466 Mr. H. H. Turner on Mr. Edgeworth's Method of 



mentioned can readily be shown to be concentric circles. 

 The centre has the minimum intensity when the difference in 

 the distances ab ac is an exact number of wave-lengths. The 

 diameters of the consecutive circles vary as the square roots 

 of the corresponding number of waves. Therefore, if x is 

 the fraction of a wave-length to be determined, and y the 

 diameter of the first dark ring, d being the diameter of the 



ring corresponding to one wave-length, then x = ^-. 



There is a slight difficulty to be noted in consequence of 

 the fact that there are two series of waves in sodium-light. 

 The result of the superposition of these is that, as the diffe- 

 rence of path increases, the interference becomes less distinct 

 and finally disappears, reappears, and has a maximum of dis- 

 tinctness again, when the difference of path is an exact 

 multiple of both wave-lengths. Thus there is an alternation 

 of distinct interference-fringes with uniform illumination. If 

 the length to be measured, the centimetre for instance, is 

 such that the interference does not fall exactly at the maxi- 

 mum — to one side by, say, one tenth the distance between 

 two maxima, there would be an error of one twentieth of a 

 wave-length requiring an arithmetical correction. 



Among other substances tried in the preliminary experi- 

 ments were thallium, lithium, and hydrogen. All of these 

 gave interference up to fifty to one hundred thousand wave- 

 lengths, and could therefore all be used as checks on the 

 determination with sodium. It may be noted, that in case of 

 the red hydrogen-line, the interference phenomena disappeared 

 at about 15,000 wave-lengths, and again at about 45,000 wave- 

 lengths; so that the red hydrogen-line must be a double line 

 with the components about one sixtieth as distant as the 

 sodium-lines. 



LX. On Mr. Edgewortrr\s Method of Reducing Observations 

 relating to several Quantities. By H. H. Turner, M.A., 

 JB.Sc, Fellow of Trinity College, Cambridge*. 



IN the Philosophical Magazine for August 1887, Mr. F. Y. 

 Edgeworth invites attention to a method of reducing 

 observations relating to several quantities, which he has sug- 

 gested as a substitute for the ordinary process of the " Method 

 of Least Squares." I have applied this method to an example 

 for a particular case of two variables, and venture to offer the 

 following remarks and suggestions for consideration. 



* Communicated by the Author. 



