The quest for an understanding of the internal dynamics of the most fundamental systems in nature, the Hadron, continues. The theory of Quantum Chromodynamics, developed to describe these systems, explains many of the interactions which occur in the Hadron. This theory however cannot presently be solved analytically in the low-energy regime, the realm of non-perturbative QCD. Therefore in the place of these solutions, models of the baryon are used which treat the baryon as a system of three constituent quarks. These models however predict an excited baryon spectrum that has a higher density of states than that which has been observed experimentally. This is the so-called “missing resonance” problem. With the ultimate goal of finding evidence for the existence (or non-existence) of these resonances, quantities called “polarization observables” can be measured. These quantities which occur when the constraint of polarization is imposed on the reactions are highly sensitive to resonance production. In recent years, both single- and double-polarization experiments have been carried out at Jefferson Lab in Newport News, Virginia with the goal of resolving this missing resonance problem. One such polarized photoproduction experiment used linearly polarized photons incident on an unpolarized LH2 target. The analysis of a double meson final state from this polarized photoproduction data utilizing the power of a kinematic fitter has the ability to make highly accurate measurements of these observables. The analysis of γ p → p π + π - reactions and the extraction of two such observables, Is and Ic, is discussed.