178 Mr. N. Campbell on the 



The object might be thought to be achieved if we could 

 express the Absolute Coordinates as algebraical functions of 

 the Relative Distances and the Times by means of equations 

 (1) and (2). But, since there are more variables than there 

 are equations, we cannot do so unless we introduce more 

 equations relating the variables. Now, whatever form these 

 additional equations are given, they will introduce, implicitly 

 or explicitly, Partial Accelerations. But Partial Accelera- 

 tions are concepts which have no meaning apart from 

 dynamics ; hence the additional propositions which we in- 

 troduce in order to render equations (1) and (2) determinate 

 are dynamical propositions of some form or other : the 

 ideas contained in them differ just as much in their nature 

 from ideas which are necessary for the definition of Relative 

 Motion as those contained in the ordinary equations (3) and 

 (4). We must conclude, therefore, that it is impossible to 

 define Absolute Motion without the use of concepts which 

 appear less fundamental than those which are necessary for 

 the definition of Relative Motion. 



To sum up. If it be asked, Is " motion " absolute or 

 relative ?, the answer is, Both. If it be asked, " Is Absolute 

 Motion a concept as fundamental and necessary for the 

 student of physics as Relative Motion ? " or " Can it be 

 related in as simple a way to the results of observation ? %> 

 then the answer is, No. 



§12. In discussions* concerning u absolute motion" a 

 concept is often introduced which is called iw the velocity of 

 the solar system in space," or " relative to the stars/' It is 

 desirable that a brief consideration should be given to the 

 nature of this concept. 



The introduction of this concept is usually prefaced by the 

 statement that we can (ideally at least) determine the velocity 

 of the sun relative to any star, both in and at right angles to 

 the line of sight. There seems a tendency to overlook the 

 obvious fact that, if by " the relative velocity of two particles " 

 is meant change of their distance with time, there can be no 

 sense in speaking of a determination of the relative velocity of 

 two particles " in or at right angles to " the line joining them. 

 If only these two particles are known the idea of direction 

 is impossible ; the particles change their distance, but it is 

 meaningless as yet to inquire whether their motion is in or 

 at right angles to the line joining them. The measurements 

 which are actually made on the sun and stars concern the 

 rate of change of the relative distances of two stars or of 



* See e.(j. Schuster, " A Plea for Absolute Motion," Xat. lxxiii. p. 462. 

 i?rof. Schuster's remarks show very clearly the confusion between Motion 

 and motion to which attention has been drawn. 



