288 DR. L. N. G. FILON ON THE 



The correct value for the load is given by 



It is therefore a formula 



X = X +F(W +W+yW 2 ) 

 which has to be fitted. 



Assuming for the present that for monochromatic light the relative retardation is 

 strictly proportional to the load, we have, for the band of the r th order, kf = k/r, where 

 k is the same constant for observations of all orders. Thus 



rX = -rAo + fcWo + i-W + fcyW'. 



Suppose we have p observations, the first step is to take a number of differences AX 

 corresponding to differences AW sufficiently large to minimise the effects of accidental 

 irregularities and to form the fraction 



2(AX)/2(AW) = {(AX)/(AW)} r , 



the suffix r denoting that the band observed is of the r fh order. 



If our p observations correspond to values of W differing by a constant increment 

 AW, and if we take differences of X corresponding to differences <?AW, we obtain 

 pq equations 



If these be added up, we have 



r\ . 1 

 iq(p- 



-X. -AW = 



. . 

 q(p-q) .=1 



where W = mean value of W. 

 We have then 



........ (21). 



A comparison of the values of r (AX/A W) r then enables us at once to discover whether 

 a correction yW 3 is needed for the observations or not. 



For most of the glasses examined the values of r(AX/AW) r do not indicate a 

 correction of this type of sensible amount. In doing the reductions for such glasses y 

 has been taken equal to zero. 



For one glass y has a sensible value. In this case a suitable value of y having been 



