PHARMACODYNAMICS OF SALTS AND DRUGS 97 



say the amount of work just sufficient to kill protoplasm in unit 

 time, say 24 hours the concentrations of the two ions which will 

 just accomplish this work must stand in some numerical relation to 

 their potential energy content. What is that relation ? 



To bring out this relationship, I have plotted the curve in Fig. i, 

 which expresses the relationship between the ionic potential of the cation 

 and the dilution (V) of the minimum fatal dose. By dilution is meant 

 the number of liters of solution containing one gram equivalent of the 

 salt. From an inspection of this curve it will be seen that we are 

 dealing with a logarithmic function; that is, the dilution increases 

 enormously in a logarithmic ratio to the ionic potential. The dilution, 

 for example, increases 100,000 times while the ionic potential increases 

 about five times. 



By inspection of this curve one may write the general equation: 

 log IO V=KE . i 



In this formula E is the ionic potential, V the dilution, and K the con- 



log V 

 stant of proportion. If, however, we place v. =^T, it will be 



seen that this formula is not in the right form, since E for some ions is 



jr 



zero. Nor does the formula log V ^ . give constant results. In 



~ 



this formula E c + E a represents the sum of the potentials of the anion 

 and cation. Nor could it be anticipated that such a formula would 

 give a proper result, since what we have to express is the difference of 

 potential between the salt and the protoplasm, and this formula 

 expresses only the relation between minimum fatal dose and the 

 absolute potential of the various ions. Before setting up any theo- 

 retical formula, it is necessary to get clearly in mind just in what the 

 difference in potential between the protoplasm and the salt consists. 

 d) Derivation of a theoretical formula expressing the relationship 

 between minimum fatal dose and the available potential energy of salt 

 solutions. We have now found out how to measure the potential 

 of the potential energy of the salt solution; it is necessary that we 

 discover also how the potential of the potential energy of the proto- 

 plasmic system is to be determined, since our formula involves both 

 these factors, the available potential energy being the difference be- 

 tween the potentials of the salt and the protoplasm. 



