SHAPLEY— STAR CLUSTERS. 341 



most recent information dates from the time the hght we now re- 

 ceive left its remote origin in the ckister, and what has occurred 

 there during the last 360 centuries is beyond our power of finding 

 out. On the basis of our knowledge of the probable causes of these 

 past conditions, we may believe with good reason that the cluster 

 is now much as it was 36,000 years ago. Such an interval of time 

 is of small consequence in the life history of a gigantic stellar sys- 

 tem ; but while these pulses of light have been coming across the 

 intervening fraction of unending space a thousand human genera- 

 tions have come and gone ; man has emerged from a vague, unre- 

 corded past and in fleeting succession all his historically known na- 

 tional civilizations have slowly evolved, flourished in vaunted per- 

 manence and supremacy, and quickly relapsed into oblivion or poor 

 mediocrity. We recall, too, that of all the globular clusters whose 

 radiation is continually streaming toward the earth, Messier 13 is 

 one of the very nearest. 



With the distance of the cluster knowm, we readily translate an- 

 gular dimensions, as measured on the surface of the sky, into linear 

 dimensions. Thvis, by the definition of parallax, the angular value 

 o". 00009 corresponds in the Hercules cluster to one astronomical 

 unit — the distance separating sun and earth. By transferring a 

 linear scale to the cluster, therefore, as in the accompanying illus- 

 tration (which does not include the outlying stars), we m^ay deter- 

 mine the separation of the individual stars, the number in a given 

 volume, and numerous other facts concerning the physical structure 

 of the system. 



It is worthy of emphasis that in determining the distance of the 

 Hercules cluster we have at the same time derived the distances of 

 its tens of thousands of stars. The absolute values of these dis- 

 tances appear to be accurately known ; and certainly the distances 

 of these stars relative to each other are known with an accuracy 

 that is unequalled in ordinary parallax work, for in any given 

 globular cluster the distance of all the stars from the earth may be 

 accepted as the same, with an error of less than one per cent. We 

 are thus in a position to make some general investigations of the 

 inter-relationships of the brightness, colors, numbers, and positions 

 of stars ; and, because of so little uncertainty in the relative distances 



