556 



NATURE 



\Oct. 9, 1879 



ing the importance of the results which the observation 

 of them bids fair to offer concerning the nature of the 

 sidereal universe, the variable stars have not attracted so 

 much attention as other even less important phenomena 

 in the starry heavens, and one cause of this must be 

 sought in the circumstance, that most of these observa- 

 tions are best made with very small telescopes or even 

 with the naked eye, and while it is the duty of the profes- 

 sional astronomer to make use of the expensive instru- 

 ments, of which he has charge, the inclination of the 

 amateur astronomer in this country often leads him in the 

 same direction. However, the attention of those who 

 take an interest in the science but cannot afford a large 

 outlay, cannot too often be urged towards this kind of 

 observation, that while it so much needs their help is so 

 thoroughly within their reach. 



The best method is due to Argelander, a follower of 

 Bessel. who was considered the first authority on the 

 subject during his lifetime. It was propounded in his 

 " Aufforderung an Freunde der Astronomic zur Anstel- 

 lung von ebcn so interessanten und niitzlichen, als leicht 

 auszufiihrenden Beobachtungen Uber mehrere wichtige 

 Zweige der Himmelskunde," which appeared in Schu- 

 macher's /ij//;-fe(:/^y«>- 1844, a periodical seldom met with 

 in this country, which may in a measure explain the 

 comparatively little attention that has been given to this 

 subject on the part of British amateurs, who have so 

 energetically followed up more complicated investigations. 

 The success of those who have spent even a short time 

 on these observations may be considered a sufficient 

 appeal, and we venture to hope that the following short 

 sketch of the easiest and most convenient method will be 

 acceptable to some of the readers of Nature who have 

 not Argelander's lengthy paper at hand. The observa- 

 tions are in reality far simpler than the description 

 of them looks. The stars visible to the naked eye are 

 arranged in six classes according to their brightness, 

 but it is often doubtful to what magnitude we shall 

 refer an object, because we are able to judge about 

 much smaller differences than those that distinguish 

 two magnitudes, the number of which is therefore too 

 small. The smallest difference perceptible to the average 

 sight is a tenth of a magnitude, and we are therefore able, 

 by a method of sequences, to reach a considerable accu- 

 racy. Researches on variables have further this advan- 

 tage that we do not want to know the absolute magnitude 

 but only the brightness relatively to certain other stars. 

 These comparison-stars must be chosen witli intervals of 

 not above a half magnitude, and be situated as near the 

 variable as they can be had, for the transparency of the 

 air is often different not only in different altitudes, but 

 also in different azimuths — nay even owing to aqueous 

 vapour and chemical causes at times in the same place. 

 Observations near the horizon should be avoided, and 

 near the zenith the position is difficult. Twilight, moon- 

 light, and lamplight would likewise interfere, and above 

 all it must be avoided to observe from a lighted room. 

 Against the moon or a distant gas-lamp m a town a 

 screen can be used. If clouds are near they will render 

 the comparisons uncertain. Cirro-stratus commencing to 

 descend from high in the atmosphere is particularly 

 deceiving. The estimation of stars of the first magnitude 

 is difficult, and an evenly illuminated background in this 

 case rather an advantage, or a slight fog, but in the latter 

 case and when detached clouds are on the sky the obser- 

 vations have to be repeated with an interval of a few 

 minutes, because fogs arc rather irregular ; at other times 

 an observation may be secured in a few minutes, and 

 more observations the same night are only required in 

 case of quickly changing stars. They generally give 

 identical results, but two or more observers are an advan- 

 tage, though their estimations may have constant differ- 

 ences, because various colours affect individual eyes 

 differently. No attempt need be made to look simul- 



taneousl)- at both stars, because the sensibility of the eye 

 in different spots is different, and this error would not be 

 eliminated. Look first at one star, then turn quickly to 

 the other, look at that and return to the first again, it is 

 well to turn the eye a little to the side, when watching a 

 star. It appears then brighter, because the middle of the 

 retina is tired with constant work. The comparison of 

 stars barely visible is to be avoided. The results, together 

 with the nature of the circumstances, should be noted at 

 once, and in the dirk. It will be remarked that the 

 causes of error, referred to above, are not sensibly re- 

 moved by using photometers, and other errors may be 

 introduced by such cornplicated apparatus. Faint stars 

 may be observed through a binocular. The glass used 

 should be colourless, always the same, and the distance 

 between the eye-glasses carefully adjusted. It must be 

 confessed that this kind of work cannot be carried out in 

 places where the sky does often not clear for months, as 

 in North-West Ireland ; on the other hand the English 

 climate seems favourable. It is often blue sky, if only 

 partly, and no superior definition is required. At present 

 this part of astronomy is mainly dependent upon the 

 labours of Julius Schmidt, of Athens. Some knowledge 

 of the constellations is necessary, and that may be gained 

 from Argelander's or Heis's Uranometries. In case the 

 research be extended to telescopic stars Argelander's 

 large atlas should be procured. It is known that Pogson 

 at Hartwell and iVIadras has made diagrams of stars 

 round the variables, which would be very useful. 



The difterences are noted in "steps," each of which is 

 equal to a tenth of a magnitude. If the comparisons are 

 doubtful but most give one star, a, larger than another, b, 

 it is said that a is one step above? : a\b. If at all ^1 

 times a seems larger than b, it is two steps above \\. : a2b. -^^ 

 If the difference is remarked at a glance, a is three steps 

 above b : a^b. Still greater difference is denoted a 4 b, 

 which is occasionally used, though so great a difference 

 cannot be estimated so exactly as a smaller one, the 

 probable error of which is much below one step, so that 

 it is preferable to give the comparisons in half steps. 

 For exercise Argelander's comparison stars can be used 

 from " Astronomische Beobachtungen auf der Stern- 

 warte zu Bonn," vol. vii., 1869. The steps might not 

 be exactly identical in all cases, but they ought not 10 

 deviate much. The variable should not only be com- 

 pared with the greater and smaller star but also with the 

 mean of them, which is very accurate. From each 

 comparison follows then the brightness of the variable, 

 and the average of these is taken first in the common 

 manner, next allowing weights inversely proportional :o 

 the number of steps, and the means of the two is assumed 

 as the definitive result. Of course this is more estimated 

 than computed, and the two results agree generally. 



From magnitudes thus obtained in a scale of steps the 

 epochs of maxima and minima are next sought, fron 

 which follows the period, which is the principal element. 

 When a sufficient number of periods are available it can 

 be seen whether this is constant, and if not, one must try 

 to find a formula which will give the length at any time. 

 A good many periods are about 300 days, but many 

 only a few days. The brightness in the two principal 

 phases will generally be found irregular if the period be 

 so. Some stars have more than two maxima and minima 

 during the same period. Next we project on a paper ruled 

 in squares the brightness of the variable with the time as 

 abscissa, counted from the nearest preceding maximum 

 and expressed in parts of the respective period. The 

 curve drawn as nearly as possible through the points, 

 whose weights may be indicated by circles round them, is 

 called the light curve, and on that we can read off the 

 brightness for any moment, but it is not always possible 

 to treat the observations thus en masse y sometimes single 

 periods have to be separately discussed, and indeed when 

 it is great we -can arrive at some results from a single 



