364 



SCIENCE 



[N. S. Vol. XXXIII. No. 845 



tity of the process of constructing theories 

 in the realms of natural science and of 

 developing mathematics by the postula- 

 tional method will undoubtedly be of great 

 value to the former in showing what is 

 really essential, and to the latter in in- 

 spiring almost endless points of view. 



It is not necessary to cite more ex- 

 amples to show that mathematics owes 

 much to astronomy, especially in the field 

 of analysis. If it were proper to strike a 

 balance it could probably be shown that the 

 debt has been more than repaid, but in 

 these unselfish sciences the privileges of 

 foreign service are cherished as much as 

 the treasures of domestic achievements, and 

 therefore we content ourselves with the 

 recognition of the interrelations. 



In closing I may point out the truism 

 that these interrelations are not limited to 

 astronomy and mathematics. It is to the 

 glory of astronomy that in it were initiated 

 the two most fundamental intellectual 

 movements in the history of mankind, viz., 

 the establishment of the possibility of sci- 

 ence and of the doctrine of evolution. Our 

 intellectual ancestors in the valleys of the 

 Euphrates and the Nile and on the hills of 

 'Greece looked up into the sky at night and 

 :saw order there and not chaos. By pains- 

 ftaking observations and calculations they 

 •discovered the relatively simple laws of the 

 •motions of the heavenly bodies, whose in- 

 variable and exact fufilment led to the be- 

 lief that the whole universe in all its parts 

 •is orderly and that science is possible. In 

 the modern world this conclusion is so com- 

 imonplace that its immense value is apt to 

 be overlooked, but a study of the supersti- 

 :tions and the hopeless stagnation of those 

 portions of jnankind which have not yet 

 ;made the discovery gives us some measure 

 • of its worth. The modern supplement to 

 the conception that the universe is not a 

 -tjhaos.is that not only is it an orderly uni- 



verse at any instant, but that it changes 

 from one state to another in a continuous 

 and orderly fashion. This doctrine that 

 science is extensive in time, as weU as in 

 space, is the fundamental element in the 

 theory of evolution and the completion of 

 the conception of science itself. The ideas 

 of evolution in a scientific form were first 

 applied to the relatively simple celestial 

 phenomena. More than a century before 

 the appearance of Darwin's "Origin of 

 Species, ' ' and the philosophical writings of 

 Spencer, another Englishman, Thomas 

 "Wright, published a book on the origin of 

 worlds. Laplace's nebular hypothesis gave 

 the geologists a basis for their work, which 

 in turn paved the way for that of Darwin. 

 For half a century now the doctrine of 

 evolution has been a fundamental factor in 

 the elaboration of all scientific theories, and 

 its influence has spread to every field of 

 intellectual effort. It has been the good 

 fortune of mankind that his skies have 

 sometimes been free of clouds and that he 

 has been able to observe those relatively 

 simple yet majestic and impersonal celes- 

 tial phenomena which have not only led to 

 so important results as the founding of sci- 

 ence and the doctrine of evolution, but 

 have strongly colored his poetry, philos- 

 ophy and religion, and have stimulated him 

 to the elaboration of some of his most pro- 

 found mathematical theories. 



P. E. MOULTON 

 Univeesitt of Chicago 



STATISTICS OF GERMAN UNITEBSITIE8 



The twenty-one German universities show 

 an enrollment for the winter semester of 

 1910-11 of 54,822 students, as against 52,407 

 students last winter. During the past five 

 years there has been an increase in registra- 

 tion of no less than 12,432 students. Curi- 

 ously enough, the winter enrollment exhibits a 

 decrease, although only of a few students, 

 against the previous summer semester, in which 



