171] THE GOLDFISH AS A TEST ANIMAL— POWERS 51 



will approach a straight Hne where the direction of the curvature changes 

 (See the portion A to B, curve CABG, Figure 1). The nearness with which this 

 portion approaches a straight hne depends on the values of M, Ki, and K2 as 

 compared to X. Thus the theoretical velocity of fatahty curve complies with 

 the actual experimtis^a' velocity of fataUty curve. 



The above equation though conforming in a general way to the experimen- 

 tal data, is doubtless incomplete. It is only an attempt at a mathematical 

 expression which might be taken to represent the experimental data and should 

 be corrected for other factors not taken into consideration here. 



The vahdity of the equation is further emphasized by the work of Burge 

 (1917) in which he shows that both ether and chloroform not only destroy the 

 catalase of the blood of an anesthetised animal but also inhibit the production 

 or the hberation of the catalase by the liver. In other words there are two 

 factors. One is the effect of the poison in inhibiting the Hberation or produc- 

 tion of an enzyme and the other is the continuous action of the poison in des- 

 troying the enzyme which has already been formed or hberated. Both these 

 factors are expressed in the theoretical equation. 



A mathematical study of the equation shows that as X decreases in value, 

 Y becomes zero. This value of X corresponds to the threshold of toxicity 

 concentration. When X is decreased below this point, Y becomes imaginary. 

 This is in keeping with experimental data, as very small amounts of certain 

 active substances do not inhibit but stimulate metabohc processes. 



