It is shown that, if the new neutrino implied by the Reactor Neutrino Anomaly exists and is in fact characterized by the suggested relatively high mass squared difference and reasonably large mixing angle, it should clearly reveal itself in the oscillometry measurements. For a judicious neutrino source the new oscillation length L14 is expected shorter than 3m. Thus the needed measurements can be implemented with a gaseous spherical TPC of modest dimensions with a very good energy and position resolution, detecting nuclear recoils following the coherent neutrino-nucleus elastic scattering. The best candidates for oscillometry, yielding both monochromatic neutrinos as well as antineutrinos, are discussed. A sensitivity in the mixing angle theta14, (sin(2theta14))^2=0.1 (99 %), can be reached after a few months of data handling.
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