178 Dr. Norman Campbell on the 



use o£ the older method are the members of the National 

 Union of Computers (if there is such a body) who might 

 be thrown out of a job if the proposed method were adopted. 

 Since the only justification for the older method which has 

 so far stood the test of criticism is that it is practically 

 convenient, I maintain that the mere proposal of a more 

 convenient method throws the onus probandi on those who 

 refuse to use it. 



2. The three problems. 



There are three sets of circumstances in which the need 

 may arise for adjusting " inconsistent " observations. 



(1) A number of measurements which do not agree 

 completely are made directly on a single magnitude, for 

 instance, the length of some definite rod or the time of 

 some definite process. It is required to determine from 

 them the " true value."" The rule universally adopted is 

 that the arithmetic mean of the measurements should be 

 selected as the true value*. We shall see that its validity 

 mio-ht be established directly by experiment. It is doubtful 

 whether the necessary experiments have actually been per- 

 formed, but I shall assume that the universal acceptance of 

 the rule shows that no experiments conflicting with it have 

 been made, and that, therefore, if it were suitably tested, 

 it would be established directly. 



The matter is exceedingly important because on the 

 acceptance of this rule are based, either explicitly (as by 

 Gauss) or implicitly, the rules for solving the two remaining 

 problems. Any theory of error which is to lead to practical 

 rules must assume that in this case some rule is known for 

 determining the true value from the inconsistent obser- 

 vations. If we did not accept the arithmetic mean as the 

 true value, we should have to accept some other mean if any 

 progress was to be made. 



(2) A number of measurements have been made on 

 several magnitudes between which a relation is known. 

 The arithmetic means of the measurements made on each 

 magnitude do not obey this relation ; consequently they 

 cannot be the true values. It is required to adjust the 

 observations so as to obtain true values which do obey 

 the relation. For example, the magnitudes may be the 

 three angles of a plane triangle : their sum must be 180° ; 



* Some modification of this statement may be necessary if " systematic 

 error " is suspected. Such error will be discussed in the sequel. I do 

 not think it can arise if the conditions contemplated are fulfilled strictly, 

 and the measurements are made directly on a perfectly defined system. 



