800 M. L. Loreriz on the Identity of the 



and the designation O be introduced, after another integration in 

 reference to t we have 



MS— 2* 



(dfL 2 du\ 

 \cLv + a*dt)' 



Since we kave a \/2 = c, we have returned to the first equa- 

 tion (A) ; and the two others may by analogy be deduced from 

 this. The constants which should have been added in the two 

 integrations in reference to t have been here omitted, because it 

 is clear that such arbitrary constants would have no significance 

 in the present case. 



This result is a new proof of the identity of the vibrations of 

 light with electrical currents ; for it is clear now, not only that the 

 laws of light can be deduced from those of electrical currents, but 

 that the converse way may be pursued, provided the same limiting 

 conditions are added which the theory of light requires. Thus we 

 are in a position to deduce by calculation alone the inducing 

 action of free electricity as defined by KirchhofFs equations (2), as 

 well as the inducing action of variable electrical currents, borh 

 of which are contained in equations (A), by simply starting from 

 those facts which are necessary to deduce the laws of light, and 

 afterwards adding a single member to the differential equations 

 found between the so-called components of light. This member ex- 

 presses in a correct manner the absorption of light in good conduc- 

 tors of electricity, and disappears for perfectly transparent bodies. 



Without dwelling more minutely on the consequences of the 

 results obtained here, which manifestly lead us a step further to- 

 wards developing the idea of the unity of force, and open a fresh 

 field for future inquiries, I shall in conclusion call attention to the 

 conclusions which we are entitled to draw with some degree of 

 probability as to the mode of action of light, and how we are 

 placed as regards the physical hypotheses concerning light. 



Were we to attempt to represent the laws of electrical currents 

 in such a manner that they would be generally valid for given 

 heterogeneous bodies, and not merely for homogeneous bodies 

 with constant conducting-power, this would appear to be best 

 effected by starting from the differential equations, and regarding 

 a and k as variable magnitudes. This would be more especially 

 in agreement with the general equations found in the theory of 

 light for heterogeneous media ; besides, those limiting conditions 

 which must be fulfilled for homogeneous bodies would then be 

 contained in the differential equations and could be deduced from 

 them. In this manner, however, a form corresponding in sim- 

 plicity to the equations (A) could not be attained for hetero- 

 geneous bodies; and this must then be considered a special 

 case obtaining alone for homogeneous bodies, while the differen- 



