282 DR L. N. G. FILON ON THE 



The parts A, B, C refer to observations for tension : A', B', C' to observations for 

 pressure. In the columns headed W a (n = 1,2, 3) are placed the observed weights, 

 the suffix n indicating the order of the band observed, bands in pressure observations 

 being taken of a negative order. The same notation will be kept throughout. The 

 columns headed X^ contain the observed value of the wave-length of the light quenched, 

 in tenth-metres. They are deduced from circle readings of the spectroscope, the law 

 connecting these circle readings with the wave-lengths being obtained from 

 observations of a known comparison spectrum. The spectrum of the arc between 

 carbons soaked in calcium salt was used for this purpose. 



Now, if we look at Table I., A., under the heading AX,,,.,., we see that the differences 

 of the observed X for unit differences of W have a fairly constant average value, as is 

 well shown on taking differences corresponding to differences of W of three units. 

 This is done in the column headed 3AX ob8 of Table L, A. 



It would seem, therefore, that the relation between X and W is approximately 

 linear. This impression is found to be confirmed when differences are taken in 

 Table I., B, C, A', B', C'. In each case the differences are sensibly constant, 

 especially if we bear in mind that an experimental error of 1 tenth-metres is to be 

 expected. 



There are some local inequalities, some of which will be shown later to be probably 

 significant, but as a first approximation it seems we may assume a linear relation 

 between X and W. 



Fig. 6 shows the observed X plotted to W for the set of observations of Table I., B'. 

 The observations obviously lie very close to the straight line given by the equation 



X = 949 + 145W. 

 This equation was obtained by assuming a formula 



X = Xo + fcW .......... (13). 



k = -= was obtained by taking the mean value of the differences in the columns 



(JL W 



headed 3AX, )t<i of Table L, B', and X,, was then determined from the condition that 

 the best straight line must pass through the centre of gravity of the observations. 

 The equation (13) clearly leads to the relation 



or, R being the relative retardation for a band of th order, 



R = n*W/(l-Xo/X) = CTr/(l-X,,/X), 



where T = effective tension, T = thickness, C = a constant independent of the 

 wave-length. 



