RETROSPECT AND PROSPECT. 7 4*7 



have advanced through the study of the changes of figure 

 to an increasing appreciation of an underlying unity. 

 In many of the organs of living creatures the unity 

 seems to lie outside the organs themselves, as the unity 

 of a machine which exists in the design of the maker 

 adapting it to a certain purpose; whereas in the ani- 

 mated world it seems to be inside the objects of Nature. 

 The sciences of life have accordingly forced upon us 

 more and more the conception not only of orderly 

 arrangement, but also of a unifying principle that 

 is, Individuality. 



These two conceptions of Order and Individuality are 

 as little new as are the various conceptions of purely 

 scientific thought, most of which, as has been shown, 

 have been handed down to us from earlier times. They 

 have accordingly been defined and studied by phil- 

 osophers from antiquity. The various positions which 

 thinkers have taken up with regard to them during the 

 nineteenth century have, however, been characteristic 

 of the age, and have been very largely influenced 

 by the conceptions of Order and Unity which science 

 itself has elaborated. In this connection it is of 

 importance to note that the idea of Order or 

 arrangement has only within the nineteenth century 

 met with a comprehensive mathematical treatment ; and, 

 so far as that of Unity is concerned, it can also be 

 said that the mathematical sciences have in the course 

 of the nineteenth century for the first time approached 

 the analysis of the allied idea of Continuity, which 

 indeed plays an increasingly important part in many 

 scientific theories. It may even be held that the 



