324 THE GRAMMAR OF SCIENCE 



" acting in a straight line." Furthermore, if the " change 

 of motion " is to be that of a body, not a particle, then we 

 naturally ask which point of the body will have its motion 

 changed in the direction of a straight line. We are thus 

 again brought face to face with the fact that the motion 

 of " bodies " is far more complex than is in the least in- 

 dicated by this law. 



Lord Kelvin and Professor Tait have restated the 

 Second Law in the following form : — 



When any forces whatever act on a body, then, whether 

 the body be originally at rest or moving with any velocity 

 and in any direction, each force produces in the body the 

 exact cliange of motion zvhich it zuould have produced 

 had it acted singly on the body originally at rest. 



These conclusions they consider really involved in 

 Newton's Second Law. The same difficulty repeats itself 

 here with regard to the interpretation of the term " body," 

 Further, the law thus expressed denies the possibility of 

 "modified action" (pp. 317-21), and the likelihood that 

 in certain cases the velocity of corpuscles may help to 

 determine their mutual accelerations (p. 294). It thus 

 asserts the absolute validity of that synthesis which we 

 have termed the parallelogram of forces, and which we 

 have ventured to suggest cannot be dogmatically asserted 

 of corpuscles of all types. "^ 



Law III. — To every action there is always an equal and 

 contrary reaction, or the mutual actions of any two bodies 

 are ahvays equal and oppositely directed. 



If we replace " bodies " by " particles " — for the mutual 

 action of two bodies is more complex than a reader just 

 starting his study of mechanism would imagine, if he 

 naturally interpreted mutual action as corresponding to 

 mutual acceleration in some one line — the above law is 

 identical with our Fifth Lazu (p. 303), and therefore we 

 need not repeat the qualifying discussion of our § 1 1. 

 See Appendix, Note LL. 



1 It is worth noting that Lord Kelvin has been foremost in insisting on 

 the multiconstant character of elasticity, a property which is certainly most 

 readily described by this very hypothesis of modified action. 



