This is the formula from ANSI PH2.5 - 1979.
ASA Dev - 1979.jpg
This is the formula for the Fractional Gradient Method as described in the Aug 1943 paper American Standard Method for Determining Photographic Speed and Speed Number, Journal of the Optical Society of America.
Fractional Gradient - Dev - 1943.jpg
BTW, I'd like to see someone substantiate the 1/3 stop speed statement. Let's try to support statements with facts and help reduce the propagation of myths and hearsay.