292 M. L. Lorenz on the Identity of the 



will show that other values are also possible. The first equa- 

 tion (A) may also be written in the following manner : — 



c 

 which expression in the case of a= ^ leads us back to the first 



equation (1), whereas, if a were. assumed to be infinitely great,it 

 would obtain just the form which would result from Neumann's 

 electrodynamical theory. And as this theory also agrees with 

 experiment, it is obvious that a is not defined by it, and must 

 for the present be regarded as an indeterminate magnitude. 

 Yet it must be very great, of the same order as c, to allow the 

 following members of the series to be considered infinitely 



c 

 small. If, for instance, a= —7=, the above equation will repre- 



v 2 

 sent a mean between Weber's and Neumann's theories. 



It now becomes necessary to obtain, in another manner, a de- 

 termination of these undefined constants, and, if possible, seek a 

 confirmation or correction of the results found. It might then 

 be attempted, by using the indication of the formula, that 

 electrical actions require time for their propagation, to find a 

 probable hypothesis of the mode of action of dynamical elec- 

 tricity, by which results might be obtained similar to those already 

 found. I have found that this may be effected in several ways ; 

 this method, however, quite loses its value, because its signi- 

 ficance would entirely depend on finding an hypothesis which 

 in and for itself is more probable than all others. After careful 

 investigation of this point, I have completely given up the idea 

 of getting any good from physical hypotheses ; and we can only 

 develope the consequences from the results found, and. inquire 

 whether this does not furnish an indication towards answering 

 the question. 



For a given function </>, provided the point x y z is within 

 the limits of the integral, we have 



where 



(^)JI)'^'*H.-^) 



= — 4nr<j>{t 9 x,y 3 z) } _ 



d* d 2 d 2 

 A 2 is written for -^+_ g + _ s . 



(5) 



The proof of this theorem, which moreover is not difficult to see, 

 is found in my paper in Crelle's Journal, vol. lviii. By its aid 



