198 THE GRAMMAR OF SCIENCE 



type of motion, corresponding to change of position, is 

 termed motion of tra7islatio7i ; the second type, correspond- 

 ing to the change of aspect of a rigid body, is termed 

 motion of rotation. 



% -x. — Ricrid Bodies as Geometrical Ideals 



Just as the former motion is described by the purely 

 ideal conception of a point moving along a curve, so the 

 latter is also made to depend on geometrical notions, 

 namely, those of a rigid body turning about a line passing 

 through a point. What, in the first place, do we mean by 

 using the term rigid body ? The real man is moving his 

 limbs and bending his body, and generally changing his 

 form at each instant of the motion. Now the reader 

 may feel inclined to say : Replace the man by a 

 wooden table or chair, and we shall have a rigid body. 

 But this is only popular language, and what we are seeking 

 is an accurate or scientific definition of rigidity. Such 

 a definition is usually given in the following words : — 



A body is said to remain rigid during any given 

 motion when the distances between all pairs of its points 

 remain unaltered throughout the whole duration of the 

 motion. 



But we see at once from this definition that we have 

 replaced the real body, the group of sense-impressions 

 which forms part of the picture constructed by our 

 perceptive faculty, by an ideal geometrical body possess- 

 ing " points," and that it is a property of this body — exist- 

 ing only on the ideal map on which conception plots out 

 preception — that we are defining. It is quite true that 

 the geometrical ideal of a rigid body is a better descrip- 

 tion of a wooden chair than of the flexible body of a 

 man ; yet what is a " point " on the chair, and what is 

 the '' distance " between a pair of points ? How, again, 

 am I to ascertain accurately that such distances remain 

 unaltered during the motion ? The very idea of distance, 

 when clearly appreciated, involves the geometrical con- 

 ception of points and does not correspond to anything in 



