462 OHM ON THE GALVANIC CIRCUIT. 



designate by I, I', and I" the lengths of the parts P, P', P" ; and 

 lastly, let w''^ and u-^ represent the values of v!' and u at the 

 place of contact where x = o, and Wg and u' the values of u and 

 u' at the place of contact where x = I, and u'c^ and ii!\ the values 

 of u' and u" at the place of contact where a- = / + V, then we 

 obtain 



U\ =/" (Z + /' + ?") + 6-" U, =C 



U^ —fl + C U\ —f I -ir c' 



u\ =/' {I + Z') + c' u\ =/" (Z + r) + c". 



If we call a the tension which occurs at the place of contact 

 where x =■ o, a' that at the place of contact where x= I, and «" 

 that at the place of contact where ^ = Z + Z', we obtain, if we 

 pay due attention to the general rule stated in the preceding 

 paragraph, 



a =/" (Z+ V + 1") + d'-c 



a! =fl-fl + c-d 



a"=/'(Z + Z')-/"(Z+Z') + c'-c", 

 and hence 



a 4- a' + a!' =f I +/' V + /" Z". 



But from the considerations developed in § 13, when x and 

 w represent the power of conduction and the section for the 

 part P, / and J the same for the part P', and jc" and co" for the 

 part P", at the individual places of contact, the following condi- 

 tional equations are obtained : 



^du\ ^ ^, ^, {dy[\ _ ,j, J, /du"\ 

 \dx) \dx/ \dx )' 



where ( -r- ), ( -j— )i ( 7 — ) represent the particular values 



of -T-, -j—, -j — , belonging to the places of contact. From 



the equations stated at the commencement of the present para- 

 graph for the determination of the electroscopic force in the 

 single parts of the circuit, we obtain for every admissible value 

 of ^, 



Tx^-'' 'dhc'^^ ' Tx'^J ' 

 by which the preceding conditional equations are converted 



into 



x«)/= x'a;'/' = x"«;"/". 



From these, and the equation between/,/', and/" above de- 



