Prof. Lorenz on the Theory of Light, 419 



find the refractive ratio by means of the serial developments of the 

 former memoir, that it can also assume this more general form ; 

 but it is difficult to indicate the conditions under which this will 

 occur. It appears, however, that this case must arise when the 

 interval between two similar points of a body is not small rela- 

 tively to the wave-length. For this reason, for instance, a trans- 

 parent body ceases to be transparent when pulverized. 



If we now place the results of the former memoir side by side 

 with our present ones, we perceive that our object — namely, to 

 deduce all the phenomena of light, which do not depend upon 

 unknown, electrical or chemical forces, from our fundamental 

 equations — is now attained ; for the explanation of Double Re- 

 fraction, of Circular Polarization, of Chromatic Dispersion, of Re- 

 flexion, and of Refraction results from them as a simple conse- 

 quence. The general theory of diffraction may here be passed 

 by, for it can afford no control of our theory. For homogeneous 

 bodies, it is easily deducible from our equations ; but as soon as 

 the phenomenon is complicated with simultaneous reflexion and 

 refraction, the difficulty lies even more in finding the conditions 

 which correspond to each particular experiment than in the cal- 

 culation itself; and agreement between calculation and experi- 

 ment would rather prove that the conditions had been rightly 

 chosen, than be a control of the theory. I think therefore 

 that I may regard the accuracy of our fundamental equations as 

 fully established, and I will in the sequel direct attention only 

 to a few further consequences of the results that have been 

 obtained. 



The periodic coefficient co occurring in our equations may be 

 expressed, as has already been done in the previous memoir, in 

 a general manner by the equation 



where 12, e p , &c. are constants. According to this formula, we 

 consider the body as made up of several systems of parallel layers, 

 whose thickness is ot p , and whose perpendicular makes with 

 the axes of coordinates angles which are determined by their 

 cosines a p , b p , c p . Further, let a, b, c be the velocities of pro- 

 pagation which the components possess in the directions of the 

 three axes, while a lA , a^, a 3)3 are connected therewith by the 

 equations 



X2 2 _ X2 2 _ f2 2 



These last magnitudes, like « 1)2 , &c, in the former memoir, can 

 now be determined from the constants of the body; and for 



