534 THE GRAMMAR OF SCIENCE 



A line, the points of which are conceived as having no relative 

 accelerations in the direction of the line, is defined as having 3. fixed 

 dircctioji in space. Perceptually a material straight line, string or 

 wire, removed from the influence of other matter, is to be represented 

 on the conceptual model by a line " fixed in direction," provided that 

 when it is cut in twain there is no tendency for its parts to separate, 

 or they still appear as the parts of a continuous material straight 

 line. 



Given a perceptual body, which can be conceptually represented 

 as rigid, how are we to ascertain whether it is to be conceived as 

 spinning or not ? For example, is the earth rotating about its axis, 

 or is the whole vault of the heavens itself turning round — which will 

 best enable us to describe our perceptual experience ? The answer 

 lies in determining whether a line drawn perpendicular to the axis of 

 the earth is to be conceived as " fixed in direction " or not. Theoretic- 

 ally we might determine the problem of the earth's rotation in the 

 following manner. Fix perpendicular to the axis of the earth a wire, 

 the parts of which are not subjected to gravitation or to the resistance 

 of the atmosphere, and observe on its being divided whether the parts 

 remain the continuous parts of a material line or not. This experi- 

 ment would of course be impossible, but it may bring to the reader's 

 mind what Newton understands by absolute roiatiott. The effect, 

 however, of the relative acceleration of the parts of the earth, if it 

 exists, may be measured in other ways. For example, it would lead 

 to an apparent lessening of gravitational acceleration at the equator, 

 and, if the earth were not quite rigid, to a flattening at the poles. 

 When, therefore, without rearranging any other portions of gross 

 " matter " we can have a body in two states, in the one of which no 

 mere division of the parts leads to discontinuity of the body as a 

 whole, and in the other mere division does lead to discontinuity, then 

 in the latter case we suppose that there will be, and in the former case 

 that there will not be relative acceleration of the parts. When this 

 relative acceleration of the parts manifests itself, although the 

 elementary parts may have no relative velocity in the line joining 

 them, we can describe it by aid of a spin about some axis. Since 

 this spin does not seem to have reference to any external system, 

 Newton termed it absolute motio7i of rotation. The name is an 

 unfortunate one, as it suggests the possibility of an absolute motion 

 (p. 206). What we have to deal with are perceptual facts which can 

 only be conceptually described by supposing points at different dis- 

 tances from the earth's axis to have different velocities relative to the 

 stellar system. The. Jixity of directioit in a line which we have con- 

 ceptually defined by absence of mutual acceleration between its parts, 

 appears to coincide with fixity of direction relative to the stars, but it 

 must be remembered that Galilei first stated the principle of inertia 

 for bodies moving with regard to the earth, because the motion of the 

 earth relative to the stars was insensible for most motions at its 

 surface. It in no way follows that Newton's extension of the 



