/)/?/( 7.v(;-/'(»/.v/ iMi'iiD.isci: of nfo-Mrsii ciRcrns <in^ 



riiiis ciMulilions (4) {(») an- obtaiiu'd diai tl> frmu (.'iS) ((iO». Tin- 

 Ull-h.ind iiuiuIhts of ("iS) (tiO) salisfv the i(U'nlit\ 



+ (/.,,/?,.,. - /,,,/?,,.)/),... = 0. (til ) 



Sul)siiiutin^; (ol)-(n3) and (n8) -((50) in this idi-ntity ((>1 ). and r.iiional- 

 i/inn. i'<iiiaiit>n {'-i) and its equivalent (21) are i>l)iaine<i. 

 l-"i>r the jjeneral network of Kij;. 7, 



Lu=Lx'+u, L„ = w. /..■..=/.;+/.;. 



/?„ = /?,+/?;. /?,., = /?•.. Rvi = Ri+R^, ; (••2) 



Dn = D: + Ih. Dvi^Ih. /)■..■• = />- + /)3. • 



wliere L/, L«' . and Li are defined by (17) (HI). For this set of ron- 

 siants. branch "2 is made the i)ranch common to tiie two meshes; the 

 choice of branch 3 as the common branch would not affect the final 

 fornuilas. Substituting these values ((52) in (4()). (o4), (oO) (o.i), 

 and (.")8) (60). ecjuations (7)-(15) are obtained directly. 



Thus Theorems I and I\' are completely proxed. Theorems II 

 and III are \erifie<l by the actual formulas for the elements given in 

 Tables I and II, and by the census of networks presented in Table III. 



I am indebted to Dr. (ieorge A. Campbell for ins()iring the writing 

 of this pa|x?r and for six-cific advice upon many points, and to Miss 

 Frances Thorndikc for the preparation of the tables and figures. 



