448 THE PRINCIPLES OF SCIENCE. 



has crept into several works which allude to this subject. 

 Mr. Mill, in treating of the Elimination of Chance/ re 

 marks in a note l that the mean is spoken of as if it were 

 exactly the same thing with the average. But the mean, 

 for purposes of inductive inquiry, is not the average, or 

 arithmetical mean, though in a familiar illustration of the 

 theory the difference may be disregarded. He goes on to 

 say that, according to mathematical principles, the most 

 probable result is that for which the sums of the squares 

 of the deviations is the least possible. In Bowen s Treatise 

 on Logic (p. 439), we find the Method of Least Squares 

 mentioned as a mode of finding the most probable result 

 in those cases in which the arithmetical mean is not an 

 applicable expedient for determining the probability. It 

 seems probable that these and other writers were misled 

 by Dr. Whe well s remarks on the subject ; for he says k 

 that The Method of Least Squares is in fact a Method of 

 Means, but with some peculiar characters. . . . The 

 method proceeds upon this supposition ; that all errors 

 are not equally probable, but that small errors are more 

 probable than large ones. He adds that this method 

 * removes much that is arbitrary in the Method of Means. 

 It is strange to find a mathematician like Dr. Whewell 

 making such remarks, when there is no doubt whatever 

 that the Method of Means is only an application of the 

 Method of Least Squares. They are, in fact, the same 

 method, except that the latter method may be applied to 

 cases where two or more quantities have to be determined 

 at the same time. Many authorities might be quoted to 

 this effect, but it will be sufficient to mention Lubbock 

 and Drink water, who say , If only one quantity has to be 



System of Logic, bk. iii. chap. 17, 3. 5th ed. vol. ii. p. 56. 

 k Philosophy of the Inductive Sciences/ 2nd ed. vol. ii. pp. 408, 409. 

 1 Essay on Probability, by J. W. Lubbock and J. E. Drink\vat er, 

 Useful Knowledge Society, 1833, P- 4 1 - 



