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



critical values in the ultra-violet, the stress -optical effect will very likely be largely 

 increased. 



In order to show the accuracy with which the observations above determine the 

 value of X , the straight line passing through the origin and through the centre ot 

 gravity of the observations has also been plotted on fig. 6. 



Its equation is 



X = 175-35. W, 



and on looking at the diagram it is obvious that no such straight line can fit the 

 observations. 



Further, it will be shown that all the observations, not merely of the glass 1809, 

 but of the six other glasses examined, conform to a first approximation to the 

 linear law. 



16. Significance of this Linear Law. 



We have now to enquire how far this linear law has a physical meaning otherwise 

 than as the expression of the trivial result that within a certain range of values all 

 continuous variation is approximately represented by a straight line. 



In previous papers, when C and X were the quantities plotted, the relation was not 

 well expressed by a straight line, the observations lying, in some cases, on a very 

 decided curve (see ' Camb. Phil. Soc. Proc.,' vol. XII., Part V.). The observations 

 which led to such curves were therefore re-reduced. The glasses selected which 

 showed the effect most strongly were the Jena lead glasses O 1 52 and S 57. 



Both of these were very closely fitted by a linear relation between X and W. 

 How close the fit was may be inferred from Table II. below, which shows the 

 observed and calculated values of X for one set of experiments with S 57, which is a 

 very heavy flint glass, containing 80 per cent, of PbO. 



In the table, W denotes pressure in kilogrammes applied by means of a compressing 

 apparatus described in the paper referred to, and the entries in the column headed 

 X,.., are computed from the formula 



X = 3 1 24 '9 + 4 -51 36 W. 



The other sets of observations of S 57 and O 152, which have been re-reduced, 

 show equally good agreement between the observed values of X and those calculated 

 from a formula of type (13). 



Now the mean residual in Table II. is less than 5 tenth-metres, whereas the 

 probable error of determination of the centre of a band is about 10 tenth-metres. 

 Thus the law appears to fit the observations as closely as is possible within the limits 

 of experimental error. It is worth noting that with these glasses, which contain a 

 high percentage of lead, no deviations from the law, such as will be shown later to 

 take place in some borosilicates, appear to exist. 



Nevertheless one important experimental fact throws doubt on the universal 

 validity of the linear law, even for lead glasses. POCKELS has shown (' Ann. d. 



