The breakdown voltage of degassed and gas-saturated transformer oil has been measured as a function of concentration of organic additives known to affect the breakdown strength of the oil. By using a wide range of additive concentrations, it is shown that the existence of optimum concentrations in the breakdown voltage against concentration characteristics which have hitherto been reported is in fact only one phase of a more complex relationship between breakdown voltage and additive concentration. The characteristics are markedly affected by the presence of gases dissolved in the oil