balancing and funny units
Gram-inches and inches per second are both commonly used in balance but they cannot be converted one to another as your many correspondents have said. They describe completey different parameters.
Gram-inches tell you how to calculate what to put where. For example 175 gram inches can be a 25g weight placed 7 inches from the spinner or a 7g weight at 25 inches. It says absolutely nothing about the residual vibration velocity in inches per second but merely suggests that if you do it the prop is correctly balanced within the recommended limits. It also tells you what you must remove if you are taking the prop off to fit elsewhere.
All sorts of "funny" units have come along because rather than having electronic calculators, engineer had to create a set of units that landed within a decade of each other from one extreme to another if they wanted to keep the slide rule work manageable or sometimes within measureable commonsense. There is no point in measuring with a micrometer what you will mark with chalk and cut with an axe. Thus R-R chose the coarser Centigrade Heat Unit for example in preference to the British Thermal Unit. Spark plugs had millimetric threads because the first suppliers were French or German and everyone else followed suit, even KLG and Lodge. Balance weights seem to be popular in gram sizes but all the propeller loadings I have done involved inches.
At school the purists insisted on the poundal as unit of force with the pound as unit of mass. At university commonsense prevailed and the lb-wt was the unit of force so the unit of mass was conveniently upped to 32.174 lbs [numerically "g" pounds] and called the slug. For years, even after the Marshall Plan was history, the most accurate milling machines read off in inches not microns or millimetres. Aircraft got built to inches and thousandths thereof.
Mass and Weight? Generally speaking you cannot readily tell what the mass is. The only practical thing to do is "weigh" it and trust that the acceleration due to gravity is uniform enough not to affect the outcome. Not true in space shots.
Any way, enough gabbling. gram-inches are darn useful "egg" numbers that relate directly to who makes what and how do I make it better whereas inches second relate to "chicken" of vibration wot is left over once I have dun fiddling.
Even so the two-bladed prop has certain bad gyro properties compared to the lovely three-blader so even inches per second vibration will have a value that might be "good" on a two blader but definitely "bad" on a three blader.
Then of course you cannot get three-quarter inch plumbing... it is 20mm and sold, not by the metre, oh no. Betcha it is sold ny the foot.