414 Prof. Lorenz on the Theory of Light. 



of the propagation of light in homogeneous media can be deduced, 

 as well as the laws of diffraction (when this is not complicated 

 with simultaneous refraction and reflexion), those of interference, 

 of the polarization of the diffracted ray, and of the decrease of 

 the intensity of the light emitted by a luminous point with the 

 square of the distance. I need not now stay to discuss the man- 

 ner in which these laws are deduced from the familiar equations, 

 and I will consider it as well known and established that the 

 equations are true for homogeneous media. It results from the 

 form of the integrals that light may be regarded as a wave-motion, 

 without nevertheless our being able to form any kind of notion 

 as to the nature of this wave-motion, as must be sufficiently evi- 

 dent from what has gone before. The integrals further show 

 that a) is the velocity of propagation. 



Passing on to heterogeneous bodies, we see at once that the 

 determination of the notions of intensity and plane of polarization 

 is to a certain extent arbitrary, inasmuch as these cannot be expe- 

 rimentally ascertained for heterogeneous bodies. The plane 

 of polarization is arbitrarily fixed as for homogeneous media, 

 while for the determination of the intensity we have the rule 

 that the intensity of all the refracted and reflected light is equal 

 to that of the incident light when the refracting body is perfectly 

 transparent and homogeneous : whether such a medium is actu- 

 ally to be met with in nature is of no consequence. In order to 

 arrive at this, we might have multiplied the components by some 

 power of ft) and then have fixed this power by the condition 

 already made, as was done in the previous memoir; but we shall 

 soon see that this is already accomplished in the above equation 

 of intensity. 



In the previous memoir I have deduced the laws of double 

 refraction, of circular polarization, and of chromatic dispersion 

 from the differential equations; moreover the principles which 

 are to serve to calculate the reflexion and refraction of light 

 result from the integration of the equations, inasmuch as I have 

 found that the four magnitudes 



dec dy dec dz 



have the same value on both sides of the plane of coordinates 

 y z y which we assume as the limiting surface of the two media. 

 Before trying to develope further the consequences of the results 

 already obtained, I will show how a theory of the reflexion and 

 refraction of light which agrees perfectly with experiment, may 

 be deduced from the last limiting conditions. 



It is well known that Neumann, in his classical work on the 

 reflexion and refraction of light, treated this problem in a very 



