264 BULLETIN OF THE UNIVERSITY OF WISCONSIN. 



Lommel 1 makes the same arguments as Helmlioltz except for 

 the force A, but considers the "action to follow Newton's law of 

 friction," and, hence, his fundamental equations become : 



d 2 u d 2 u d „ 



m d^ = a2 d^" T/ * a dt (IJ - u) (22a). 



d a U d dU 



m ' dF= ± ^dt (U ~ u) ~ aJ U-r 2 df (22b), 



Lommel gave the first set of signs but Ketteler 2 and Voigt 3 

 argued that the lower set should be used. Lommel 4 replied, 

 still defending his first position, but, in the opinion of Glaze- 

 brook, 5 without success. 



Solving equations (22) and (23) 



B a _AT/ _A*_ \ 



mm' A» m \A» m _1 / 



M 2 o~ X2 o — 1= /—* \1 7~B' \ s A 2 (23a). 



(A. 3 V / B' V A. 2 



B' 3 /B 2 



„ v B' A 3 mm' \m' / m 



Ketteler 6 makes a third suggestion. He supposes the action be- 

 tween ether and matter to be proportional to the acceleration in- 

 stead of the velocity as suggested by Lommel, therefore, ex- 

 pressing the force A thus : 



<5 2 

 A = ^(U-u) ( 24). 



The resulting equations when solved can be reduced to those of 

 Helmholtz by making Ba 2 == B". Ketteler 7 has written a large 



1 Lommel, Wied. Ann. III., p. 339. 

 3 Ketteler, ibid. XVIII., p. 387. 

 » Voigt, ibid. XVII., p. 468. 



* Lommel, ibid. XIX., p. 908. 



5 Glazebrook, B. A. A. S Report, 1885. p. 222. 



• Ketteler, Theoretische Optik, p. 78. 



7 Ketteler, Wied. Ann. XVI., p. 86; XII., p. 383; XV., p. 613; XVIII., pp, 337, 631; XXI., 

 pp. 199, 178; XLIX., pp. 382, 509; LIII., p. 823. 



