Pharmacodynamics of Salts and Drugs 105 



\ogK. = K{E},+K-E}!-I^) (5) 



TilogT^i^^ • (6) 



That is, the logarithm 0} the ratios 0} the dilution of the minimum 

 jatal doses 0} two salts, divided by the difference oj the sums of the ionic 

 potentials oj the two salts, is a constant. 



This formula is very similar to that derived by me empirically 

 from a study of the dilutions of the minimum fatal doses of salts 

 toward the eggs of Fundulus heteroclitus. The empirical formula was 



V„ 



Va- 



Ea— Eo 

 2o. 15 + 0.02 Ea 



In this formula Ea and Eg were the decomposition tensions of the 

 salts. 



If we take instead of 2 the base of the Naperian logarithms 2.718, 



and instead of ; ^ we write K, this goes over into the form 



0.l5 + 0.02£a ' ° 



Taking natural logarithms 



log F<,=log Vo-K{E,-Eo) 



\og^^=-K{Ea-Eo) . 



' o 



This, in other words, is the same expression as that already derived, 

 using the decomposition tension; i. e., the sum of the solution tensions 

 of the ions, in place of the sum of the ionic potentials. 



The formula may also be derived in another way. If V is the 

 dilution of the minimum fatal dose, and if we let X represent the 

 difference between the sum of the ionic potentials of protoplasmic 



dv 

 ions and salt ions, obviously from the form of the curve -3- varies 



with its f)osition on the curve, that is with V 



dx ' 



.-. log V=KX + C=KiE^ +B-E-E)+C . 



An application of this formula to the results of McGuigan and 

 myself give the following values for K. In each case it is assumed 



