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diff --git a/35613.txt b/35613.txt new file mode 100644 index 0000000..6c370d0 --- /dev/null +++ b/35613.txt @@ -0,0 +1,878 @@ +The Project Gutenberg EBook of A Plan for Securing Observations of the +Variable Stars, by E. C. Pickering + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: A Plan for Securing Observations of the Variable Stars + +Author: E. C. Pickering + +Release Date: March 19, 2011 [EBook #35613] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK SECURING OBSERVATIONS--VARIABLE STARS *** + + + + +Produced by Walter MacDonald II + + + + + A PLAN + + FOR + + SECURING OBSERVATIONS + + OF THE + + VARIABLE STARS. + + + BY + EDWARD C. PICKERING, + DIRECTOR OF THE HARVARD COLLEGE OBSERVATORY. + + + + + + CAMBRIDGE: + JOHN WILSON AND SON. + University Press + 1882. + + + + + + + + + + A PLAN FOR SECURING OBSERVATIONS + + OF THE VARIABLE STARS. + + ________ + +FOR several reasons the investigations here proposed are especially +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 acquired +by practice. As a portion of the investigation will probably lead to +the discovery of interesting objects, the observations 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 professional astronomer, in consequence of his greater +skill, instrumental 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 particularly +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 examined 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 home, 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 varying degree +of brightness at different times. The following classification of +them is believed to be a natural one. (Proc. Amer. Acad. xvi, 1, 257.) + +I. Temporary stars, or those which shine out suddenly, sometimes +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 _omicron Ceti_ and _chi Ceti_. + +III. Stars undergoing slight changes according to laws as yet +unknown. Examples, _alpha Orionis_ and _alpha Cassiopeiae_. + +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, _beta Lyrae_ and _delta +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 phenomenon recurs with +such regularity that the interval between successive minima may be +determined in some cases within a fraction of a second. Examples _beta +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 +suspected objects, which will be examined in the same way, and +announced at once if they prove to be of interest. It is essential +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. Hitherto 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 therefore 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 observations. +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 discovered 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 surprising +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 particularly 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 variables 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 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 1/25 and for four 1/125, 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. Conversely, if no such variation is detected we +may be almost certain 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 +minimum 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 impossible 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 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 9/10 that the star will have its full +brightness. For two evenings the chance will be (9/10)^2 for three +(9/10)^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 recommended 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 adjacent 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 several days, or for observers in different +longitudes to make the 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 probability +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_ +represent 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 examination, +or if one appears brighter as often as it appears fainter than +the other, we may denote this equality by _av_ or _va_, these terms +having precisely the same meaning. If one of the stars is suspected +to be brighter, that is, if it appears sometimes brighter and +sometimes fainter, but more frequently brighter, the interval +may be designated as one grade. The observation may be written +_a_ 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 magnitude. +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 alpha +Ursae Minoris_, 2.2 magn.; gamma _Ursae Minoris_, 3.0 magn.; delta +_Ursae Minoris_, 4.4 magn.; 51 _Cephi_, 5.4 magn.; lambda _Ursae +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 +observation 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 of the stars. +These difficulties are avoided by the following 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 interval 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 _b_, we may have _a_ 8 _b_ +or _a_ 9 _b_. An advantage 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 compare two +stars rather than three. Each method has its advantages, 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 selecting comparison stars, +the proximity of a brighter star is very objectionable, causing a +large error, which varies with the magnifying power used. Double +stars should be avoided if the power 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 designations +or right ascensions and declinations? Have you Heis' Atlas Coelestis +Novus, the Uranometria Argentina, the Durchmusterung, 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 reference, +it is essential that all the observations should be made according +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 condition +of the sky, as "clear," "hazy," "passing clouds," etc. The time +of beginning and ending work should also be noted. One +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 associated. 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 +Harvard College Observatory, Cambridge, Mass. An acknowledgment 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 observations 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 participate 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 amateurs +will find it a benefit to accustom themselves to work in a systematic +manner, and that they will thus receive a training 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 appreciate 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. PICKERING. + +HARVARD COLLEGE OBSERVATORY, +Cambridge, Mass. + + + + + +End of the Project Gutenberg EBook of A Plan for Securing Observations of +the Variable Stars, by E. C. 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