470 Reducing Observations relating to several Quantities. 



These equations were discussed by Mr. Thackeray in the 

 Monthly Notices of the Royal Astronomical Society ; and his 

 solution, obtained by simple addition of the equations with 

 large and those with small coefficients of y, was 



a?=l"'432, 



y = 0"-014. 



It is possible that the number and distribution of these 

 points of intersection afford real information as to the value 

 and accordance of the observations. But, in practice, a 

 single solution, although its singularity may be somewhat 

 fictitious, is preferable to a variety ; and unless some ad- 

 ditional criterion for extracting a single solution from the 

 median loci can be obtained, it is to be feared that we have 

 here a somewhat serious objection to this method on the score 

 of convenience. 



The extension to the case of three variables is obvious : the 

 three normal equations, or rather the planes which they repre- 

 sent, are replaced by three broken-plane loci, made up of 

 individual planes corresponding to the separate observations. 

 These loci may intersect in a finite portion of a plane, one or 

 more finite lines, and one or more points : and the multiplicity 

 of solutions is obviously liable to increase largely with the 

 number of variables. 



Mr. Edgeworth claims as advantages for the new method 

 that 



(1) It is considerably less laborious than the Method of 

 Least Squares. 



(2) In the case of Discordant Observations it is theoreti- 

 cally better. 



So far as my slight experience entitles me to express an 

 opinion on these points, I should say that 



(1) is very doubtful. In trying a new method much time 

 is liable to be wasted ; but there wouid, I imagine, never be 

 quite the same straightforwardness about the new method 

 which makes the method of least squares so easy, although 

 somewhat long. 



(2) is somewhat counterbalanced by the failure to give a 

 unique solution. 



