  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:
$\sin^2{(2\theta_{14})}$=0.05 (99{%}) for two months of data handling with
$^{51}$Cr.
