180 On the Principles of Dynamics. 



It is clear then that the " velocity of the solar system in 

 space " is not related to physical measurements by the simple 

 relation which obtains in the case of Relative Velocity : the 

 assertion of the relation implies the proposition that physical 

 space has three dimensions, a proposition which is not implied 

 by the assertion of the relation A. Therefore, if it could be 

 shown that this velocity was identical with the Absolute 

 Velocity of any system without introducing dynamical con- 

 ceptions, the object which was defined in § 11 would not 

 be attained. But I do not think that even so much can be 

 achieved. Dr. Schuster* points out that the values of V 

 and of its " components" v x , Vy, v z are the same whatever n stars 

 are chosen, so long as n is large enough. Hence, he argues, 

 the velocity V must be independent of the stars and belong 

 to the sun alone. But in saying that the velocity is inde- 

 pendent of the stars he can only mean that physical action 

 between the sun and the stars has not determined V. But 

 44 physical action " implies Partial Accelerations, unless the 

 complete interpretation of physical phenomena in terms of 

 the conceptions of dynamics is rejected. Hence his proposi- 

 tion involves Partial Accelerations, which are dynamical 

 concepts dependent for their meaning on equations (3) and 

 (1) : his further remarks have no interest for us from our 

 present point of view. 



§ 13. One final remark must be made on the subject of 

 u absolute rotation." To some people it appears to be very 

 wonderful and incomprehensible that, " while no experiment 

 can detect a uniform absolute velocity of the whole of a 

 dynamical system, yet experiment can detect a uniform 

 absolute rotation of such a system." From what has been 

 said it is clear that, if the statement in inverted commas is 

 to have any meaning, we must, in our notation, write 

 Absolute Velocity and Absolute Rotation. The statement 

 then becomes equivalent to the following : — 



If in the equations of dynamics we substitute for the 

 Absolute Coordinates x m , y m , z m , &c, other quantities, x' m , 

 y'm, c'm, &c, defined by 



x'm = Xm + Clxt -J* h x , if m = X m + d y t + by, &C. 



(a*, ... by, &c. being constants) , 



then the values of r mn , &c. obtained by solving the equations 

 are unaltered. But if we substitute for the Absolute 



* Loc. cit. 



