For a two active arm bridge with nominally equal resistances, Equation 1 becomes after substitution of 
R1=
R3=0, 
R4=
R, and
R2= -
R4 = -
R:
(1")
(Remember that when R2 is in tension, R4 is in compression and vice versa.
This means that 
R2 and 
R4 will have opposite signs.)
Recalling that the change in resistance of a conductor is linearly related to the strain by:
(2")
(Equation 2 of the Theory of Operation of Strain Gauges).
Rearrange Equation 2" into the form:
(3")
and substitute into Equation 1" yields (after some rearrangement):
(2)
