187] THE GOLDFISH AS A TEST ANIMAL— POWERS 67 



the portion of the velocity of fatality curve that approaches a straight line 

 when prolonged cuts the X-axis and k = a. constant. This straight line which 

 is thus drawn has been designated as the theoretical velocity of toxicity curve. 

 The concentration of the toxic substance represented by the point on the X-axis 

 cut by the theoretical velocity of fatality curve has been designated as the 

 theoretical threshold of toxicity concentration. 



5. It has been suggested that relative toxicities of substances be expressed 



by the formula T =-\/ when only data which fall within the portion 



a 



of the velocity of fatality curve which approaches a straight line are used. 

 6 = angle made by the theoretical velocity of fatality curve cutting the X- 

 axis and a = the theoretical threshold of toxicity concentration of the substance 

 tested. This expression does not represent either the absolute or the exact 

 relative toxicities of the substances since it is based only upon the portion of 

 the velocity of fatality curve which approaches a straight line, but has been 

 chosen since it is a natural criterion and not an arbitrary one. 



6. Four modifications of a definite survival time of the goldfish method of 

 pharmacodynamic assay work as suggested by Pittenger and Vanderkleed 

 have been proposed. 



a. A definite survival time of the goldfish can be employed provided that 

 the concentration of the substance to be tested is within the range of concen- 

 trations in which the velocity of fatality curve approaches a straight line. 



b. The average survival time of a number of goldfish in a solution of the 

 substance to be tested can be applied as ordinate to a standard survival time 

 curve and the strength of the solution can be read directly from the abscissa 

 provided this data falls within the limits of the survival time curve which 

 approaches an equilateral hyperbola, i.e., where the velocity of fatality curve 

 approaches a straight line. 



c. The average survival time of a number of goldfish killed in a solution 

 of the toxic substance to be tested can be substituted in the equation y{x-a) 

 = k and the value of :v determined which will be the concentration of the solu- 

 tion of the substance tested, provided the survival time of the goldfish is 

 within certain maximum and minimum of survival time, the reciprocals of 

 which when plotted as ordinate and the concentrations of the solutions used 

 as abscissa will approach a straight line, 3/ = survival time of the goldfish, x = 

 concentration of solution of the toxic substance in which the goldfish are 

 killed, a = the theoretical threshold of toxicity concentration, and ^ = a constant 

 depending upon the substance tested. 



d. The average survival time of the goldfish killed in a solution of the 

 substance to be tested can be applied to a graph which has been prepared to 

 show the values of k in different concentrations of the substance with survival 

 time interpolated at the top of graph and the concentration of the solution 

 can be read directly from the abscissa. (See Figs. 25 and 26.) 



