1875.] Theory of Duplex Telegraphy. 61 



(i). Any variation of the resistance in the total system has the least 

 possible disturbing effect on the receiving instrument. 



(ii). Any disturbance of balance can be eliminated by an appropriate 

 movement of the two acting coils or their armatures, without 

 disturbing balance in the distant station. 



(iii). Conditional maximum magnetic moment of the receiving instru- 

 ment. 



(iv). Conditional maximum current. 



Addendum I. 

 Here I wisli to give some additional explanations and corrections with 

 reference to the 1st and 2nd parts of this investigation. 



In J. A. S. B., Vol. XLIII, 1874, Pt. II, p. 20, I have substituted 

 c' = L' + P " 

 without stating that this expression for <?' is only approximately true. 

 The correct expression for c' is clearly 



l +* + l" + p" 



which approximates closely towards U + p" if I" + p" is sufficiently small as 



compared with i. This for any line in good electrical condition, will always 



be the case. 



At page 9, in the foot note, for " as nearly as possible equal" read " as 



nearly as possible proportional.'''' 



d ' C 

 At page 20, — = L (a* - g*) + 2 a.g (d - g) = o 



d C 

 should be —=— = L (a 2 — g 2 ) + 2 a {a d — # 2 )= o 



At pages 19 and 224 after having shewn that 



a +f=ff + d 

 I conclude at once that on account of equation VI (a d — g f ' = o) 



a=g=d = f ... ... ... VIII 



while mathematically it follows only that 



a=g 

 and d = f 



These two equalities do certainly not contradict equation VIII but they 

 do not necessitate it. 



The additional reason why equation VIII should be chosen follows 

 from the balance condition 



ad — b c = o 



ad 



• • o =■= ■ — 



e 



