by errors of observation1 that  
the observation of such objects does not
 seem now to be advisable4 ,doubtless   
many such so-called variables are really
 due to errors caused by moonlight1 the 
proximity of brighter stars1 varying    
position of the images on the retina of 
the observer1 and other similar causes4 
,they will not therefore be considered  
further in this paper4  ,the stars of   
the fourth class as compared with the   
second are relatively few in number1 and
 the changes in light small4 ,while many
 of them need observation1 especially to
 determine their light curves more      
precisely1 it is advised that this work 
be left to those who have acquired a    
high degree of skill in these           
observations4 ,that the work may be of  
value it is essential that the errors   
should be extremely small4 ,as1 however1
 nearly all are visible in an           
opera-glass1 a skilful observer         

unprovided with a telescope may secure  
valuable results by their observation4  
,this remark applies with especial force
 to many of those discovered in the     
southern heavens by ,dr4 ,gould4  ,the  
phenomena of the ,algol stars are in    
many respects the most striking of any4 
,the rapidity of the changes1 their     
surprising regularity1 and the          
comparative rarity of these objects1    
combine to render the discovery of each 
new one a matter of unusual interest4   
,as in the case of stars of the fourth  
class1 however1 the study of their light
 curves should be left to those who have
 acquired especial skill in this work4  
,this is particularly desirable1 when1  
as in this case1 the unaided eye enters 
into competition with photometric       
apparatus1 by which1 as some think1 it  
should properly be altogether replaced4 
,an elaborate bibliographical work on   
the variable stars has been undertaken  
at this ,observatory by ,mr4 ,chandler4 
,it will include the collection of all  

available published observations of     
known or suspected variables4 ,a        
catalogue of suspected variables has    
thus been prepared1 doubtless containing
 many stars which are really important  
variables4 ,but it is also likely that  
many objects have been introduced in the
 list by errors in the original         
observations4 ,such stars often appear  
in one catalogue after another of       
suspected variables1 and it is difficult
 to prevent the continued circulation of
 such an error4 ,of course if an        
experienced observer at any time        
estimates a star as above or below its  
normal brightness1 it is impossible to  
prove that the observation was not      
correct1 and the star really variable4  
,no amount of subsequent observing could
 prove that it had not then1 and then   
only1 an abnormal brightness4 ,we can1  
however1 prove that in all probability  
it does not belong to one or more of the
 above classes1 and thus make it more   
and more probable that the observation  

is due to an error4 ,if the star varies 
in light by one magnitude1 what will be 
the chances that we shall get a series  
of observations having a range of       
variation of one fifth of a magnitude8  
,evidently on the average1 there will be
 only one chance out of five that any   
observation shall fall in the same fifth
 of a magnitude as another4 ,the chances
 for three such observations will be    
only #a_/be and for four #a_/abe1 etc4  
,these ratios expressed decimally are   
4#b1 4#jd1 4#jjh1 #jjaf1 4#jjjc1 etc4   
,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      
magnitude1 it is obvious that if the    
variations of the star are large1 a few 
observations would generally establish  
this fact4 ,if the star belongs to class
 four1 observations on half a dozen     
evenings would hardly fail to show the  
variation4 ,conversely1 if no such      
variation is detected we may be almost  

certain that the star is not a variable 
of that class1 or at least that the     
variation1 if any1 is not large4 ,if the
 star belongs to class two1 it will     
change so slowly when near its maximum  
or minimum that a variation might not be
 noted if the observations are near     
together4 ,an interval of several months
 should therefore be allowed to take    
place1 or perhaps it would be better to 
wait until the star is again visible the
 following year4 ,the total variation in
 light is usually so great in these     
stars that the change will often be     
visible at the first glance4  ,to prove 
that a star does not belong to the fifth
 class is a matter of much greater      
difficulty4 ,in fact it is almost       
impossible to prove that it may not be  
an ,algol star with a long period       
between the minima4 ,since these stars  
may have their full brightness for nine 
tenths of the time1 it is obvious that  
they may be examined again and again    
without happening to be seen at the time

 of a minimum4  ,on the other hand1     
during a considerable portion of the    
time when it is varying1 the light will 
be so much less than usual that a       
careful measurement is not needed to    
detect the change4 ,moreover1 it will be
 useless to look for an increase of     
light1 and the observation may be so    
planned as to detect a diminution only4 
,if we assume that only during one tenth
 of the time the change in light will be
 sufficient to be perceptible1 the      
chance on any given evening will be #i  
out of #aj or #i_/aj that the star will 
have its full brightness4 ,for two      
evenings the chance will be 7#i_/aj7b   
for three 7#i_/aj7c1 etc4 ,these        
quantities expressed decimally are 4#i1 
4#ha1 4#gc1 4#ff1 4#ei1 4#ec1 4#dh1 etc4
 ,even after seven nights' observations1
 on which no change is noted1 it will   
only be about an even chance that the   
star may not still be of the ,algol     
type4 ,a different method of observing  
is therefore recommended when the star  

is supposed to belong to this class4    
,select for comparison a star slightly  
fainter1 so that a moment's glance will 
satisfy the observer that the suspected 
variable is the brighter4 ,it is only   
necessary to repeat this observation    
night after night4 ,if the star is      
bright enough to be visible with a field
 glass1 a few seconds will be sufficient
 for this observation after the observer
 has become familiar with the vicinity4 
,the fact that the light is normal1 and 
the time to the nearest minute1 should  
be recorded after each observation4     
,when convenient1 it is well to repeat  
the inspection two or more times during 
the night1 as in determining the period 
all the observations will have a value1 
provided that they are separated by     
intervals of more than two or three     
hours4 ,if the star is ever found below 
its normal brightness1 comparisons      
should be made with the adjacent stars1 
and continued as long as possible1 or   
until it has regained its usual         

brightness4 ,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 several days1 or for      
observers in different longitudes to    
make the same observations4 ,if it could
 thus be watched for a week or fortnight
 by enough observers to avoid           
interference by clouds1 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          
discovered4  ,the problems to be        
undertaken may be defined as follows3-- 
#a4 ,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 magnitudes4  #b4 ,to observe   
the stars whose variability is suspected
 and prove either that they are really  
variable1 or that in all probability    
they do not belong to the first1 second1

 or fourth class4 ,if any are thought to
 belong to the fifth class1 to watch    
them until such a variation is proved1  
or is shown to be improbable4  ,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 system4         
,herschel and ,argelander have          
independently invented what appears to  
be the true method to be followed4 ,if a
 star is seen to be very nearly equal to
 several others1 from their light we can
 at any time define its brightness4 ,it 
is essential that at least one of the   
stars selected should be a little       
brighter1 another a little fainter1 than
 the star to be observed4 ,the range    
within which its light is known is thus 
also defined4 ,such observations will   
far exceed in value any direct estimate 
of magnitude4 ,when stars are to be     
compared many times1 it is convenient to
 designate them by letters for brevity4 

,let v represent a star which is        
suspected to be variable1 and a an      
adjacent star of nearly equal           
brightness4 ,owing to fluctuations in   
the atmosphere1 each star will appear to
 be constantly varying in brightness4   
,if the stars appear equal after a      
careful examination1 or if one appears  
brighter as often as it appears fainter 
than the other1 we may denote this      
equality by av or va1 these terms having
 precisely the same meaning4 ,if one of 
the stars is suspected to be brighter1  
that is1 if it appears sometimes        
brighter and sometimes fainter1 but more
 frequently brighter1 the interval may  
be designated as one grade4 ,the        
observation may be written a #a v or v  
#a a1 the brightest star being named    
first4 ,if one star is certainly        
brighter than the other1 the difference1
 however1 being very small1 so that they
 sometimes appear equal1 the difference 
will be two grades1 and may be written a
 #b v or v #b a4 ,greater intervals may 

be estimated as three or four grades1   
but such observations have much less    
value4 ,it is found in practice that a  
grade thus estimated will slightly      
exceed a tenth of a magnitude4 ,a useful
 exercise for an observer is to select  
two stars of known magnitude and several
 others of intermediate brightness4     
,arrange them in a series in the order  
of brightness1 and estimate the         
intervals in grades4 ,the difference in 
magnitude of the first stars divided by 
the total number of grades gives the    
value of one grade4 ,by using different 
intermediate stars1 the same standard   
stars may be employed repeatedly4 ,the  
following well-known polar stars will be
 convenient1 since they are always      
visible3-- a alpha ,ursae ,minoris1 #b4b
 magn42 gamma ,ursae ,minoris1 #c4j     
magn42 delta ,ursae ,minoris1 #d4d      
magn42 #ea ,cephi1 #e4d magn42 lambda   
,ursae ,minoris1 #f4e magn4 ,the above  
method is essentially that of           
,argelander4 ,sir ,william ,herschel had

 already employed a method which        
differed mainly in his notation1 a 4 1  
and -- being equivalent to one1 two1 or 
three grades4  ,in all work of this kind
 the observer must look directly at the 
star he is observing at the moment1 and 
never try to compare two stars by a     
simultaneous inspection of both4 ,after 
examining one star until he has a       
distinct impression of its average      
brightness1 freed from the momentary    
changes due to atmospheric disturbance1 
he should observe the other in the same 
manner4 ,alternate observations of the  
two stars1 each observation lasting for 
a few seconds1 will give a truer        
impression than can be derived from a   
simultaneous observation in which the   
two images must be differently placed on
 the retina4  ,the principal objection  
to this method is the difficulty of     
determining the value of a grade1 as it 
is liable to vary with the observer1 the
 time1 the condition of the air1 and the
 brightness of the stars4 ,these        

difficulties are avoided by the         
following method4 ,select two stars for 
comparison2 one1 a1 slightly brighter   
than the star to be measured1 v1 the    
other1 b1 slightly fainter4 ,the        
interval between a and b should never   
exceed one magnitude4 ,estimate the     
brightness of v in tenths of the        
interval from a to b4 ,thus1 if v is    
midway between a and b the interval will
 be five tenths1 and we may write a #e  
b4 ,if v is nearly as bright as a1 we   
may have a #a b or a #b b2 if v is not  
much brighter than b1 we may have a #h b
 or a #i b4 ,an advantage of this method
 is that larger intervals in brightness 
may be used between the comparison      
stars1 and accordingly less distant     
stars employed4 ,an increase in distance
 of the stars always renders the        
comparison more difficult4 ,we can also 
obtain many independent comparisons by  
using several comparison stars4 ,if we  
have m stars brighter and n fainter1 we 
shall only have m  n independent        

measures by the method of grades1 while 
we may have m n comparisons by          
estimating tenths1 since estimates may  
be made in terms of the intervals       
between each brighter and each fainter  
star4 ,on the other hand1 especially    
when observing stars not very near      
together1 it is a decided advantage to  
have to compare two stars rather than   
three4 ,each method has its advantages1 
and that to be used should doubtless    
depend on the temperament of the        
observer4  ,several precautions are     
needed to secure the best results4 ,no  
observations should be made near the    
horizon2 and1 when the objects examined 
are at any considerable zenith distance1
 stars differing several degrees in     
altitude should be avoided4 ,if the     
stars are bright and there is no choice1
 a correction may be made for the error 
due to the varying absorption at these  
different altitudes if the time of      
observation has been noted4 ,when using 
a telescope or opera-glass1 the stars   

should be brought in turn to the centre 
of the field1 as when near the edge they
 will not appear of their true          
brightness4 ,this is found to be better 
than placing them at equal distances    
from the centre4 ,in selecting          
comparison stars1 the proximity of a    
brighter star is very objectionable1    
causing a large error1 which varies with
 the magnifying power used4 ,double     
stars should be avoided if the power    
used is sufficient to show the          
companion4 ,comparing stars of different
 colors is also objectionable4  ,any    
persons who desire to take part in these
 observations are requested to          
communicate with the writer1 and send   
answers to the questions given below4   
#a4 ,what is the location of your point 
of observation8 ,in the city or in the  
country1 on the ground1 from a roof1 or 
from a window8 ,is any part of your     
horizon obstructed1 or can you observe  
in all parts of the sky8  #b4 ,what is  
the aperture1 focal length1 and name of 

maker of your telescope8 also the lowest
 magnifying power and largest field of  
view you can obtain with it8 ,have you a
 field-glass or opera-glass8  #c4 ,can  
you identify bright and faint stars from
 their designations or right ascensions 
and declinations8 ,have you ,heis'      
,atlas ,coelestis ,novus1 the           
,uranometria ,argentina1 the            
,durchmusterung1 or other maps and      
catalogues of the stars8  #d4 ,would you
 prefer to observe the known or the     
suspected variables1 or to divide your  
time between them8  ,for convenience in 
making the reductions and for future    
reference1 it is essential that all the 
observations should be made according to
 the same system4 ,observers are        
accordingly requested to adopt the      
following form4 ,use half-sheets of     
letter paper 7eight inches by ten71     
writing only on one side and leaving a  
margin of half an inch for binding4     
,begin with a new sheet every evening1  
and write the date and location         

7township and state7 on the first line4 
,each sheet when completed should be    
signed1 and all should be numbered      
consecutively4 ,when several sheets are 
used on the same night1 the date should 
be entered on each4 ,the record should  
be made in pencil1 and all subsequent   
remarks or corrections added or         
interlined with ink1 taking especial    
care not to obliterate or render        
illegible the original record4  ,a      
general statement should be made each   
evening of the condition of the sky1 as 
clear1 hazy1 passing clouds1 etc4 ,the  
time of beginning and ending work should
 also be noted4 ,one line should be     
assigned to each comparison4 ,the hour  
and minute should be written to the     
left1 and the comparison next to it4    
,the right-hand half of the line will be
 left blank for reducing the            
observation4  ,certain evenings or      
portions of evenings must also be       
devoted to the selection of the         
comparison stars of suspected variables4

 ,if they are contained in maps which   
are available1 the letters assigned to  
each star may be marked on the maps and 
lines drawn to show with what suspected 
variable star they are associated4 ,if  
preferred1 a sketch may be made of the  
neighboring stars and the letters       
entered on them4 ,this sketch with a    
proper description should be entered on 
the observing sheets described above1   
and a copy should be retained for       
reference4 ,every month the observations
 will be interrupted by moonlight1 and  
accordingly1 three or four days before  
the full moon1 all the sheets that have 
accumulated should be mailed1 addressed 
,harvard ,college ,observatory1         
,cambridge1 ,mass4 ,an acknowledgment   
will be sent at once1 so that if this is
 not received a second notification     
should be sent4  ,to attain success it  
is particularly important that the plan 
should not be local or national4        
,observers in the southern hemisphere   
are much needed1 and for some purposes  

those in various longitudes4 ,it is     
hoped that among the many amateurs of   
,europe1 and especially of ,england1 may
 be found some ready to participate in  
this work4 ,no restriction regarding the
 observations or publication is         
intended2 but it is hoped that a large  
addition to our present knowledge of the
 variable stars may be secured1 without 
interfering with what would otherwise be
 obtained4 ,copies of this pamphlet and 
further information will be furnished on
 application4 ,any persons desiring to  
participate are requested to address the
 writer1 sending answers to the         
questions given above4 ,the details will
 differ with each observer1 and will be 
arranged by correspondence4 ,apart from 
the value of the results attained1 it is
 believed that many amateurs will find  
it a benefit to accustom themselves to  
work in a systematic manner1 and that   
they will thus receive a training in    
their work not otherwise easily obtained
 outside of a large observatory4 ,the   

lesson should be taught that time spent 
at a telescope is nearly wasted1 unless 
results are secured worthy of           
publication and having a permanent      
value4 ,those who have once accomplished
 such work are likely in the future to  
appreciate its value1 and will often    
continue to do useful work in some other
 department of practical astronomy1 if  
not in that of variable stars4 ,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 stars4  
,,edward ,c4 ,,pickering4  ,,harvard    
,,college ,,observatory1 ,cambridge1    
,mass4