prior to the application of the model to large detector geometries with greater PMT coverage.

   Material           Light Yield (photons/MeV)                 Quenching Parameter (mm/MeV)
  ---------- ------------------------------------------- -------------------------------------------
    WbLS-1     19.9 $\pm$ 1.1 (stat.) $\pm$ 2.0 (sys.)    0.70 $\pm$ 0.12 (stat.) $\pm$ 0.07 (sys.)
    WbLS-2    108.9 $\pm$ 0.8 (stat.) $\pm$ 10.9 (sys.)   0.44 $\pm$ 0.01 (stat.) $\pm$ 0.04 (sys.)
      LS       9156 $\pm$ 42 (stat.) $\pm$ 916 (sys.)     0.07 $\pm$ 0.01 (stat.) $\pm$ 0.01 (sys.)

\[tab:OptimalVals\]

Detector A
----------

The simulated and measured photoelectron (PE) distributions for Detector A are given in figure \[fig:DetAResults\]. Quality cuts to the data were applied in the same way as Detector B. The measurement of 475 MeV protons in water are not shown. The mean number of observed photoelectrons for all measurements and simulations are given in table \[tab:MeansDetA\].

   Sample   Incident Proton Energy   Photomultiplier   N$_{PE}$, Measured   N$_{PE}$, Simulated
  -------- ------------------------ ----------------- -------------------- ---------------------
   Water           475 MeV             Downstream        1.3 $\pm$ 0.0         1.6 $\pm$ 0.2
   Water           475 MeV              Upstream         1.2 $\pm$ 0.1         1.2 $\pm$ 0.1
   Water           2000 MeV            Downstream        33.0 $\pm$ 0.2       32.4 $\pm$ 3.2
   Water           2000 MeV             Upstream         1.2 $\pm$ 0.0         1.4 $\pm$ 0.1
   WbLS-2          475 MeV             Downstream        4.7 $\pm$ 0.0         4.6 $\pm$ 0.5
   WbLS-2          475 MeV              Upstream         4.6 $\pm$ 