175] THE GOLDFISH AS A TEST ANIMAL— POWERS 55 



substance as that tested which has previously been very carefully prepared 

 by killing a number of goldfish and placed in the hands of workers as a standard 

 curve. For example, if the average survival time of a number of goldfish 

 killed in an unknown Li CI solution was 150 minutes it is seen that the ordinate 

 representing 150 minutes survival time will cut the LiCl survival time curve, 

 LIJM (Fig. 1) at the point R and the normality (0.207 N.) of the LiCl solution, 

 can be read directly from the abscissa. For this method to be most exact the 

 point R must fall within the portion I to J of the survival time curve, i.e., the 

 survival time of the goldfish must be within the portion of the curve where it 

 corresponds to the portion of the velocity of fatality curve that approaches a 

 straight line. 3. A number of goldfish can be killed in an unknown and the 

 average of the survival time determined and data applied to the equation of an 

 equilateral hyperbola, y{x-a) = k, where }» = survival time of the goldfish, x= 

 amount of substance used per liter, a = theoretical threshold of toxicity con- 

 centration, and k = 2, constant. For example the average survival time of a 

 number of goldfish killed in an unknown LiCl solution is 150 minutes. By 

 substituting in the equation the value of the constants (a =0.1 25 N. and k = 

 12.37 for LiCl) we have 150(a;-0.125) = 12.37. Solving ic=0.207 N. which is 

 the strength of the unknown, k approaches a constant only when the velocity 

 of fatality curve approaches a straight line. See Figure 1. The deviation 

 of the velocity of fatality curve from a straight line increases progressively as 

 the distance preceeding and following the portion A to B increases, and at the 

 same time the survival time curve deviates from that of an equilateral hyper- 

 bola. Curve CABG, Fig. 25, is a graphic representation of this fact [See Shel- 

 ford (1918) for detail of this curve]. Ordinate of curve represents k [k — y{x-a)\. 

 If the survival time required to kill the goldfish is less than 45 minutes k is 

 greater than 12.37 and if it requires longer than 210 minutes k is less than 12.37. 

 Thus to apply this equation to LiCl the survival time of the goldfish must 

 not be less than 45 minutes nor longer than 210 minutes. This range of sur- 

 vival time must have been previously determined for each substance to be 

 tested. 4. Curve CABG, Fig. 25, when time is interpolated on abscissa 

 (see abscissa at top of graph), can be utilized directly to determine the strength 

 of the unknown, both where k approaches a constant and where ^ is a variable. 

 Thus to determine the strength of an unknown apply the average survival 

 time of a number of goldfish which have been lulled in the unknown to the 

 curve CABG, Fig 25, and read the normality of the unknown directly from 

 the abscissa. For example, if the average survival time of the goldfish killed 

 in an unknown LiCl solution is 150 minutes it will be found that this corresponds 

 to the point R of the curve CABG. Then read directly from the abscissa 

 0.207 N. which is the strength of the unknown LiCl solution. Again for most 

 exact determinations, concentrations represented from A to B must be used. 

 This curve is of special interest and value in that it emphasizes the variability 

 of k. 5. A few experiments can be run with different concentrations of the 

 substance to be tested and the survival time of the goldfish in each experiment 



