Actually . . .
He preferred to take cold baths, then the whim hit him. "I think I'll take a hot bath." he found a missing appendage . . . and the rest is history. :-)
"...upon displacing water in his tub and realizing he had found a way to measure volumes,..."
Actually this is wrong. He discovered the concept of specific gravity. He was able to use it to show the king that his crown wasn't pure gold, as the story goes. As I recall the crooks that tried to pull a fast one on the king suffered some bad consequences. Maybe we need a king.
"He preferred to take cold baths, then the whim hit him. "I think I'll take a hot bath." he found a missing appendage . . . and the rest is history. :-)"
By your logic, it must have been a cold bath, otherwise as this mysterious appendage began to grow his volume would have increased and he'd still be Eurekaless to this day.