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New highly transparent, hydrophobic silica aerogels with refractive indices of 1.01 to 1.07 have been produced by Aspen Aerogels, Inc., and select tiles have been tested using an electron beam at the DESY, Hamburg facility. A diffusively-reflective threshold Cerenkov counter was designed and constructed for the purpose of evaluating the aerogels, and can accommodate aerogel tile areas of up to 20 cm by 20 cm. Measurements of the performance of the counter using the new aerogels as Cerenkov radiators are given in terms of photoelectron yields and a figure of merit.