476 Mr. E. F. Muirhead on the Laws of Motion. 



merely relative rotation these forces are zero ; in true rotation 

 they exist in greater or less degree." * 



Thereafter comes the well-known experiment of the rotating 

 vessel of water. 



Now the first criterion helps us only in a negative way, by 

 enabling us to deny the attribution of true rest to both of 

 two systems when they are moving relatively to each other. 



The second criterion involves reasoning in a circle. Force is 

 defined as that which produces change of motion ; hence to 

 define unchanged or uniform motion as that which takes place 

 when no force acts does not carry us beyond the previous 

 definition, and is nugatory. 



The third criterion, taken along with the first, implies a 

 physical fact, viz. that when two bodies severally show no 

 centrifugal force, they have no rotation relative to one 

 another. 



Consider now Law II. It amounts merely to a definition 

 of force, specifying how it is to be measured. 



This has been recognized by several writers. Some, how- 

 ever, have expanded it into the further assertion that when 

 two forces act simultaneously on a body, each produces its 

 own effect independently of the other, in accelerating the body's 

 motion. But such a statement is entirely nugatory if we 

 keep by the kinetic definition of force. It is then simply an 

 identical proposition like " A is A/' as will be seen by sub- 

 stituting in the statement " acceleration of mass M for " force.''' 



We now perceive that even the residuum of meaning which 

 remained after our criticism of Law I. and the statements 

 regarding Absolute Motion seems to disappear. For we 

 were supposed to recognize a body absolutely at rest by the 

 absence of centrifugal force. But force is recognizable only 

 by its accelerative effect, while the acceleration must be 

 reckoned relative to a body absolutely at rest, which rest, 

 again, we cannot recognize until we know absolute motions. 

 We are thus reasoning in a circle. 



Law III. This law at first sight undoubtedly seems to 

 express an experimental fact. We may therefore be sur- 

 prised to find that Newton deduces one case of it (viz. that of 

 two mutually attracting bodies) from Law I. (see Scholium 

 to the Axiomata). 



This seeming paradox arises from the fact that in this 

 Scholium Newton makes Law I. apply to a body or system 

 of finite size, and not necessarily without rotation. This 

 assumes that there is some one point (centre of Inertia) 



* Newton's Principia, Scholium to the Defmitiones. 



