Looking at the packaging, I believe this early version of Dawn was meant to go up against Dial.
This is an Ebay listing.
The decription, in part, says:
“In 1959 Procter & Gamble introduced a new bar of soap to the market.
“They called this soap Dawn. (Not the dish soap, we will get to that later)
“It was meant to compete with Lever companies Dove Brand of Soap.
“Procter and Gamble test marketed this soap in three test cities.
They were: Cincinnati, OH; St. Louis, MO; and Phoenix, AZ.
“They started production of this soap in August of 1959 and ceased production in March of 1960.
“Well after P&G ceased production of the Dawn Bar Soap they still had retained the trademark name “Dawn” and in 1972 they launched a new type of dish soap and called it Dawn.
“The story gets better. During our research of this soap we were in contact with procter and gambles corporate archives division as well as the Smithsonian National Museum of American History in D.C.
“It was there that we discovered they have a very large collection of soaps, telling the history of how its evolved in America. Their collection was missing this soap until now. Our family recently donated a set to the Smithsonian’s Medicine and Science Division at the National Museum of American History.
“The Curator stated to us that this is an invaluable addition to their records.
“The Photos included in this listing show a bar of soap opened up. We opened one package to see what the soap looked like and to photograph it. We are keeping that opened set so the set you purchace will still be sealed in its original packaging from 1959.
“The packaging has P&G’s old logo of a man in the moon overlooking 13 stars which hasn’t been used since 1985.”