Manchester Memoirs, Vol. Hi. (1908), No. 10. 5 



place, a new science, that of abstract hydrodynamics, 



which analyses the interaction of uniform inertia and 



simple fluid pressure, and is in itself one of the most 



elegant and perfect constructions of modern mathematics. 



As a result of these thorough investigations, we are now 



more familiar with the limitations of the so-called vortex 



theory of atomic constitution, than with the initial 



successes of this mode of representation of physical 



reality. But limitation ought not to be taken to imply 



failure. Human reason is finite in its potentialities : it is 



not competent to frame a picture of the activities of the 



cosmos, of which it is itself a part, such as can bear 



Comparison with actuality throughout the whole range of 



phenomena. It is of course absurd, as we are often 



reminded with much insistence, especially in recent years, 



to imagine that a material atom is merely a vortex ring 



in fluid ; but, on the other hand, we can never know any 



object, even an atom, intrinsically, but only through its 



relations with other objects, and the picture of atoms as 



motional configurations subsisting in some way in the 



universal plenum, and not merely objects foreign to it, is 



possibly the greatest expansion which our modes of 



thought on these matters have received since Descartes ; 



and it has come to us, or has at any rate been made 



definite, through the vortex illustration. 



This procedure, the study of the relations of the 

 universe by the construction of working models, easily 

 apprehended as a whole, is not restricted to external 

 nature. A considerable part of present activity in 

 abstract mathematics seems to consist in the construction 

 of schemes of representation, such as will elucidate the 

 inner scope and connexion of the processes of mathe- 

 matical thought, involving analysis of the ideas of 

 number and magnitude, limit, infinity, etc. It is signifi- 



