Accurate radio velocities are much easier to measure than optical velo
cities, particularly when derived from molecules. Thus substantial (10
km s(-1) y(-1)) changes were discovered while simply monitoring 22 GH
z water masers near the nucleus of NGC 4258, which is probably in cons
equence a massive blackhole. More speculatively, some methanol maser h
ot spots in compact I-Ill regions may be associated with proto-planeta
ry objects, which would make them amenable to study. It is therefore t
imely to look for contributions that measurement of secular velocity c
hanges might make to Astronomy. We discuss a methodology and identify
several contexts that could be informed by an abundance of intense, na
rrow lines, such as those observed from methanol.