66 ILUNOIS BIOLOGICAL MONOGRAPHS [186 



SUMMARY OF CONCLUSIONS 



1. The survival time of the goldfish {Carassius carassius L.) has a very 

 definite relation to the concentration of the solution of the toxic substance 

 used. This relation of the survival time of a goldfish to the concentration 

 of the solution of the toxic substance follows a common general law with a 

 very few exceptions which can be expressed as follows. 



a. There is a concentration of each of the toxic substances tested which 

 will just cause the death of a goldfish and concentrations below this will not 

 cause death. This concentration has been designated as the threshold of 

 toxicity concentration. 



b. In concentrations of a toxic substance just above its threshold of toxicity 

 concentration the velocity of fataUty of the goldfish (as measured by the re- 

 ciprocal of the survival time of the goldfish) is increased very slowly with in- 

 crease in concentration of the solution of thetoxic substance. 



c. In stronger concentrations the velocity of fatahty is increased more 

 rapidly with the increase in the concentration of the solution. 



d. And finally at very high concentrations the increase of velocity of 

 fataUty is again less rapid in proportion to the increase in concentration of the 

 solution. 



2. The survival time curve which is plotted by letting ordinate represent 

 survival time of the goldfish and abscissa represent normaUty or the amount 

 of substance used per 1. of water is not an equilateral hyperbola but is logarith- 

 mic in function. 



3. A curve, the velocity of fatality curve, which is formed by plotting 

 the reciprocal of the siu-vival time of the goldfish as ordinate and concentration 

 of the solution as abscissa resembles a curve which can be expressed by Y= 



— = M=normalrateof metabolism of a goldfish, 



t , / M , KsMz 1 , 



M-z KKM-z) X 

 2= loss of rate of metaboHsm of the goldfish when in a solution a toxic sub- 

 stance, Y= reciprocal of the survival time of the goldfish, and Ki and K2=two 

 constants depending on the nature of the metabolic process or processes in- 

 volved and the nature of the toxic substance used. 



4. The velocity of fatality curve approaches a straight line when the nor- 

 mahty or amounts of toxic substance used per 1. of water will not kill the 

 goldfish in less than 45 minutes and do6s not require longer than 210 minutes. 

 Data within these limits when survival time of the goldfish is plotted as ordinate 

 and the concentration of the toxic substance as abscissa forms a curve which 

 approaches an equilateral hyperbola and can be expressed for all practical 

 purposes by the equation y(jx-a) = k, where a = distance from the origin where 



