July 23, 1920] 



SCIENCE 



71 



endow the other fields ; and so far as I am con- 

 icerned, at least, I am willing to admit that 

 this striking contrast is a fair measure of our 

 ignorance with respect to what is going on in 

 these other fields. . 



Turning our eyes upward towards the sky 

 we see the friendly stars, for they seem friendly 

 to one who cultivates their acquaintance. 

 Symbols, they are, of permanence and stability 

 for they maintain their light and their 

 positions unchanged century after century. 

 In order to gauge their distances we have only 

 to imagine our sun moved far enough away 

 that its light is reduced to that of ordinary 

 starlight. Our imaginations are utterly im- 

 potent to grasp the ninety-three millions of 

 miles which separate us from the sun, but 

 this distance, great as it is, must be taken 

 three hundred thousand times to bring us even 

 to the nearest star; and even this prodigious 

 distance is less than the average distance be- 

 tween the stars. It is hard to appreciate the 

 vastness of astronomical space. If two un- 

 like things can be compared, we might say that 

 the vastness of astronomical space is compar- 

 able with the vastness of the number of atoms. 

 Imagine, if you please, fifty millions of atoms 

 placed side by side. Their total span would 

 be one centimeter. Imagine then the number 

 of atoms in a cubic centimeter of water. It is 

 something like 3 X 10^. Think then of the 

 number of atoms in the ocean, or in the entire 

 earth ; or worse still, in the entire solar system. 

 It turns out that there are something like 

 6 X 10^^ atoms in the entire solar system. But 

 if we give to the sun its fair share of the empty 

 space about it, about twenty cubic parsecs, we 

 can say that the sun's share of space is 6 X 10^^ 

 cubic centimeters; so that if all the atoms in 

 the solar system were uniformly distributed 

 throughout the sun's share of space there would 

 be ten cubic centimeters of space for each 

 atom, and relative to their respective sizes the 

 distances between the atoms would be just 

 about the same as the distance between the 

 stars. Under these conditions the inhabitants 

 of an electron would have much the same prob- 

 lem in determining the ordinary properties of 



matter that we have in determining the collec- 

 tive properties of the stars. 



In the process of extending our conceptions 

 of space the astronomers have been magnifi- 

 cently in the lead. In the extension of our 

 conceptions of time, however, they have al- 

 lowed the geologists to take the lead, although, 

 even without any specific evidence, one would 

 be willing to admit that astronomic time must 

 exceed geologic time as greatly as astronomic 

 space exceeds geologic space. As would be ex- 

 pected direct evidence is very hard to get, as 

 the three hundred years since the invention of 

 the telescope, and the two hundred years since 

 exact observations in the modern sense of the 

 word began, is far too short an interval for 

 much change to have occurred. The proper 

 motion of the great majority of the stars is 

 less than one second of are in a century. In a 

 million years these motions will be less than 

 three degrees; and motions of this magnitude 

 occur in the field of ordinary masses in about 

 one second. On this basis one second would 

 correspond with a million years, and the three 

 score years and ten of human existence would 

 correspond to over two million billion years. 

 In our conceptions of ordinary time we have 

 risen to a point where a human lifetime seems 

 short. Shall we ever attain a viewpoint where 

 the corresponding astronomical period seems 

 short? 



Just as in the kinetic theory of gases the 

 collisions lof the molecules are the important 

 events from a dynamical point of view, so in 

 our galaxy of stars the close approach of two 

 stars is dynamically an event of fundamental 

 importance. An approach as close as the earth 

 is to the sun would be a close approach, and 

 for any one star such a close approach may be 

 expected once in four million billion years, or 

 a little more than the corresponding lifetime. 

 The importance of these close approaches will 

 be appreciated if it is borne in mind that it is 

 the only method which we know by which a 

 star could be destroyed so that its identity 

 would be lost; for, notwithstanding the 

 temporary stars, internal explosions scatter- 

 ing the remains beyond the possibility of a 

 gTavitational reassembling is unbelievable, and 



