Indeed, if llie eluslir loire luid tlie iiileiisilv oorrespondiiig to this 

 tbnmda, the s((iuire oF the freqiioiev of (lie free vibrations would 



liave, bv (7), the vabie »,/ -\ . The e(|ualion ';15) woidd then 



take the form (17). 



In the next paragraphs the hist tei'ni in (19^ will however be 

 omitted. 



As to the time t, it will [)e found to be considerably shorter than 

 the time between two successive encounters of a molecule. Hence, 

 if we wish to maintain the conception here set forth, we must sup- 

 pose tiie regular succession of vibrations to be disturbed by some un- 

 known action much more rapidly than it would be by the encounters. 



We may add that, even if tliere were a resistance proportional to 

 the velocity, tjie vibrations might be said to go on undisturbed only 

 for a limited length of time. On account of the damping their amplitude 

 would be ronsideral)!y diminished in a lime of the order of magnitude 



»t 



— . This is comparable to the value of t which, bv (18), corresponds 



9 



to a given magnitude of //. 



§ 7. The laws of propagation of electric ^•ibrations are easily 

 deduced from our fundamental equations. We shall begin by sup- 

 posing that there is no external magnetic field, so that the terms 

 with § disappear from the equations (14). 



Let the propagation fake place in the direction of the axis of z 

 and let the components of the electromagnetic vectors ail contain 

 the factor 



e'" '-?--', ......... (20) 



in which it is the value of the constant q that will chiefly interest 

 us. There can exist a state of things, in which the electric vibrations 

 are parallel to X and the magnetic ones parallel to Y, so that 

 ^'ï) '^i, ^x i^iid -^P,, are the only components differing from 0. Since 

 diiferentiations \\itii respect to t and to c are equivalent to a 

 multiplication by in and by — I n (j respectively, we have by 

 [2) and (3) 



1 1 



q .Py =—£);„ q (l-j. = — Spy . 



Hence 



and, in virtue of (1), 



2>,, = r' q' ti\ 



The llrsi of iho e([uations (14) leads therefore to the following 



