136 Mr. F. Y. Edgeworth on the 



question was that the most advantageous value is to be pre- 

 ferred to the most probable; the answer to the second question 

 was in great part a statement of most probable values. The 

 connexion between principle and practice was not very clearly 

 indicated. I now attempt to supply this deficiency. 



In reducing observations, whichever end, the most probable 

 or most advantageous, we propose, there are two methods of 

 pursuing it — according as the first step of our investigation 

 is determined only by considerations of convenience, or is 

 expressly directed to the end. The former method begins by 

 assuming that the queesitum is some simple function of the 

 observations (in particular the weighted arithmetic mean), and 

 goes on to calculate the constants so that the value obtained 

 may be either that which is most frequently right, or that which 

 is most advantageous, account being taken not only of the 

 frequency but also the seriousness of error. The latter pur- 

 sues the same ends without any initial step in the dark ; 

 making choice, not from a particular family, but from the 

 whole world, of functions. The former method is described 

 by Laplace as applicable to " observations non faites encore "*; 

 the latter to " observations deja faites." DeMorganf repeats 

 this distinction. It must not be inferred that, as DeMorgan's 

 expressions suggest, the latter method has over the former the 

 superiority of a posteriori probability over a priori. In pur- 

 suing the former method we do not act like him who, having 

 to infer the contents of an urn J, falls back upon the a priori 

 probability that one constitution is as likely as another, with- 

 out availing himself of the result of drawings from the urn. 

 We do not propose to ignore the observations, or what is 

 known of their generation, when we seek a workable formula 

 of reduction expressed in terms of the observations. Such 

 a formula might be supposed framed after, as well as before, 

 the observations are made ; just as the more perfect formula 

 might be framed before as well as after. You must of course 

 first catch your hare before you can cook it, whether plainly 

 or elaborately ; but you may write out the receipt for either 

 culinary process as well before as after the capture. Accord- 

 ingly I venture to suggest that the distinction under consi- 

 deration might be more safely expressed by the terms relative 

 and absolute. Both methods seek a maximum; the former 

 subject to a condition, the latter not. The absolute method 

 would generally be allowed to be more perfect theoretically ; 

 the relative method has hitherto been supposed to be the only 



* Theorie Analytique, Book II. chap. iv. art. 23 ; p. 365, National edition. 



t Encycl. Metrqpol. § 89. 



J Of. Laplace, Essai Philosophique, Principes, v, vi. 



