MOTION, FORCE, MATTER 319 



involved. Thus, suppose that A and B are two bodies, and 

 that u is the rate at which the distance between them is in- 

 creasing. Then u is a relative velocity. The Absolutist says 

 that it must be due to absolute motions in A or in B or in 

 both, and that all that we can say about them is that their 

 difference is equal to u." 1 



The difficulties inherent in the conception of the Absolute 

 Theory are apparent. What is that ultimate frame of ref- 

 erence according to which all motions are, in the final anal- 

 ysis, absolute? Newton's formulation is not particularly 

 helpful. "If a place is moved, whatever is placed therein, 

 moves along with it. . . . Wherefore entire and absolute 

 motions can be no otherwise determined than by immovable 

 places; and for that reason I did before refer those absolute 

 motions to immovable places, but relative ones to movable 

 places. Now no other places are immovable but those that, 

 from infinity to infinity, do all retain the same given posi- 

 tions one to another; and upon this account must ever re- 

 main unmoved; and do thereby constitute immovable 

 space." 2 Absolute space seems thereby to be entirely postu- 

 lational. Attempts have been made in the history of science 

 to locate this absolute system of reference in terms of a 

 material entity. C. Neumann, for example, assumed the 

 existence somewhere in physical space of a completely im- 

 movable body called the "body Alpha," 3 to which all 

 motions are to be referred. Alternative choices for this 

 ultimate point of reference are certain of the "fixed" stars, 

 and (until fairly recent times) the ether. The arbitrary char- 

 acter of all such systems of reference is obvious. 



Correlational character. Motion is commonly defined as 

 the time rate of change of position, or as the first derivative 

 of space with respect to time. The correlational character of 

 this definition is clear; motion is incapable of definition 

 without at least the notions of "space" and "change," the 



1 Scientific Thought, pp. 97-98. 2 Newton s Principia, p. 80. 



3 Ueber die Principien der Galilei- Newtonschen Theorie (Leipzig: Teubner, 1870), 

 p. 15. 



