June 18, 1909] 



SCIENCE 



971 



at different points. I can mathematically plot 

 the point where he will die. 



That one chart shows to this committee in a 

 graphic form, better than any argument could, 

 the position of a drug in a food, as compared 

 with the food itself. They are diametrically op- 

 posite. The lethal dose of one is the normal dose 

 of the other, and vice versa. Therefore the argu- 

 ment de minimis as far as harmlessness is con- 

 cerned is a wholly illogical and non-mathematical 

 argument, and can be demonstrated by calculus 

 to be so. 



The reader is urged to refer to the more 

 formal statement in either of the other pub- 

 lications, and to note the confusion of thought, 

 by virtue of which deviation from the per- 

 pendicular line is (correctly) treated as the 

 measure of injurious effects in the case of 

 food, but deviation from the horizontal (!) 

 line, as the measure in the case of drugs. 



The argument contains three fallacies so 

 patent that (to adapt words employed by the 

 witness in criticism of those who hold the 

 opposite opinion)' " it seems astonishing in 

 these days of rigid scientific investigation that 

 such fallacious reasoning can be seriously in- 

 dulged in for the sake of proving " the harm- 

 fulness of minute quantities of non-condi- 

 mental preservatives. 



First and most important. Absolutely no evi- 

 dence is offered that the curves actually have 

 the form which is assumed for them. 



Second. " Food ^^ " can not be regarded 

 as the lethal dose in the same sense that 

 " preservative ^= 100 " is a lethal dose. 



Third. Quantity of food and injurious ef- 

 fects can not be measured in the same direc- 

 tion in a diagram purporting to show the 

 relation between them. 



It seems almost incredible that, repeated by 

 the author as the argument has been over and 

 over again during the past three years, recast 

 in language, scanned by his assistants, none of 

 these fallacies has been convincingly borne in 

 upon his mind. 



A lethal dose of any substance is the quan- 

 tity which, administered at one time, is suffi- 

 cient to cause death. To assume food^O 

 a lethal dose is to assert the absurdity that 

 food (and indeed every individual food sub- 



^ Page 249 of the evidence. 



stance) must be taken every minute of one's 

 life. On the other hand, it is undoubtedly 

 true that excessive quantities of food (and of 

 individual foods) produce injurious effects. 

 Logically, therefore, the food curve in Dr. 

 Wiley's diagram, whether it refers to food in 

 general or to any individual food, should — 

 after touching the right vertical axis at " 100 

 normal dose " — turn back to the left, and 

 reach a true point of lethal dose at a point 

 above 100. That is to say, it should have the 

 general form represented by ABC in Fig. 2. 

 If there be such a thing as a lethal dose of 

 food, is it not the quantity represented by this 

 point above 100 rather than the zero quantity ? 

 This diagram makes it clear that the cases of 



Fig. 2. Possible Forms of Curves Representing 

 Injurious Effects of Foods and of Food Preserva- 

 tives. 



food and preservative are not diametrically 

 opposite, as maintained by Dr. Wiley. Evi- 

 dently the principle that any substance which 

 is injurious in any quantity is injurious in all 

 quantities, however small, is absurd as applied 

 to food substances. And there seems no justi- 

 fication for laying down any principle " de 

 minimis " which shall apply solely to preserva- 

 tives or to non-condimental preservatives, or 



