"Isn't it strange that Harry -Smith Hampshire in writting uses the word Arc in the Throwaway Oversway. So I will in future use the word Arc instead of Arch."
Use whatever word you like.
You will still be WRONG if you think that it exists in the BACK.
What is being described is a shape of the OVERALL BODY. Which does indeed appear as an arch. But if you carefully study a truly expert dancer, you will find a STRAIGHT LINE from pelvis to sternum or higher. It's an OVERALL arch, approximated by STRAIGHT LINES - one in the back, on in the upper leg, one in the lower leg, etc.