524 Transactions. — Chemistry and Physics. 



X (which we are going to take as absolutely accurate, 

 theoretically). It is common to take the mean of both quan- 

 tities, a process that often leads to the use of a few more 

 decimal places. A more satisfactory process is to either mea- 

 sure dY/dX or else estimate it from antecedent knowledge of 

 the likely curve, and then make a graph of the measures of 

 each datum point and analyse it by means of the curve of 

 dY/dX, which will be usually a straight line. From this we 

 can get the probable (fortuitous) error, and also make a note 

 of discordances, which is not always possible when the mean 

 merely is taken. 



li. A further advantage lies in the fact that we can avoid 

 taking the mean value for X, and take instead a convenient 

 adjacent value which has few integers, the last few significant 

 figures being made noughts. This affords a vast saving in 

 tabulation and in computation. 



15. It may be thought by some that such matters as are 

 being advanced are refinements for which time is too short ; 

 but the writer would appeal to those who may have honestly 

 tried to get a reliable value for any physical constant which is 

 not absolutely simple or else fundamental — even a there or 

 thereabouts value — whether an enormous amount of labour 

 has not been absolutely wasted by the neglect of such prin- 

 ciples. 



Least Squares. 



16. An assertion will now be given which it is believed 

 can be substantiated by reference to some recent text-books — 

 that if a formula be applied to the results of observation so 

 that the sum of the squares of the residual quantities or 

 deviations of observed quantities from those calculated is a 

 minimum with regard to the constants of the formula, then 

 this formula may be referred to as the best, or even the most 

 probable, and, in fine, that such application is a strictly 

 scientific process. It must not be supposed for a moment 

 that it is intended to convey that this view is held by accurate 

 thinkers, but simply that it is observable that others have 

 been led by the beauty of the method, and the very evident 

 desirability of possessing a method of computation which 

 should be free from personal bias, into an unwarrantable and 

 indiscriminate promulgation of the formal procedure of the 

 method. 



17. There are two distinct objections to the mode of com- 

 putation which has been described, and which it is hoped may 

 be described as " least squares" without misunderstanding — 

 namely : (1) That least squares observably tends to eliminate 

 the application of the judgment to the indications of a graph, 

 and, further, that it tends to make systematic deviations 



