Notices respecting New Books. 159 



particles which can be no other than * the renowned fundamental 

 equation of Bessel's theory of the pendulum " ! ! 

 This equation is 



#^=-("'+»i) (»> 



These two equations form the basis of this new theory of Optics ; 

 and it is difficult to see that it obtains from them any firmer 

 support than the other theories which have been put forward do 

 from the special form of reaction assumed in each of them. In 

 fact, as Ketteler has shown himself, the theory is, except in one 

 point which seems hardly essential, identical in its results with 

 that which follows from supposing that 



Helmholtz puts 

 and Lommel 



F(|,0=/3 2 | 2 (4-£). 



r(^,r)=/3 2 ^-o. 



The equations are integrated (on pages 98 and following) and 

 lead to a formula connecting the refractive index and the period 

 which has been verified by careful experiments by Ketteler, and is 

 undoubtedly an exceedingly close approximation to the truth. 



Ketteler's own equations (VII ) (p. 98), with his interpretation 

 of the constants, seem to contradict the third law of motion com- 

 pletely, though a slight alteration in the meaning of the con- 

 stants will remove this fatal difficulty. 



The foundations of the theory of double refraction appear to be 

 even less secure. The quantity denoted by B in equation (2) is 

 supposed to be a function of the direction — for a transparent 

 medium g' vanishes. The displacements are shown not to be in 

 the wave-front, and while in the term v 2 £ the whole displacement 

 is introduced, in the other terms, it is only the component of the 

 displacement resolved in the wave-front with which we have to 

 deal. It is assumed that aether and matter-particles vibrate in 

 parallel directions, and from this it follows that C is a constant 

 independent of the direction. The complete equations are given 

 on p. 309. 



The surface conditions developed by Ketteler are not those 

 which hold between two elastic solids. His fundamental prin- 

 ciples are given correctly on p. 1.30, but in applying (1), " the 

 principle of continuity," he neglects the resolved part of the dis- 

 placement normal to the interface, and hence avoids the dif- 

 ficulty of dealing with the pressural wave of Green's theory, which 

 he considers (p. 275) has played " eine ominose Bolle" in theore- 

 tical optics. 



* The italics are ours 



