236 Prof. K. Pearson on certain Properties 



(Experiment 2). Condenser No. 1, of the same lot, shows a 

 loss of 1*45 per cent, at frequency 140, which is 45 per cent, 

 greater loss than Nos. 3 and 4 give. Of the second lot, No. 6 

 gives a large loss (Experiment 5), and other experiments 

 which one of us has made by other methods show that all the 

 other condensers of this lot have losses nearly the same as No. 6, 

 excepting No. 10, which gives the smallest loss of any, *74 per 

 cent, in one case and '78 per cent, in another (Experiments 6 

 and 7). Condenser No. 2 shows by other methods the same 

 loss as 3 and 4. Hence we have the following singular 

 results : — All of the first lot except one have a loss of 10 per 

 cent, on high frequencies, and the exceptional condenser has a 

 loss of 1*45 per cent. All the condensers of the second lot have 

 substantially the same losses, about 1*5 per cent., and the excep- 

 tional one is scarcely more than one half as much as the others; 

 the exceptional one of the first lot having the same loss as all but 

 one of the second. There is no possibility of a confusion of 

 numbers, for they were plainly stamped when purchased, and 

 the capacities of the first and second lots are very different, as 

 already stated. Our experiments do not indicate the reason 

 for these large differences ; but the existence of such differ- 

 ences is fully confirmed by measurements made by wholly 

 independent methods, and which will shortly be published. 



Wesleyan University, 

 Middletown, Conn., Sept. 1, 1898. 



XV. On certain Properties of the Hyper geometrical Series, 

 and on the fitting of such Series to Observation Polygons in 

 the Theory of Chance. By Kabl Pearson, F.R.S., 

 University College, London*. 



1. TN a paper entitled " Mathematical Contributions to 

 JL the Theory of Evolution : Part II. Skew Variation 

 in Homogeneous Material " t, I have pointed out that the 

 following series, of which the skew-binomial is a special case 

 (w=oo), 



pn(pn-l) (pn — 2) .... (pn— r + 1) 

 n(n — l)(n — 2) (n — r+1) 



( x ! r 9 n , r(r-l) gn(qn-l) 



V pn — r + 1 1.2 (pn — r + l)(pn—r + 2) 



r(r-l)(r-2) qn{qn-l){qn-2) ^ 



1.2.3 {pn — r + l)(pn — r + 2)(pn — r + 3) 



* Communicated bv the Author. 



+ Phil. Trans, vol. clxxxvi. p. 360 (1895), 



