292 THE GRAMMAR OF SCIENCE 



are not compelled to consider the distance AB vanishingly 

 small like the dimensions of the particles themselves.^ 

 On the other hand, there appear to be many physical and 

 even chemical phenomena which cannot be described by 

 replacing the motion of a prime-atom, chemical atom, or 

 molecule by the motion of a point. In this case the line 

 joining the two corpuscles becomes a meaningless term, 

 and we have really to deal with the relative motion of 

 groups of elements, constructed very probably from the 

 motion of simple ether-elements. 



When, however, we ask of ether-elements whether we 

 are to consider them as mutually accelerating each other 

 in the line joining them, we are at once stopped by the 

 difficulty that we have reason for supposing non-adjacent 

 ether-elements do not influence each other's motion at all 

 (p. 286). But if we turn to adjacent ether-elements, the 

 line joining them vanishes with the dimensions of the 

 elements when we try to conceive the ether as absolutely 

 continuous (pp. 178, 271, and 290). Discontinuity of 

 the ether may carry us over this difficulty and allow us 

 to consider ether-elements as mutually accelerating each 

 other's motion in the direction of the line joining them, 

 but such discontinuity reintroduces one of the problems 

 which the conception of the ether was invented to solve 

 (pp. 178 and 274). We may be quite safe in postulating 

 that when an ideal geometrical surface is supposed drawn 

 and fixed in the ether its points will have a motion rela- 

 tive to each other upon its form being changed ; the 

 points of the surface will tend to return to their original 

 positions with accelerations depending on their change of 

 relative position. But when we assert that this is due to 

 ether-elements mutually accelerating each other's motion 

 in the line joining them, we may, after all, be postulating 



1 It will be noticed in this case that if we take the motion of A relative to 

 B, the ray and tangent to the path or orbit of A are respectively parallel to 

 the tangent and ray to the hodograph or path of Q. This is expressed in 

 technical language by saying that the orbit of such a motion is a link-polygon 

 (funicular polygon) for the hodograph as a vector-polygon (force-polygon), 

 and this forms the basis of a graphical method of dealing with central ac- 

 celerations. 



