DISPERSION IN ARTIFICIAL DOUBLE REFRACTION. 289 



formed, corrections were applied to the observed load and the observations re-reduced 

 with y = 0. 



From this point onward, therefore, y may be taken zero in the reductions, k is 

 then equal to r (AX/A\V) r . 



In practice the values of r(AX/AW) r vary slightly with different r's. In most 

 cases, li.i \\r\rr. a sitHiricnt ly I^MM! tit is nlitaineil l>y taking for / tlir iiu-an \alin- of 

 r (AX/AW) r and reducing the observations of different orders by means of this single 

 value. In one glass MIMIKK'S law did not seem to hold quite exactly, and the 



observations of different orders were reduced independently. 



| 

 k having been determined, AO+ - W is found from the condition that the best fitting 



straight line 



X = Xo+-W +-W. (22) 



r r 



must be satisfied by the mean values X = X, W = W. 

 We thus obtain equations 



A,= 



2A, = 



3A 3 = 3Xo + JtW = 3X 3 - 



etc. 



Two of these equations are theoretically sufficient to determine Xo and W . In 

 practice three are often obtained. The three equations are then solved by least 

 squares. The solution is given by 



Xo = (3A 3 -A,)/2, 

 kW = (Ai + 2A,+3A s )/3-2Xo. 



From the values of k, Xo, W so determined X has been computed from the 

 formula (22) and compared with the observed value. 



18. Tables of Results. 



The following gives a table of the constants Xo, /fcW , k for the various sets of 

 observations. Observations corresponding to tension and pressure are distinguished 

 by the letters T, P respectively. 



When X,,, k, kW t are known, the wave-length of the band of r* h order is computed 

 from the load by the formula (22). The average discrepancy in tenth-metres between 

 X thus calculated and X observed, for each set of observations, is entered in the column 

 headed (O-C). 



VOL. CO VII. A. 2 P 



