52 ILLINOIS BIO LOGIC A L MONOGRA PHS [172 



COMPARISON OF CURVES OBTAINED BY OTHER WORKERS 



Warren (1900) in his work on Daphnia was first to call attention to the fact 

 that when aquatic animals are killed by placing them in solutions of a toxic 

 substance if the survival time is plotted as ordinate and the concentration of the 

 solution as abscissa, the points when joined wiU form a curve closely resem- 

 bling an equilateral hyperbola. Warren considered all of his data as complying 

 with this curve. Either he experimented with solutions which would fall 

 within the concentrations where the velocity of fatality curve approaches a 

 straight line or he disregarded data obtained outside this range of concentra- 

 tions. Warren saw the similarity between his curves and the curves represent- 

 ing Boyle's law and explained his results by supposing that the toxicity of a 

 substance above a definite amount (the writer's theoretical threshold of toxicity 

 concentration) depended upon the number of molecules which beat on the body 

 of the Daphnia per unit of time. Ostwald (1905, 1907) was next to call atten- 

 tion to a similar curve formulated from data obtained by killing Gammarus 

 in different concentrations of sea-water or the constituents of sea-water. 

 Ostwald, disregarding the extremes of his data, claimed that the curve v/as 

 not an equilateral hyperbola and applied the modified absorption formula, 

 tC"' =Ki or t(C-n)"' =Ki (Ostwald 1907) (see page 3,3). Kfizenecky (1916) 

 next noted the resemblance to that of an autocatalytic curve of a curve which 

 he obtained by determining the time required for an annelid worm, Enchy- 

 traeus humicultor, to recover in ordinary tap water after having been in a 

 solution of a toxic substance for one minute, when time was plotted as ordinate 

 and concentration of the solution as abscissa. The curve obtained by Kfi- 

 zenecky resembles the writer's velocity of fatality curve. Krizenecky ex- 

 plained his results in terms of osmotic pressure. Clayberg (1917) called atten- 

 tion to such a curve and called it an hyperbola but m.ade no attempt to show 

 how nearly it approached an hyperbola or its variations. None of these 

 workers have seen the significance of the entire curve nor did they construct 

 what is designated by the writer as the velocity of fatality curve. Neither 

 did they suggest the possibility of its utilization in physiological testing nor 

 attempt to connect their entire data with life processes. Gregersen (1916) 

 in his investigation on the antiseptic value of gastric juice found that the 

 disinfecting value of gastric juice was in direct proportion to the free acidity 

 and that the product of the survival time of the bacteria and the titration 

 number was almost constant. This in fact represents an equilateral hyperbola 

 but such a relation was evidently not noted by Gregersen. Warren also showed 

 that V, ben the survival time of Daphnia killed in a constant concentration of a 

 toxic substance at different temperatures was plotted as ordinate and tempera- 

 ture as abscissa a similar curve was formed. 



