Prof. Lorenz on the Theory of Light, 415 



complete manner ; and the results of his calculation have been 

 universally confirmed by experiment. The suppositions from 

 which he sets out seem, nevertheless, at the first glance quite 

 opposed to ours : his luminous vibrations are situated in the 

 plane of polarization and in the plane of the wave, the inten- 

 sity of the light is measured by the square of these vibrations, 

 and, finally, his four limiting conditions are quite different from 

 ours. If, however, we disregard the arbitrary physical significa- 

 tion which he has assigned to his light- components, it appears 

 at once that he has used different auxiliary magnitudes from 

 ourselves. We will denote these new components by P 3 r/ } f, 

 and we will in the first place investigate the relation between 

 these and our own. 



In the previous memoir it has been shown that, for a periodi- 

 cally heterogeneous body, the components £, t], J can be deve- 

 loped in series whose terms contain the variable factor 



cos(&£ — Ix— my — nz— A), 



wherein k, I, m, n are constants, and A, on the other hand, in 

 general a function of x, y, z, which becomes a constant in the 

 first three terms only. The portion of these series which con- 

 tains A as a variable, indicates a periodic motion changing with 

 the periodicity of the body ; while the other portion of the com- 

 ponents, which we will denote by f g , rj 8i £ s , represents the proper 

 visible motion propagating itself in plane waves. 



In accordance with the differential equation (A), we have 



k 2 



— 2 % = m{mg- l Vt ) -n(Z?- n% s ) + . . . . , 



the subsequent terms containing merely the other portion of the 

 components. By multiplication by f we get from this equation 



5 r =«f>f -i%) -<(#.-«!.)+. • • • 



The intensity of the visible light, which we will denote by I s , is 



that portion of the expression — d^ + ^ + f 2 ) which contains A 



only as a constant; and to determine this we easily get the 

 equation 



i.= I* [N -■o* + K- »h)* + «- W] • 



The same intensity, expressed by means of Neumann's compo- 

 nents, gives 



Besides, f a , i? s , f s are proportional to the cosines of the angles 



