Intelligence and Miscellaneous Articles. 379 



If we develop the left side according to sin- and cos- and put 

 their factors singly =0, we get two equations for B and I : — 

 J o A + W BcosS-?^sinS = 0; 



W BsinS+?^cosS=0. 



From the last equation it follows that 



t«J=-^ (2) 



The change of phase is therefore the greater the smaller T is — that 

 is, the higher the tone is. For the amplitude we find 

 -r> AJ n cos£ 



or 



W 



B= AE 



W 2 A , 4tt 2 Q 2 



V W 2 T 2 



From this formula it follows that the amplitudes are not all altered 

 in equal measure, but they become proportionally smaller for tones 



for which is greater. But this becomes smaller for T greater ; 





 that is, the higher the tone the smaller will be its amplitude ; and this 



47T 2 Q 2 



is so much the more the case the greater 2 is — that is, the less 







the resistance and the greater the value of Q the electrodynamic 

 potential. Large coils, therefore, especially with iron cores, operate 

 prejudicially. 



In his article " Telephon und Klangfarbe"*, Helmholtz showed 



4- 2 2 

 that with the telephone also it depends on the expression ^ 2r p 2 , 



but in exactly the inverse sense, so that in the telephone the higher 

 tones have the advantage over the deeper ones — thus giving the 

 peculiar result, that in the telephone the tone is heightened, but in the 

 microphone it is made deeper. 



A combination of the telephone with the microphone can now be 

 produced in which the electric conveyance operates generally no 

 change in the tone. This combination is to serve for the giving, 

 while for the receiving instrument a telephone is made use of in 

 the usual manner. If we further denote by M the fluctuation of the 

 magnetic moment in the telephone of the giver, we find the follow- 

 ing as the equation for the current- waves excited by means of such 

 a system, in accordance with the above way of considering the sub- 

 3 ect : ~ T , w . dM n di 



* Wied. Ann. v. p. 448 (1876). 



