44 ILLINOIS BIOLOGICAL MONOGRAPHS [164 



death. The relative toxic activities of the substances will vary according to 

 the criterion used. Only a glance at figure 23 is required to convince one 

 that there -will be a marked rearrangement in the relative toxic values of the 

 elements when different survival times are used as criteria. For example, 

 if a 120 minute survival time is chosen as a criterion the relative toxicities of 

 the elements as chlorides with normality as the standard of measure will 

 be arranged from the most toxic to the least toxic in the following order: — Ba, 

 K, Li, Sr, Ca, Mg, and Na, and with a 60 minute survival time they will be 

 arranged as follows: — K, Ba, Ca, Li, Sr, Mg, and Na. Thus there is a marked 

 rearrangement of the relative positions of the elements with a change from a 

 120 minute survival time as a criterion to that of a 60 minute survival time. 

 It is the opinion of the writer that it is the employment of different criteria 

 that is responsible more than any other one thing for the differences of opinions 

 of workers on the toxic values of the elements. The fact is not denied that the 

 elements may have different relative activities toward different organs of the 

 same animal as well as toward different animals (Kahlenberg and Mehl 1901). 

 By a study of the survival time curves shown in Figure 23 it is seen that the 

 activity of each element is a law unto itself, and thus there is no one expression 

 that will include all specificities of the salts or toxic substances. But a standard 

 criterion may be derived. From a study of the velocity of fatality curves it 

 is seen that there are two variables and that these vary independently of each 

 other. 1. The concentration necessary to just kill the goldfish varies with the 

 element. 2 The acceleration of the change of direction of the survival time 

 curve, i.e., the increase in the velocity of fatahty is different in each of the 

 salts and does not necessarily have any relation to the amount of the salt neces- 

 sary to just kill the goldfish. The value of the first factor is shown by the 

 position of the point C and the second by the slant of the velocity of fatality 

 curve. But since the slant of the velocity of fatahty curve is not uniform for 

 all concentrations of a substance the theoretical velocity of fatahty curve will 

 be considered. This curve bears the same relation to the physiological activity 

 of the substance as the true velocity of fatality curve. Thus the relative 

 toxicities of substances due to the first factor can be measured by the reciprocal 

 of a, the distance P from the origin O. That due to the second can be meas- 

 ured by the tangent of the angle XPB, 6. (See Figure 1.) Both these factors 

 must be taken into consideration in a criterion or an expression representing 

 the relative toxicity of a substance. The tangent 9 increases as the toxicity 

 increases with respect to the slope of the theoretical velocity of fatahty curve, 

 i.e., the rapidity with which the activity of the substance increases with in- 

 crease in concentration and the distance of the point P from the origin O or 

 a decreases as the toxicity increases with respect to the theoretical threshold 

 of toxicity concentration, i.e., as the theoretical threshold of toxicity concen- 

 tration decreases. Thus it is seen that these two factors are the reciprocal of 

 each other. This relation can be expressed mathematically by the equation^ 



