Prof. Lorenz on the Theory of Light. 413 



mical forces. Hence, conversely, only the fundamental equa- 

 tions can be in turn deduced from these phenomena, but nothing- 

 like a physical theory : as well might we expect to deduce such 

 a theory from the phenomena of reflexion in a concave mirror or 

 from the refraction of a lens, as from diffraction or double refrac- 

 tion &c, On the contrary, the physical explanation is probably 

 hidden under the unknown forces already referred to. 



If we now try to find the three partial differential equations 

 which are to be the foundation of the theory, we soon discover 

 that the intensity and plane of polarization cannot be directly 

 introduced into such equations, but that auxiliary magnitudes 

 dependent upon these must be taken instead. Let these auxi- 

 liary magnitudes be f, r), J; they may be spoken of simply as 

 light-components. I will not now dwell longer upon the manner 

 in which the three differential equations are arrived at in my 

 former memoir ; for after they have been found it is immaterial 

 how this has been done ; their truth must be evidenced by their 

 capability of accounting for all the phenomena of light, with the 

 exception of those which depend upon unknown forces. These 

 equations, in a somewhat altered form and without the dashes 

 over the components, are as follows : — 



d_(d% _ dn\ d_/c% _ d£\_ 1 d*% 



?/ dz\dx dz/~ cd* 



dy\dy dx) dz\dx dz) a? df- 



Ll d A _ ^\_ _f*7^? _ c h\- JL ^ 

 dz \dz dy) dx \dy dx) ~ a? df i 



dx\dx dz) dy\dz dy) 



>. • • (A) 



df 



In addition to these equations, and complementary to them, 

 we have two others, which express the dependence of the inten- 

 sity and the position of the plane of polarization upon the com- 

 ponents £, rj, £ the intensity of the light being determined by 

 the equation 



and the plane of polarization by the equation 



£(xi-x)+ V (y'-y) + Z(zi-z)=Q } 



where x\ y f , z' are the current coordinates of this plane. The 

 components are therefore proportionate to the cosines of the 

 angles which the perpendicular to the plane of polarization 

 makes with the three axes of coordinates respectively. 



The magnitude co is a function of x, y, and z, which for homo- 

 geneous media becomes a constant. In these cases the equations 

 assume a well-known simple form, whence the well-known laws 



