158 hertz's researches on electrical waves. 



Tbeu, if the resistance of the couductor is small, 



m_L 7r-v/P C 



lu the case of the resonance experimeuts, the capacity C was approx- 

 imately the radius of the sphere forming the terminal, so that C=15 

 centimeters. The co-efficient of self-induction was that of a wire of 

 length ?=150 centimeters, aud diameter d=^ centimeter. 



According to Neumann's formula, 



'cos e 



-d s d s', 

 which gives in the case considered 



-//' 



P=2 I { logi^- 0.75^ = 1902«^ 



As however it is not quite certain that Neumann's formula is ap- 

 plicable to an open circuit, it is better to use von Helmholtz's more 

 general formula, containing an nndetermined constant /c, according to 

 which 



P=2/ ('log ^^'-0.75 +^-^^). 



Putting A-=l this reduces to Neumann's formula; for A'=0 it reduces 

 to that of Maxwell ; and for fc= — 1 to Weber's. The greatest difference 

 in the values of P obtained by giving these different values to 1c would 

 not exceed a sixth of its mean value, aud therefore for the purposes of 

 the present approximation it is enough to assume that k is not a large 

 l)ositive or negative number; for if the number 1902 does not give the 

 correct value of the co-efficient for the wire 150 cm. in length, it will give 

 the value corresponding to a conductor not differing greatly from it in 

 length. 



Taking P = 1902*^"'., we have tt v'C)T'=531''"'., which represents the 

 distance traversed by light during the oscillation, or, according to Max- 

 well's theory, the length of an electro-magnetic aether wave. The value 

 of T is then found to be ( ^ 7r(r,l)o-o;o o o) 1-77 hundred millionths of a second, 

 which is of the same order as the observed results. 



The ratio of damping is then considered. In order that oscillations 

 may be i)ossible the resistance of the open circuit must be less than 



For the exciting circuit used this gives 676 ohms as the 



=^-Vc 



upper limit of resistance. If the actual resistance r is sensibly below 



rj 



this limit, the ratio of damping will be e''\ The amplitude will there- 

 fore be reduced in the ratio 1:2.71 in 



2P_2r / P_676_215 



rT~7rrV C~lr7~r~ 



oscillations. Unfortunately we have no 'means of determining the re- 

 sistance of the air space traversed by the spark, but as the resistance 



