Prof. Edgeworth's Problems in Probabilities. 171 



It may suffice, therefore, that attention has been called to a 

 theory alternative to that of v. Helmholtz, and which seems, 

 to me at least, much simpler and more probably true. 



An undoubted knowledge of even the sign of the potential 

 of mercury in contact with an electrolyte would go a great 

 way towards settling the question at issue. According to my 

 view, it is probably negative. V. Helmholtz 's theory is founded 

 on the assumption that it is positive ; but, notwithstanding 

 the rather decided way in which this assumption is at first 

 stated*, no real proof is given ; and the subsequent remark 

 ("ware z. B. das Queksilber positiv"f) indicates the recognized 

 provisional character of the assumption. It lies with those 

 who would give to the provisional theory of v. Helmholtz 

 the character of an ascertained law of Nature to provide a 

 knowledge of the true value of the hypotheses on which it is 

 based before it can carry the weight they propose to attach to 

 it, or serve as a reliable support for the further researches 

 already dependent on it. 



XX. Problems in Probabilities : No. 2, Competitive Examina- 

 tions. By Professor F. Y. Edgeworth, D.C.L.% 



I^HE following study is related to the first number of the 

 series § as being another instance of the Probability- 

 calculus applied to a practical interest. In a paper on " The 

 Statistics of Examinations," which was published in the 

 September number of the Journal of the Royal Statistical 

 Society for 1888, and in a sequel to that paper which will 

 shortly be published in the same Journal, I have made an 

 estimate of the extent to which the results of competitive 

 examinations depend upon the accident of one examiner 

 rather than another equally competent being appointed to 

 mark the work of the candidates. Referring to those papers 

 for a fuller exposition of the statistical data and the practical 

 conclusions, 1 propose here to abstract the mathematical 

 reasoning. 



The fundamental axiom is the proposition, evidenced by 

 analogy and specific experience, that the marks given by 

 different examiners to the same piece of work are apt to be 

 arranged according to some law of error or facility-curve 

 which is constant for the same class of examiners and work 

 examined. The analogy between errors of observation and 

 discrepancies in marking is evident. But, as the transition is 



* Wissenschaftliche Abhandlungen, i. p. 934. f Ibid. p. 936. 



% Communicated by the Author. 



§ See Philosophical Magazine, October 1886. 



