This was a product of Amon L. Scoville & Co. It probably went on the market around 1853. A package/label I saw said it was entered according to an act of congress in 1861 (trademark registered).
The Circassian Hair Oil was probably invented by someone other than Scoville. Most of the preparations they marketed were bought from the originators. In the 56 Philadelphia Directories (see Ferran), there were advertisements for "Ferran's Circassian Hair Oil." This may very well have been the original Circassian Hair Oil in the pontilled bottles. The 1873 Scoville Almanac listed two sizes of the Hair Oil, but so far, only one is known.