310 Mr Edgeworth, On observations and statistics. [May 25, 



,, ',.'■'.-. „ i n ii increase of volume ,, ," 



the " violence as defined by —. ~ -, — ; would not repre- 



J time ol explosion 



sent the relative destructive effects of explosions in free air. 



Various experimental methods of treating the question of 

 " break up " were described, and further communication was re- 

 served pending the result of experiments still in progress. 



(4) Observations and statistics. By F. Y. Edgeworth. Com- 

 municated by J. W. L. Glaisher, M.A. 



[Abstract.'] 



The paper begins with a classification of the different cases 

 which the (two) chief problems denoted by the title present : eight 

 different principles of division are laid down. For example one 

 division is between the cases where the weights of facility-curves 

 are given beforehand, and where they are to be inferred from the 

 observations (cp. Glaisher, Mem. Astron. Soc. XL. p. 103). Under 

 this head it is remarked that many writers seem unduly to assume 

 the modulus as known in cases like the statistics of male : female 

 births; when they treat the m + n events as so many independent 

 black and white balls drawn from an urn. The fluctuation of the 

 ratio, as inferred from the facts, the returns, is often very different 

 from that assigned by such a simple hypothesis. 



Another distinction is between facility-curves (other than pro- 

 bability-curves) which are, or are not, finite. The writer offers a 

 simple proof of the law of error in the former case, disproof in the 

 latter case. 



Another distinction is between (a) observations so numerous 

 as to present by simple induction or inspection the law of their 

 genesis (the method of Quetelet, Mr Galton with his quartiles, 

 deciles, &c, Mr Airy in his determination of modulus, &c), and 

 (/3) the case where the data are viewed as samples, from which 

 we are to ascend by way of inverse probability to the genesis of the 

 observations (the method pursued by, e.g., Merriman in finding 

 modulus and mean). 



Under the first heading, Mr Galton's method (Phil. Mag., 1878) 

 of finding the number of elements in a " binomial" is criticised. 



Under the heading of inverse probability, it is attempted to 

 examine its foundations: whether, e.g., in determining inversely 

 the modulus we are to assume as having a priori equal proba- 

 bility the different values of c (the modulus), or of c\ or of h 



(=-), or of h 2 — all plausible and inconsistent. There is reached 



a conclusion agreeing with Laplace's first principle (Introduction, 

 Theorie Anal). 



