Another important use of extreme values is as a test of numerical theories. Two apt il lustrations of this application of figures are afforded by that practical science which deals most largely in possibilities — Forensic Medi cine. M. Orfila, in his " Trait e des Exhuma tions," states that it is possible to determine approximatively the stature of the skeleton and of the body by measuring one of the cy lindrical bones; but instead of testing the value of this conclusion by making use of the extreme values, he contents himself with a rough average. It appears. however, that if we take several cylindrical bones having the same length, and compare them with the cor responding ascertained stature of the skeleton, the extreme statures are very wide apart. Of seven ulnas, for instance, having each the same length (viz. 10 inches, 8 lines), one cor responded to a stature of 6 feet 1 inch, and another to a stature of only 5 feet 5 inches. The difference of 8; inches shows the possible error which might be committed by trusting to this standard of comparison, and demonstrates its futility.
The other illustration is afforded by the well-known test of the absolute weight of the foetal lungs. It used to be laid down as a rough average that in still-born mature chil dren the weight of the lungs was one ounce, and in children that were horn alive two ounces. More accurate observation showed
that this rough guess was very far from the truth. It was only, however, by the aid of extreme values that the utter worthlessness of this test could be proved. It resulted from the collation of a moderate number of ob servations that the lowest weight before and after respiration were the same to an unit, while the greatest weight of the lungs of still born children, in two instances, surpassed the greatest weight of the lungs of children born alive. Nothing could more clearly demon strate the insufficiency and invalidity of this test.
The same general principle which applies to averages applies also to the extremes, namely, that the value of the extremes in creases with the number of observations from which they are selected. It is obvious, how ever, that a larger number of facts will be re quired to arrive at a true extreme value than to obtain a close approximation to the true mean ; 10,000 facts, for instance, may give a true mean duration of life for the inhabitants of any country ; but as many millions may not happen to embrace the greatest attainable age.
The same principles, then, apply both to the mean and to the extreme values derived from observation. To obtain a correct mean or a probable extreme, we must multiply our facts.