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y secures a considerable multiplication of the examples available for observation； and some 30 have already been discovered。
Dr Alexander Roberts； of Lovedale in Cape Colony； truly remarks that the study of Algol variables 〃brings us to the very threshold of the question of stellar evolution。〃 （〃Proc。 Roy。 Soc。 Edinburgh〃； XXIV。 Part II。 （1902）； page 73。） It is on this account that I propose to explain in some detail the conclusion to which he and some other observers have been led。
Although these variable stars are mere points of light； it has been proved by means of the spectroscope that the law of gravitation holds good in the remotest regions of stellar space； and further it seems now to have become possible even to examine the shapes of stars by indirect methods； and thus to begin the study of their evolution。 The chain of reasoning which I shall explain must of necessity be open to criticism； yet the explanation of the facts by the theory is so perfect that it is not easy to resist the conviction that we are travelling along the path of truth。
The brightness of a star is specified by what is called its 〃magnitude。〃 The average brightness of all the stars which can just be seen with the naked eye defines the sixth magnitude。 A star which only gives two…fifths as much light is said to be of the seventh magnitude； while one which gives 2 1/2 times as much light is of the fifth magnitude； and successive multiplications or divisions by 2 1/2 define the lower or higher magnitudes。 Negative magnitudes have clearly to be contemplated； thus Sirius is of magnitude minus 1。4； and the sun is of magnitude minus 26。
The definition of magnitude is also extended to fractions； for example； the lights given by two candles which are placed at 100 feet and 100 feet 6 inches from the observer differ in brightness by one…hundredth of a magnitude。
A great deal of thought has been devoted to the measurement of the brightness of stars； but I will only describe one of the methods used； that of the great astronomer Argelander。 In the neighbourhood of the star under observation some half dozen standard stars are selected of known invariable magnitudes； some being brighter and some fainter than the star to be measured； so that these stars afford a visible scale of brightness。 Suppose we number them in order of increasing brightness from 1 to 6； then the observer estimates that on a given night his star falls between stars 2 and 3； on the next night； say between 3 and 4； and then again perhaps it may return to between 2 and 3； and so forth。 With practice he learns to evaluate the brightness down to small fractions of a magnitude； even a hundredth part of a magnitude is not quite negligible。
For example； in observing the star RR Centauri five stars were in general used for comparison by Dr Roberts； and in course of three months he secured thereby 300 complete observations。 When the period of the cycle had been ascertained exactly； these 300 values were reduced to mean values which appertained to certain mean places in the cycle； and a mean light…curve was obtained in this way。 Figures titled 〃Light curve of RR Centauri〃 （Fig。 5） and 〃The light…curve and system of Beta Lyrae〃 （Fig。 7） show examples of light curves。
I shall now follow out the results of the observation of RR Centauri not only because it affords the easiest way of explaining these investigations； but also because it is one of the stars which furnishes the most striking results in connection with the object of this essay。 （See 〃Monthly notices R。A。S。〃 Vol。 63； 1903； page 527。） This star has a mean magnitude of about 7 1/2； and it is therefore invisible to the naked eye。 Its period of variability is 14h 32m 10s。76； the last refinement of precision being of course only attained in the final stages of reduction。 Twenty…nine mean values of the magnitude were determined； and they were nearly equally spaced over the whole cycle of changes。 The black dots in Fig。 5 exhibit the mean values determined by Dr Roberts。 The last three dots on the extreme right are merely the same as the first three on the extreme left； and are repeated to show how the next cycle would begin。 The smooth dotted curve will be explained hereafter； but； by reference to the scale of magnitudes on the margins of the figure； it may be used to note that the dots might be brought into a perfectly smooth curve by shifting some few of the dots by about a hundredth of a magnitude。
This light…curve presents those characteristics which are due to successive eclipses； but the exact form of the curve must depend on the nature of the two mutually eclipsing stars。 If we are to interpret the curve with all possible completeness； it is necessary to make certain assumptions as to the stars。 It is assumed then that the stars are equally bright all over their disks； and secondly that they are not surrounded by an extensive absorptive atmosphere。 This last appears to me to be the most dangerous assumption involved in the whole theory。
Making these assumptions； however； it is found that if each of the eclipsing stars were spherical it would not be possible to generate such a curve with the closest accuracy。 The two stars are certainly close together； and it is obvious that in such a case the tidal forces exercised by each on the other must be such as to elongate the figure of each towards the other。 Accordingly it is reasonable to adopt the hypothesis that the system consists of a pair of elongated ellipsoids； with their longest axes pointed towards one another。 No supposition is adopted a priori as to the ratio of the two masses； or as to their relative size or brightness； and the orbit may have any degree of eccentricity。 These last are all to be determined from the nature of the light…curve。
In the case of RR Centauri； however； Dr Roberts finds the conditions are best satisfied by supposing the orbit to be circular； and the sizes and masses of the components to be equal； while their luminosities are to one another in the ratio of 4 to 3。 As to their shapes he finds them to be so much elongated that they overlap； as exhibited in his figure titled 〃The shape of the star RR Centauri〃 （Fig。 6。）。 The dotted curve shows a form of equilibrium of rotating liquid as computed by me some years before； and it was added for the sake of comparison。
On turning back to Fig。 5 the reader will see in the smooth dotted curve the light variation which would be exhibited by such a binary system as this。 The curve is the result of computation and it is impossible not to be struck by the closeness of the coincidence with the series of black dots which denote the observations。
It is virtually certain that RR Centauri is a case of an eclipsing binary system； and that the two stars are close together。 It is not of course proved that the figures of the stars are ellipsoids； but gravitation must deform them into a pair of elongated bodies； and； on the assumptions that they are not enveloped in an absorptive atmosphere and that they are ellipsoidal； their shapes must be as shown in the figure。
This light…curve gives an excellent illustration of what we have reason to believe to be a stage in the evolution of stars； when a single star is proceeding to separate into a binary one。
As the star is faint； there is as yet no direct spectroscopic evidence of orbital motion。 Let us turn therefore to the case of another star； namely V Puppis； in which such evidence does already exist。 I give an account of it； because it presents a peculiarly interesting confirmation of the correctness of the theory。
In 1895 Pickering announced in the 〃Harvard Circular〃 No。 14 that the spectroscopic observations at Arequipa proved V Puppis to be a double star with a period of 3d 2h 46m。 Now when Roberts discussed its light…curve he found that the period was 1d 10h 54m 27s； and on account of this serious discrepancy he effected the reduction only on the simple assumption that the two stars were spherical； and thus obtained a fairly good representation of the light…curve。 It appeared that the orbit was circular and that the two spheres were not quite in contact。 Obviously if the stars had been assumed to be ellipsoids they would have been found to overlap； as was the case for RR Centauri。 （〃Astrophysical Journ。〃 Vol。 XIII。 （1901）； page 177。） The matter rested thus for some months until the spectroscopic evidence was re…examined by Miss Cannon on behalf of Professor Pickering； and we find in the notes on page 177 of Vol。 XXVIII。 of the 〃Annals of the Harvard Observatory〃 the following： 〃A。G。C。 10534。 This star； which is the Algol variable V Puppis； has been found to be a spectroscopic binary。 The period 1d。454 （i。e。 1d 10h 54m） satisfies the observations of the changes in light； and of the varying separation of the lines of the spectrum。 The spectrum has been examined on 61 plates； on 23 of which the lines are double。〃 Thus we have valuable evidence in confirmation of the correctness of the conclusions drawn from the light…curve。 In the circumstances； however； I have not thought it worth while to reproduce Dr Roberts's provisional figure。
I now turn to the conclusions drawn a few years previously by another observer； where