THE LAWS OF MOTION 291 



they are changing their relative position. Tivo co?'puscles 

 may be moving through the same position zvitJi any veloci- 

 ties^ bnt they will spurt and shmit each other's motions in a 

 perfectly definite manner, depending on their relative position. 

 If A and B represent two corpuscles moving relative 

 to the " frame " in the directions AT and BT' with the 

 velocities V and V' given by the steps OQ and O'O' 

 of their respective hodographs (p. 220), then the spurt 

 and shunt of V and V', or, as we have seen (p. 221 ), the 

 velocities of Q and Q' along their hodograph paths, will 

 be determined at each instant by the relative position of 

 A and B. Let these velocities of Q and Q', or the ac- 

 celerations of A and B, be represented by the steps Ot 



Fig. 22. 



and O'/ taken along the tangents at O and O' (pp. 216 

 and 224). Then the question naturally arises, How are 

 we to consider the spurts and shunts given by Q/ and OY 

 (p. 222) to depend on the relative position of A and B? 

 In the first place we conceive Ot and Q'/ to be parallel, 

 bnt in opposite senses (p. 207). We find it needful to 

 suppose universally that the mutual accelerations of cor- 

 puscles have the same direction but opposite senses.^ In 

 the next place it is usually assumed that this direction is 

 that of the line joining the points which represent the 

 corpuscles A and B. Now this assumption is possibly 

 correct enough "' when we are dealing with particles of 

 gross " matter," at any rate when we are discussing the 

 motion of non-adjacent particles, or those for which we 



1 That is, if A spurts B in the direction from B toward A, then B will 

 spurt A in the direction from A to B and vice versa. 



2 See Appendix, Note II. 



