I happen to have the data submitted by a reputable european engineering company for the solubility of air in an oil with a sp. gr. = 0.8942 at 60oC [→] 0.069 L/L.
Perry VI gives for air/water a Henry law constant H = 10.1[×]104, for the same conditions [→] 0.0123 L/L. The ratio : 5.6.
At zero Celsius, for nitrogen in water, Perry gives H = 5.29[×]104, resulting in a mol fraction x = 1.89[×]10-5 [→] 0.0235 L/L, lowering the ratio to ~3.2.
BTW, the Ostwald coefficients for the solubility of gases in oils were taken from table 2.9 in Engineering Tribology by Stachowiak and Batchelor, Tribology series, 24, Elsevier.