58 



ILLINOIS BIOLOGICAL MONOGRAPHS 



[178 



OP, b = OP', and c= OP". The theoretical velocity of fatality curves can be bet- 

 ter drawn and compared when it is remembered that all theoretical velocity of 

 fatality curves of any one substance when drawn on a definite scale representing 

 the reciprocal of the survival time of the goldfish and variable scales repre- 

 senting amounts of substance used per liter or normaUty of substance have 

 a definite common point of intersection. That is, if the survival time of the 

 goldfish be plotted as ordinate, and the number of cc. or g. per 1. of knowTi and 

 unknown used be plotted as abscissa the curves thus formed would constitute 

 a system of confocal conies of equilateral hyperbolae each being dragged out 

 of position a distance OP, OP', and OP" respectively. Therefore the recipro- 

 cal curves will aU intersect on the Y-axis at the point S. (Fig. 24). 



For example two hypothetical unknowni LiCl solutions could be determined 

 in the following manner. Make up six solutions from a known LiCl solution 

 as given in the following table and determine the survival time and the recipro- 

 cal of the survival time of the goldfish in each solution as recorded. Test the 

 unknown solutions No. 1 and No. 2 as shown in table XXXVIII. Plot a 

 theoretical velocity of fatahty curve for each set of data with reciprocal of sur- 

 vival time as ordinate and cc. of a solution used per 1. as abscissa l:100/t is 

 used instead of 1/t to avoid the use of fractions. One block ordinate =1 

 velocity of fatality. One block abscissa = 10 cc. of solution per 1. 



ooo mo o o o 



!S Minutes 



14 



12 



10 



8 



6 



4 



2 







-2 



-4 



0.05. 0.1. 0.15. 0.2. 0.25. 0.3. 0.35. 0.4. 0.45. 0.5N. 



Figure 25. Lithium chloride. Graph showing curve when normality is plotted as abscissa 

 and concentration minus the theoretical threshold of toxicity concentration, times survival 

 time of the goldfish is plotted as ordinate, i.e., k of the equation y(x-a) =k. The graph shows 

 the deviation of k from a true constant. The portion AB is equivalent in range to AB of 

 the velocity of fataUty curve Figure 1 . y = survival time of goldfish in minutes, x = normal- 

 it>' of the LiCl solution, a = theoretical threshold of toxicity concentration =0.125 N. and 

 k = a. constant = 12.37 which holds only between the two points A and B. 



