330 Mr. F. Y. Edgeworth on the 



4291-10 4481-85 



4392-00 (Thalen 4389'4) 4552-80 (Thalen 4551*8) 



4430-40 4560-30 



4435-20 4580-80 



4440-70 4852-90 (Thalen 4851-5) 



4445-75 (Thalen 4442'0) 4857-70 



4448-05 4899-00 



4455-00 4932-40 



We have taken all possible care to make this statement 

 accurate, and to admit no lines about which there seemed to 

 be any question. There are seven other lines not included in 

 the list, the probability of agreement of which is at least as 

 good as that upon which potassium is admitted. 



In all these experiments everything has been done to bring 

 out and show upon the photograph as much as possible. The 

 lamp, constructed for the purpose and fed by a powerful 

 dynamo, gave an arc from a half to three fourths of an inch 

 long, and burned with a loner flame and so intense a heat that 

 it could be worked for but a few minutes at a time. Anyone 

 who has carried out a series of experiments like this is alone 

 competent to appreciate the great labour and the endless 

 difficulties and perplexities that attend them. 



Our thanks are especially due to Dr. Wolcott Gribbs for his 

 hearty encouragement, and for the use of valuable apparatus 

 and chemicals. 



XLIV. The Empirical Proof of the Laic of Error. By F. Y. 

 Edgeworth, M.A., Lecturer at King's College, London*. 



THE Law of Error is here used as a short title for the pro- 

 position that Observations (including statistical returns) 

 tend to group themselves in the manner represented by the 



1 -t 

 Probability-curve y= ,- e &. The empirical proof of this 



V7TC 



proposition is obtained by comparing actual groups with the 

 theoretical arrangement. This examination of fact is most 

 efficient when there is present deductive reasoning ; both sug- 

 gesting what interrogations should be put to experience, and 

 corroborating the answers. 



The deductive proof of the Law of Error consists of a ma- 

 thematical theory which is the foundation of the Method of 

 Least Squares. According to this theory, observations tend 

 to be grouped according to the Law of Error when the follow- 

 ing conditions are fulfilled. Each observation must be one 



* Communicated by the Author. 



