^34 



KNOWLEDGE 



[OCTOBEB 1, 1894. 



distance of these objects from the earth has not yet been 

 determined. They may, on tlie one hand, be collections 

 of suns similar in size to ours and situated at vast distances 

 from the earth ; or, on the other hand, the stars composing 

 them may be comparatively small objects, lying at a 

 distance from the earth not exceeding that of some stars 

 visible to the naked eye. Perhaps the latter hypothesis 

 may be considered the more probable of the two ; but 

 there is really no reason to suppose that these collections 

 of suns are comparatively near our system. The proba- 

 bility seems to be in favour of their great distance from 

 the earth, for in all these clusters the component stars are 

 very faint. The question of the absolute size of the com- 

 ponent stars is one which has not hitherto been sufficiently 

 considered. Let us examine both alternatives, and let us 

 take the cluster Omega Centauri, as one in which the 

 number of the component stars has been actiudhj counted. 

 Assuming that the real number of stars included in this 

 cluster is ten thousand, and that they are indi\'idually 

 equal, on an average, to our sun in mass and volume, we 

 may estimate the distance and dimensions of the cluster. 

 Taking the stellar magnitudes of Omega Centauri as four 

 (as estimated at Cordoba Observatory), I find that with 

 the number ten thousand the average magnitude of the 

 component stars would be fourteen. This agrees with Sir 

 John Herschel's estimate of thirteenth to fifteenth magni- 

 tude. Now to reduce the sun to a star of the fourteenth 

 magnitude, I tind that — assuming the sun to be twenty-six 

 and a half magnitudes brighter than an average star of the 

 first magnitude, as shown by photometric measures — it 

 would be necessary to remove it to a distance equal to 

 seventy-nine million four hundred and forty thousand 

 times the earth's distance from the sun — a distance so 

 great that light would take no less than one thousand two 

 hundred and fifty-three years to reach us from the cluster! 

 Taking the apparent diameter of the cluster at twenty 

 minutes of arc, I find that its real diameter, if placed at 

 the above distance, would be four hundred and sixty-one 

 thousand five hundred and forty times the sun's distance 

 from the earth — a diameter so great that light would take 

 over seven years to cross it ! Supposing the ten thousand 

 stars which compose the cluster to be equally distributed 

 through this sphere, I find that the distance between the 

 individual stars would be about twenty-one thousand times 

 the sun's distance from the earth, or about four months' 

 journey for light. This is, of course, an enormous distance 

 — about seven hundred times the distance of Neptune from 

 the sun ; but still the distance of the nearest fixed star 

 from the earth — Alpha Centauri — is over twelve times 

 greater ; and considering the vast extent of the visible 

 universe, not to speak of infinite space, there is nothing 

 to militate against the existence of a cluster of suns with 

 the components separated fi-om each other by the great 

 distance just found. 



The distance found above for Omega Centauri is certainly 

 enormous, and might lead us to suspect that these globular 

 clusters are external universes. Judging, however, from 

 the average distance recently found for stars of the first 

 and second magnitudes, the distance of ordinary stars of 

 the fourteenth magnitude — on the supposition that they 

 are of the same size and brightness, and that their light 

 is simply reduced by distance — would be about ten times 

 greater than that found above for Omega Centauri. If, 

 then, we increase the distance of the cluster ten times, it 

 will be necessary to also increase the diameter of the 

 component stars to ten times that of the sun. This would 

 give them a volume a thousand times greater than that of 

 our sun — a result which is, of course, highly improbable. 

 If, on the other hand, we do not like to admit that each 



of the faint points of light composing the cluster is equal 

 in volume to our sun, let us diminish the distance ten 

 times. If we do so we must also diminish the diameters 

 of the component stars ten times. This would make them 

 about the size of the planet Jupiter, and it seems very 

 improbable that such comparatively small bodies could 

 retain their solar heat for any length of time They would 

 probably have cooled down, as Jupiter has done — at least 

 to a great extent — ages ago, and would not now be visible 

 as a stellar cluster. Even this reduction of the distance 

 to one-tenth of the value found above would still leave the 

 cluster at an immense distance from the earth, a distance 

 represented by one hundred and twenty-five years of light 

 travel. A reduction of the distance to one-tenth of this 

 again, or twelve and a half years of light travel, would 

 make the components about the size of the earth, and that 

 bodies of this small size could shine with stellar light 

 seems to be an untenable hypothesis. 



There is, however, another point to be considered with 

 reference to the size of the bodies composing a globular 

 cluster. This is the character of their light. I am not 

 aware that the spectrum of a globular cluster has yet been 

 thoroughly examined, but if that of Omega Centauri gives 

 a spectrum of the first or Sirian type, it would modify the 

 above conclusions to some extent. It now seems prob- 

 able that stars having a spectrum of the Sirian type are 

 intrinsically brighter than the sun. I have shown in a 

 former paper that Sirius is about forty times brighter than 

 our sun would be if placed at the same distance, although 

 the mass of Sirius is but little more than twice the sun's 

 mass. The components of a star cluster, therefore — if of 

 the Sirian type of stars — might be as bright as the sun, 

 and at the same time have a smaller mass and voiiime. 



These considerations seem to me to warrant the con- 

 clusion that these globular clusters are probably composed 

 of stars of average size and mass, and that the faintness 

 of the component stars is simply due to their immense 

 distance from the earth. 



[Mr. Gore's suggestions for determining the distance of 

 stellar clusters will be followed with interest by readers of 

 Knowledge ; but his conclusions, I venture to think, are 

 doubtful, as they are founded upon an assumption which, 

 it seems to me, we are not warranted in making — viz., 

 that it is " an untenable hypothesis " that stars of the size 

 of Jupiter or the earth could shine with stellar light, 

 because they must have cooled so that they would now be 

 dark stars, and consequently invisible to us. 



Mr. Gore might possibly be warranted in coming to such 

 a conclusion if he knew (1) that all parts of the stellar 

 universe commenced to cool down at the same period ; 



(2) that the cooling went on everywhere uniformly ; and 



(3) that there were never any collisions between stars 

 giving rise to the reheating of cooled masses. 



Such collisions seem much more probable between the 

 stellar members of a close cluster than between isolated 

 stars. In fact, if the stars of the stellar cluster are moving 

 under the influence of their mutual gravity, it seems 

 impossible to conceive of a system of motion in which 

 collisions would not occasionally occur, and the more com- 

 pact the cluster the more frequently would such collisions 

 happen, giving rise to a rekindling of the stellar brightness 

 by the conversion of energy of translation into heat. 



Mr. Gore seems to think that it is " highly improbable " 

 that any star could have a volume a thousand times greater 

 than that of our sim, while, on the other hand, he thinks 

 it "an untenable hypothesis " that any bright star could 

 have a diameter as small as that of Jupiter, or about a 

 tenth of the solar diameter. But in the case of the 



