equal electrical resistances. 349 
linear conductors the arrangement may be represented diagram- 
“matically by Fig. 5. The resistances of the parts of the connectors 
are represented by p, q,", $, h, k, as shown in Fig. 5, and these 
“resistances are very small compared with A or B. 
Fig, 5, 
: When A is in the left gap with a shunt a, while B is in the 
right gap with a shunt 0b,, the resistances of the compound con- 
~ ductors between U and W and between V and W are 
(A+p+Q)% / (B+r+s) b, 
as Gee 
A+p+qt, B+r+s+b, 
When the coils A and B are interchanged and the new shunts 
are d, and 6,, the corresponding resistances are 
Ca py eye ae Daa 
ere 4: 
As— EY far tat Gy’ Beptgt ls’ 
Aly iB Hale dey 
Since wD) and Dp 6 
we have ALA = R/ BuBy Se tak ee re eS (8). 
On replacing the geometric means in (8) by the arithmetic 
means, the quantity $(h +) cancels and we have 
,(Atptya , Gare 
2\A+ptqta, A+trt+st a 
ne GA e ae) or Ores o 
72 \Berts+l, B+p+q+b, 
a : A+pt+q a. A+r+s 
y 2114(Atptgia 1+(A+rts)[a 
ae eS a B+p+q . 
2114 (B+r+s)/b,  1+(B+pt 9/5) 
