70 INJURY, RECOVERY, AND DEATH 



into serious error. This is evident from Fig. 30 which 

 shows that while the abscissa of A at any point is just 

 half that of B, no such relation obtains among the ordin- 

 ates. 46 For example at 40 minutes, the ordinate of B 

 is twice as great as that of A, while at 4 minutes, it is 

 less than 1.1 times that of A. Hence it is evident that 

 we should compare abscissae rather than ordinates (i.e., 

 times required to do equal amounts of work rather than 

 amounts of work performed in equal times). 



The principle is sufficiently obvious where successive 

 determinations are made and curves are drawn. But 

 there is a common type of experimentation in which, for 

 various reasons, a single observation at one rate is com- 

 pared with a single observation at another rate. The 

 principle in question is then easily overlooked. In some 

 cases this leads to serious errors. 48 



It is therefore evident that when we average time 

 curves, we should, whenever possible, average abscissae 

 rather than ordinates. Thus for example, in Fig. 30 the 

 average of Curves A and B would be Curve C, obtained by 

 averaging the abscissae of Curves A and B : this gives a 

 curve whose velocity constants are the arithmetical mean 

 of those of A and B. On the other hand, by averaging 

 ordinates we obtain Curve D, which does not follow the 

 formula characteristic of the other two curves. 



It may be desirable to point out that these methods 

 may be advantageously applied to the measurement 

 of toxicity. 47 



46 We cannot avoid the difficulty by comparing the rates of the two 

 processes at a given time; for the rates so obtained will bear no constant 

 ratio to each other. Only when they are compared at the same stage of 

 the reaction will they show a constant relation; this gives the relation 

 between the velocity constants. 



48 For a discussion of this see Osterhout (1918, B) . 



4T Cf. Osterhout (1915, G). 



