Simultaneity and the JEtliev. 529 



considering a small triangle in S, whose sides are formed 

 by two lines M ; , M", which pass through Q', diverging 

 slightly from the supposed two lines of instantaneous 

 codirectionality, sind whose base is the track of a specific 

 point Y" of L, we see that the point B/ of inter- 

 section of L, first with W, and then with M/', travels 

 along L to Q', and then along L in the reverse direction to 

 meet, the point P /; . But, by taking the lines M', M", suffi- 

 ciently near to the critical directions the velocity of B/ can 

 be increased beyond any assigned limit, while that of P" 

 travelling through S remains finite. We should therefore 

 have two points proceeding over finite distances, the one 

 at a finite, the other at an infinite velocity, and reaching 

 the same point together, a thing which no question of time 

 units can render conceivable. It will be noticed that the 

 velocity of B along L is in no respect limited by, or in 

 any way dependent on, or connected with, the velocity of 

 light, which does not enter into the question at all. 



Some additional considerations are perhaps called for here 

 as being necessary to justify the attribution of a definite 

 sense of motion along L to the phase point H, where the 

 velocity exceeds that of light. For this purpose we mav 

 for simplicity suppose that the surface S is the plane of the 

 paper, and conceive an apparatus in which two very fine 

 split needles Nj and N 2 are pivoted about points O x and 2> 

 Oi and 2 being out of and above the surface 8, and situated 

 near the tangent to M through Q, and on opposite sides of 

 M with respect to Q, where Q is no longer taken as the 

 terminal point of M. Nx and N 2 are free to move in such 

 a way that each always touches M at a point, and they are 

 set iniiially with their extremities passing through S, very 

 close to Q, the needles making very small angles with M 

 where they touch the latter, and each touching M at the 

 same side of Q as its own pivoting point. 



Nj and N 2 are now caused to move so that, as L slides 

 over S, the point where ea>ch touches M continually coincides 

 with B. In this motion of L one needle will be struck by 

 L on the lower edge and raised, while the other needle will 

 be struck on the upper edge and depressed, and the direction 

 of motion of B along L can be defined according to the 

 particular needle which is struck on its upper edge. In this 

 apparatus Oi and 2 can, except for the limiting direction, 

 always be chosen so near to the tangent to M at Q, that no 

 portion of the needles need have a velocity as great as light, 

 although the velocity of B at P may be many times greater 



Phil. Mag. S. 6. Vol. 43. No. 255. March 1922. 2 M 



