454 JOURNAL OF ECONOMIC ENTOMOLOGY [Vol. 5 



It will be noticed that the toxic values of the two poisons vary in- 

 versely as the lengths- of life of the insects subjected to them, if the 

 length of life of the poisoned insects be taken to indicate the toxic 

 values of the chemicals. Then, toxic value of x is to toxic value of 

 Paris Green as 5 is to 10. 



The product of the means of a proportion being equal to the prod- 

 uct of the extremes, we have, 



10 (toxic value of x) =5 (toxic value of Paris Green). 

 Then, toxic value of x = 5-10 (toxic value of Paris Green) . 

 But toxic value of Paris Green = 1. 



Then toxic value of x = 5-10 X 1 = .50, which may be called the Poison 

 Exponent of x. 



In the case of a quicker poison than Paris Green let us suppose 

 again that the insect subjected to Paris Green dies after five hours, 

 while the insect subjected to x dies after 4 hours. 



Again the toxic values of the two poisons vary inversely with the 

 lengths of life of the insects subjected to them. 



Then toxic value of x is to toxic value of Paris Green as 5 is to 4. 



4 (toxic value of x)=5 (toxic value of Paris Green), 

 Toxic value of x = 5-4 (toxic value of Paris Green), 

 Toxic value of Paris Green =1, 

 Toxic value of x = 5-4X1 = 1.25 = Poison Exponent of x. 



It seems that we have here reached a law which may be stated as 

 follows : If the length of life of a poisoned insect may be taken to indicate 

 the toxic value of the chemical to which that insect is subjected, then the 

 toxic values of two chemicals vary inversely with the lengths of life of two 

 insects respectively subjected to them, assuming that the insects are of the 

 safne species and at the same period of their life cycle, and that environ- 

 mental conditions are equal. 



The experiments with all instars of Heliothis will give some exam- 

 ples of the actual determination of Poison Exponents. The poison 

 used was Arsenate of Iron Grasselli. A first instar larva subjected to 

 this poison died within 8 hours, while one subjected to Paris Green 

 under the same environmental conditions and at the same time died 

 within 4 hours. To obtain the Poison Exponent of Arsenate of Iron 

 Grasselli for the first instar of Heliothis, we divide 4 by 8, which gives 

 .50. The other instars were treated in a similar manner. At this 

 point a word of comment may not be out of place. The Poison Expo- 

 nent of .50 for Arsenate of Iron Grasselli for the first instar of Heliothis 

 merely indicates that a larva subjected to that poison lives twice as 

 long as a larva subjected to Paris Green, other environmental condi- 



