The product is a vintage American Hydromath Computer Oil Gravity Calculaide, which comes with a leather case. It was likely used for computing oil gravity and related calculations. The brand of the product is American Hydromath Company.

I'm unsure of the decade of manufacture but I believe it's somewhere between the 1950s and 1960s, as this person (Amelia Sadorra) was born in the 1940s and owned this originally.

Also unsure if it works but there are no electrical components and seemingly nothing missing or out of place.