technically, it doesn't measure an
amount of downness (like
fathoms), only its direction …
so i think the correct term is
downotrope 
Actually, a downometer can give you a measure of the amount of down. Swingyness can be used to measure the amount of downness via the equation T=Sqrt[2piL/g]. Swingyness is actually an intrinsic property independent of the mass so the more accurate term is swingosity. Thus...
A downotrope is a convinient tool for finding the direction of down. If the magnitude of downness is needed, the downotrope can be used as a downometer by simply measuring it's swingosity.