ON THE RELATION BETWEEN TOXICITY, RESISTANCE, AND TIME OF SURVIVAL, AND ON RELATED PHENOMENA

1. A relation between toxicity, resistance, and time of survival has been derived on the basis of the assumption that the time is a function of a parameter which is the difference between the toxicity and the resistance. Toxicity and resistance act like forces which can maintain an equilibrium-like (or stationary) state. If the equilibrium is upset, the time at which the event (death) occurs is proportional to the logarithm of the difference between toxicity and resistance. 2. It was found that if values proportional to the resistance are calculated with the proposed equation and the percentage mortality plotted against them (instead of against the time as is usual) symmetrical curves are obtained even though the corresponding mortality-time curves are asymmetrical. Assuming that the resistance varies like an error, that is, according to probability rules, theoretical mortality-time curves, similar to the experimental curves, can be constructed from the proposed equations. 3. In the case of a toxic agent acting on a unicellular organism suspended in solution, the toxicity is proportional to the adsorbed amount of the agent, as calculated with the aid of the Langmuir equation. In small concentration ranges the toxicity can be taken as approximately proportional to the concentration. 4. The variation of the temperature affects mainly the constant a which is a function of the temperature similar to that of the velocity constant of a chemical reaction (Arrhenius' law). 5. The proposed equation has been tested in four different combinations of the variables, concentration, resistance, time, and temperature. The agreement with the experiments is satisfactory. 6. Any noxious agent acting on a unicellular organism may be characterized by three constants: r, the resistance, which is the threshold value at which the agent is still fatally toxic for the organism; a, the reciprocal of the rate constant determining the specific rate (that is, the time corresponding to a difference of 1 between the toxicity and the resistance); and finally the constant γ of the function representing the relation between toxicity and concentration.