It is shown that the new neutrino with a high mass squared difference and a small mixing angle should reveal itself in the oscillometry measurements. For a judicious monochromatic neutrino source the new oscillation length $L_{42}$ is expected shorter than 1.5 m. Thus the needed measurements can be implemented with a gaseous spherical TPC of modest dimensions with a very good energy and position resolution. The best candidates for oscillometry are discussed and the sensitivity to the mixing angle $theta_{14}$ has been estimated: $sin^2{(2theta_{14})}$=0.05 (99{%}) for two months of data handling with $^{51}$Cr.
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