Vertical Earth- Air Electric Currents. 99 



set of observations, there is given a third condition, namely, 

 that ni must be greater than the distance between the greatest 

 and least observations. But this inequation (coupled with 

 the other equations) is not sufficient to determine n, i, and 

 p-?-q with any precision. 



Of course, whether a binomial or multinomial probability- 

 curve is to be adapted to a given set of observations, the set 

 must fulfil the condition th&tj-r-k* should be a small fraction*. 

 In fact the condition is frequently unfulfilled : for instance, 

 in the statistics of the duration of American marriages f, 

 where the observed j-h-fa forms a largo integer J. In such 

 cases it may be inferred that the number of independent 

 elements is too small (or their asymmetry too great) to gene- 

 rate a probability-curve. 



XII. On the Existence of Vertical Earth- Air Electric Cur- 

 rents in the United Kingdom. By A, W. Rucker, M.A., 

 F.R.S.% 



IN a paper by Dr. Adolph Schmidt, read before Section A 

 of the British Association at Oxford (Report Brit. Assoc. 

 1894, p. 570), the author stated that he had expanded the 

 components of the earth's magnetic force in series, and had 

 deduced expressions, two of which give the magnetic potential 

 on the surface of the earth in so far as it depends on (1) in- 

 ternal, and (2) external forces. " The third series represents 

 that part of the magnetic forces which cannot be expressed 

 in terms of a potential, but must be due to electric currents 

 traversing the earth's surface." The author concludes that 

 such currents amount on the average to about Ol ampere per 

 square kilometre. 



It appeared therefore desirable that this conclusion, drawn 

 from the magnetic state of the earth as a whole, should be 

 tested by means of those portions which have been most fully 

 studied. 



* Above, p. 92. 



t Given by Dr. W. F. Wilcox in " The Divorce Problem " (Studies in 

 History &c, "Columbia College, vol. i.). 



\ Many other instances in which the condition fails are given by Prof. 

 Karl Pearson in his masterly •' Contributions to the Mathematical Theory of 

 Evolution," No. II. (Philosophical Transactions, 1895). For some criticism 

 of Prof. Pearson's theory of asymmetric frequency-curves see the present 

 writer's paper on " Recent Contributions to the Theory of Statistics," in 

 the Journal of the Royal Statistical Society, Sept. 1895. 



§ Communicated bv the Physical Societv : read December 13, 1895. 



H 2 



