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orth while to pause a moment before entering on the subject。
John Goodricke； a deaf…mute； was born in 1764； he was grandson and heir of Sir John Goodricke of Ribston Hall； Yorkshire。 In November 1782； he noted that the brilliancy of Algol waxed and waned （It is said that Georg Palitzch； a farmer of Prohlis near Dresden； had about 1758 already noted the variability of Algol with the naked eye。 〃Journ。 Brit。 Astron。 Assoc。〃 Vol。 XV。 （1904…5）； page 203。）； and devoted himself to observing it on every fine night from the 28th December 1782 to the 12th May 1783。 He communicated his observations to the Royal Society； and suggested that the variation in brilliancy was due to periodic eclipses by a dark companion star； a theory now universally accepted as correct。 The Royal Society recognised the importance of the discovery by awarding to Goodricke； then only 19 years of age； their highest honour； the Copley medal。 His later observations of Beta Lyrae and of Delta Cephei were almost as remarkable as those of Algol； but unfortunately a career of such extraordinary promise was cut short by death； only a fortnight after his election to the Royal Society。 （〃Dict。 of National Biography〃； article Goodricke （John）。 The article is by Miss Agnes Clerke。 It is strange that she did not then seem to be aware that he was a deaf…mute； but she notes the fact in her 〃Problems of Astrophysics〃； page 337； London； 1903。）
It was not until 1889 that Goodricke's theory was verified； when it was proved by Vogel that the star was moving in an orbit； and in such a manner that it was only possible to explain the rise and fall in the luminosity by the partial eclipse of a bright star by a dark companion。
The whole mass of the system of Algol is found to be half as great again as that of our sun； yet the two bodies complete their orbit in the short period of 2d 20h 48m 55s。 The light remains constant during each period； except for 9h 20m when it exhibits a considerable fall in brightness （Clerke； 〃Problems of Astrophysics〃 page 302 and chapter XVIII。）； the curve which represents the variation in the light is shown in a figure titled 〃The light…curve and system of Beta Lyrae〃 （Fig。 7。）。
The spectroscope has enabled astronomers to prove that many stars； although apparently single； really consist of two stars circling around one another （If a source of light is approaching with a great velocity the waves of light are crowded together； and conversely they are spaced out when the source is receding。 Thus motion in the line of sight virtually produces an infinitesimal change of colour。 The position of certain dark lines in the spectrum affords an exceedingly accurate measurement of colour。 Thus displacements of these spectral lines enables us to measure the velocity of the source of light towards or away from the observer。）； they are known as spectroscopic binaries。 Campbell of the Lick Observatory believes that about one star in six is a binary （〃Astrophysical Journ。〃 Vol。 XIII。 page 89； 1901。 See also A。 Roberts； 〃Nature〃； Sept。 12； 1901； page 468。）； thus there must be many thousand such stars within the reach of our spectroscopes。
The orientation of the planes of the orbits of binary stars appears to be quite arbitrary； and in general the star does not vary in brightness。 Amongst all such orbits there must be some whose planes pass nearly through the sun； and in these cases the eclipse of one of the stars by the other becomes inevitable； and in each circuit there will occur two eclipses of unequal intensities。
It is easy to see that in the majority of such cases the two components must move very close to one another。
The coincidence between the spectroscopic and the photometric evidence permits us to feel complete confidence in the theory of eclipses。 When then we find a star with a light…curve of perfect regularity and with a characteristics of that of Algol； we are justified in extending the theory of eclipses to it； although it may be too faint to permit of adequate spectroscopic examination。 This extension of the theory 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