On the Law of Error and Correlated Averages, 429 



the little changeful group of interwoven thoughts that is 

 himself — is a very small part of the great Autic Universe. 

 We must shift our centre, and exchange the metaphysician's 

 narrow Ptolemaic for a broad Copernican view of existence. 



L. The Laiv of Error and Correlated Averages. 

 By Professor F. Y. Edgeworth, M.A., D.C.L* 



npHIS is a contribution to the investigation of the most 

 -L general conditions under which the exponential law of 

 error is fulfilled ; together with some applications to the 

 theory of " correlated averages" f. 



I. The simplest case in which a group of measurable objects 

 r^nge in conformity with the law of error is where every 

 member of the group is a sum of a certain number of items, 

 or elements, each of which has or has not a certain quality, e. g. 

 the colour white, or, as it may be expressed, assumes the value 1 

 or 0, with a certain average frequency (e. g. 1 just as often — 

 or half as often — as 0, in the long run) and at random, or in 



are a part of the autic universe, are shadowed by certain objective 

 changes in my brain ; and the term synergos means that other portion of 

 the autic universe which is shadowed by all the other events that happen 

 objectively in my brain. It appears from physical considerations that the 

 particular stream effects or other changes in the brain that were the 

 shadows of the perceptions I had at breakfast-time, cannot have occurred 

 alone, but were accompanied by more subtile motions or changes in the 

 brain, which were the shadow of, and thus betokened, certain closely 

 associated events then going on in my synergos. These again were suc- 

 ceeded by motions, changes, or states of strain in the brain during the 

 intervening hours, all of which were a part of the varying shadow of the 

 synergos as it underwent whatever changes took place in it during that 

 interval. Moreover, these intervening events in the brain were of such a 

 kind, as the result has proved, that they have been now followed up by 

 motions or changes in the brain which resemble those that were the 

 shadow of my thoughts at breakfast-time, and which are a part of the 

 group of events now going on in my brain that are the shadow of those 

 thoughts that constitute my mind as it exists at present. 



Softening of the brain is the shadow cast within the objective world 

 when very unfortunate events have happened in the autic universe — 

 events which have included a weakening of the power which the synergos 

 and the mind previously had of mutually acting on one another, or else 

 which have prevented the full formation within the synergos of some of 

 the intermediate links of causation spoken of above. Either of these 

 would involve a partial loss of memory. 



* Commuuicated by the Author. 



+ See Galton (Proc. Roy. Soc. 1888), " Co-relation^ and their Mea- 

 surements ; " and Weldon (Proc. Roy. Soc. 1892), " Certain Correlated 

 Variations in Crangon vulgaris-" also li Correlated Averages," by the 

 present writer in the Philosophical Magazine for August 1892. 



