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XVIII. The Adjustment of Observations. I. 

 By Norman Campbell, Sc.D* 



1. X^OR more than fifty years the method of adjusting 

 J? observations affected by experimental errors has 

 always been that originally proposed by Gauss. The rules 

 necessary for its application are embodied in the formalism 

 of the c; Method of Least Squares/' Against the method 

 and the rules by which it is applied t\vo main objections 

 have often been urged : it is said that the theory on which 

 the rules are based is not true and that, even if it were 

 true, the rules are not an accurate expression of it. No 

 serious inquirer pretends nowadays that the method can 

 be completely defended against these objections : its use 

 is justified partly on the grounds of practical convenience 

 and partly on the ground that any method not open to these 

 objections would produce practically the same results. The 

 second contention is probably valid, but it provides a justifi- 

 cation for the use of the method only if the first is also valid, 

 and if there is no method equally convenient which is not 

 open to more serious theoretical objections. I believe that 

 the first contention is not valid and that in some cases — and 

 especially in those cases of most importance in physics — 

 there is a method of adjusting observations which is at once 

 more convenient in practice and more sound in theory. The 

 object of this paper is to explain and support that view. 



Perhaps I may be pardoned for insisting at the outset 

 that my remarks deserve some attention. The theory of 

 errors has great intrinsic interest, but it is not a matter 

 to which physicists, even if they are in the habit of using it, 

 generally pay much attention. Its later developments are 

 extremely complex and highly technical, and most of us 

 do not study carefully the memoirs dealing with it which 

 appear from time to time in scientific journals. Those 

 memoirs do not generally pretend to subvert the accepted 

 rules for adjusting observations, but only to extend them 

 to somewhat unusual examples or to provide additional 

 support for them. But I do wish to subvert those rules : 

 I contend that the Method of Least Squares is an intolerably 

 cumbrous method for obtaining quite misleading results, 

 that there is a method which is incomparably simpler and 

 gives results which are not misleading, and that the only 

 persons who have any adequate reason for continuing the 



* Commuicated by the Author. 

 Phil. Mag. S. 6. Vol. 39. No. 230. Feb. 1920. X 



