388 Dr. Gerlach on the Mechanical Theory 



Now 



a : a,= L w _i^±Mn ; r.,^+&-- (a '" i+ f c/ i 



L « + & J L « 1 H-6 J 



= ~~n:\ v ~ c ) • — n( v ~ c ) 

 _ ?;— c #(«! + £)(?;— c) 



_ v — c aa^v + abv^abc — aa^ 

 ~ v l —c aa 1 v l -\-a l bv 1 —a ] bc — aa l c 3 

 hence 



A : Aj = (?; — c) : (v l —c). 



If c is negative, 



AMjss^ + o): (»i'+'c) J 

 and if c = 0, 



A : A y = v : v v 



E 



4/3. Of two closed batteries, let one have the intensity ~, the 



K 



IV 



other the intensity ^. Let both conducting wires be cut, and the 



ends of the one be joined either with the similar or the dissimilar 



EX K 

 ends of the other, by which the intensity -5 — ^ is obtained. 



E -K+ W E 



Moreover let the battery ^ be replaced by another battery -—, so 



that with a particular manner of joining the two the intensity in 

 question is unchanged. What is then the ratio of the losses A and Aj 

 of vis viva which are experienced on the one hand by the batteries 



E K E K 



t7 and ^7, and on the other the batteries ~ and ==• 

 R W R x W 



From what has been said, as well as from an independent solu- 

 tion, it follows that 



. . /E , Ka /E, K\ 



if 



E + K _ E, + K 

 K + W -Rj + w' 

 and that 



. E E, 



A:A '-r : b; 



if ^ simply denotes a conductor. 



