518 
When we now consider that: 
wu + eee bre (7) 
B Dee crd vore ie) 
and 
4 duw 
u an te ee eee rau ree (2) 
we find, after substitution of this in the formulae (5) and (6), and 
after subtraction for the entire phase difference of the two rays 
that: — 
nn Ae i ) 
nh nd 
or, on reversal of the direetion of motion, an optical effect: — 
ns 4 ue 9) 
=— 2 = lee shige Wnts Ss ear ( 
With regard to the dispersion term it is still noteworthy that 
in Fizrau's experiment with water the light is transferred from 
: 2 W OE 5 
standing water to moving: water, and or must be written in the 
c/u 
4 w 
formulae instead of —. 
Cc 
10. Derivation of formula (9) from the theory of relativity. 
After we had communicated formula (9) to Prof. Lorentz, he had 
the kindness to give us a derivation strictly from the theory of 
relativity, which will follow here. 
Let 2’, ¢’ be a system of coordinates, in which the rod AB is at 
rest; length of the rod /. 
Light motion on the lefthand side of A: 
a \ 
acorn! (¢ —= + ph) REA ca (JI) 
c 
a! 
a, cos n° (« ——-+ P's) 
v 
On the righthand side of B: 
a, cos n c= +P) A MSE eet (4) 
¢ 
v’ velocity of propagation belonging to n’. 
We easily find: 
In the rod: 
1 1 
weert) gone ar) 
