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The customary method of adjusting dosages of drugs and poisons as simple ratios of the body weight of the individual is questioned. Data recorded by F. L. Campbell on the survival time of silkworm larvae following the ingestion of sodium arsenate were used for analysis. By the method of covariance it is shown that there is a significant residual effect of individual body weight upon the rate of toxic action when the dosage is made proportional to the body weight. By graphic test the rate of toxic action seemed to be a linear function of the log of the dose per larva and the log of the body weight. Accordingly partial regression equations were computed separately for the 2nd to the 5th instars expressing the rate of toxic action in terms of these two dosage characteristics. The adjustment in dosage that was necessary to eliminate the effect upon the rate of toxic action of body size could be expressed as a size factor, wλ, where w is the body weight of the individual and h is determined from the partial regression coefficients of each equation. When based upon the reciprocal of the survival time, h increased from 1.67 to 1.96 from the 2nd to the 5th instars, but when similar values were computed for the logarithm of the rate, h was the same in all instars and averaged 1.511±0.089.Also supporting the theoretical superiority of the log rate as a measure of toxic action was the fact that the data for the separate instars formed parts of a single straight line when log rate was plotted against the log of dose adjusted by the size factor w1.5 and the statistical demonstration that the distribution of rates was significantly skewed and that of log rates symmetrical. If the adjusted dose is considered as a type of concentration, the final equation for all four instars could be written as C0.49t=309, a type of formula having wide toxicological applicability. A method is proposed for computing the mean lethal dose from the rate of toxic action.

The Size Factor in the Action of Arsenic Upon Silkworm Larvae