Dr Searle, Calculation of the electrical resistance, etc. 111 
Calculation of the electrical resistance of a certain network 
of conductors. By G. F. C. Searuez, Sc.D., F.R.S., University 
Lecturer in Experimental Physics, Fellow of Peterhouse. 
[Read 8 February 1915.] 
§1. The system of conductors is thus described in a question 
set in the Mathematical Tripos, Part I, 1914: 
“Two uniform cables A,A,..., B)B,... are divided into parts 
A,A,, A, Az,..., B,B,, B,B,,..., each of resistance r, and wires, 
each of resistance s, are used to join An etO) Di Als. GOoBax. ees 
When the cables are joined by the n wires ‘A iB, A, a cae ALB 
the resistance of the system from A, to B, is Ry. 
Ag 
—_—_=— —_ — — = 
Bo 
Fig. 1. 
Fig. 1 shows the system when n= 3. 
In order to obtain the value of R, as a function of n it is 
necessary to obtain a formula of reduction by which RF, is found 
in terms of R,_,. The necessary electrical equation is very easily 
found, if it is noted that the resistance between A, and B, when the 
cables are connected only by the n—1 wires A,B,, A;B;,... AnBr 
is equal to h,,. Then R, is the resistance between A, and B, 
in the system shown in Fig. 2, where A, and B, are joined by the 
Ao Ay 
rT 
Rn-1 
T 
Bo By 
Fig. 2. 
two conductors s and #,_, “in parallel.’ Hence we find, what 
candidates were asked to prove, that 
shy 
R, =2r+ Sane Bdge vee unease ceria Ly) 
