548 



NATURE 



[October 2, 1890 



has already been said about the relative value of the light 

 of one magnitude at the top and bottom of the curve. 



We next take a hypothetical case from Group VI. 

 Here, instead of a nebula, dim owing to absence of 

 collisions brought about by disturbances, we have to deal , 

 with a condensed body of small luminosity, the light of 

 which is strongly absorbed by a carbon atmosphere. 



We first consider the action of two subsidiary swarms, 

 one producing more light with a short period, the other 

 less light with a period say fifteen times longer. In fact 

 we have one comet with an orbit of great eccentricity and 

 short period, and another of small eccentricity and long 

 period. We will assume the periastra to be coincident. 



As the light is generally feeble, we may take the con- 

 stant luminosity of the star as of the twelfth magnitude, 

 and that it is raised to the eighth magnitude by the added 

 light of the swarms at perihelion. We have then a dif- 

 ference of four magnitudes. 



Proceeding as before we have : — 



I "5 1 addition for one magnitude 

 3-80 „ I he next 



9'54 

 23-96 



The sum of the added light gives us 38-81 of the light- 

 units adopted = (2-512)* - i. 



The continuous curve represents in Fig. 3 the inte- 

 grated effects expressed in light-units of the two added 

 light sources, and it will be seen that the result is a 

 variable with both maxima and minima also periodically 

 variable. But although both maxima and minima are 

 variable by an equal number of light-units, the effect on 

 magnitude is totally different. Whereas the minimum 

 varies by two magnitudes, the maximum only varies by 

 about one-tenth of a magnitude. 



In the hypothetical case represented, the maximum 

 varies between 7-8 and 7-9, whilst the minimum varies 

 between iq-g and 12. 



Like the curve for the variable of Group II., this may 

 also be transferred to one in which equal differences of 

 magnitudes are represented by equal spaces. 



This is shown in Fig. 4, and here again it will be seen 

 that, as in the former case, in adding a change of mag- 

 nitude at the bottom of the curve to the top of the curve 

 the magnitude-change is diminished according to the ratio 

 of light-units. 



The question now arises. Are there any stars in] the 

 heavens the phenomena of which can be represented by 

 the hypothetical curves which we have just given ? If so, 

 we shall be justified in tracing a vera causa in the hypo- 

 thesis under consideration. It may be here stated that 

 one of the received explanations of such a variability as 



Fig. s.— Light-( 



: of /3 Lyrae. 



is represented on our first hypothetical diagram is that due 

 to Prof. Pickering, who conceived that the observed effect 

 might be produced by a surface of revolution ; the 

 ratio of the axes being 5 : 3, with a dark portion at one of 

 the ends and symmetrically situated as regards the longer 

 axis.^ 



A reference to Fig. 5 will show that the hypothetical 

 curve shown in Fig. 2 strikingly represents the actual 

 light-curve of /3 Lyras (actual magnitudes are not in 

 question), and I submit therefore that the well-known 

 phenomena of that star are produced by the causes I 

 have suggested rather than by the complicated apparatus 

 suggested by Prof. Pickering, to say nothing of the earlier 

 suggestions of Maupertius and others. 



I append another diagram (Fig. 6) to show that the 

 second hypothetical curve is a close approximation to the 

 . light-curve of U Cygni, one of the best observed variables 

 in Group VI. ; and here I must express my obligations to 



* •' . ., .' Gore in " Astronomy for Amateurs," p.. 238, 

 NO. 1092, VOL. 42] 



Mr. Knott, who has freely communicated all his obserya 

 tions of this star to me, and has permitted me to publish 

 them in this form. 



Unfortunately, though the observations are of such a 

 high order of exactness, they are not continuous. The 

 parts of the curve in which the line is continuous repre- 

 sent the actual observations. The dotted lines added are 

 for the purpose of enabling a comparison to be made 

 with Figs. 3 and 4, in which the probable relations of the 

 periods and intensities of the two hypothetic swarms are 

 shown in light-units and magnitudes respectively. 



The similarity between the hypothetic case represented 

 and Mr. Knott's actual observations greatly strengthens 

 my view. . . ■ . 



It follows very clearly from the above considerations 

 thai on -my hypothesis there should be frequently found 

 rhythmical variations at the minimum, while the change 

 at maximum is so slight that our" best observers fail to 

 notice it. . . ..i... :.,_;/, 



i 



