DISPERSION IN ARTIFICIAL DOUBLE REFRACTION. 293 



19. Discussion of the Values of X , & 



The first thing which strikes the eye on looking through the results of the last 

 section is, that although tension observations of different orders and pressure obser- 

 vations of different orders are fairly well fitted by the same AO, W u , and k, the same 

 does not hold of tension and pressure ol>servation8 taken together. 



The differences in k are only what should have been expected, since k depends on 

 the adjustments. 



With regard to kW a the values for pressure and tension should theoretically be 

 equal and opposite. For if light traverse a thickness r of glass in which a residual 

 tension T n exists, a term CT,,T is added to the relative retardation when external 

 tension is applied and subtracted from it when external pressure is applied. 



Again A,, should l>e a constant for the glass, and therefore the same for tension and 

 pressure, if the stress-optical coefficient l>e independent of the nature and magnitude 

 of the load applied. 



Now Table III. shows clearly that, although the values of kW n differ in sign, they 

 are only very roughly of the same order of magnitude. 



Possibly this might be accounted for by the fact that in different experiments the 

 light did not pass through the same parts of the glass, so that the value of the 

 residual stress miglit have been different. 



The divergences in X are considerable ; AU appears systematically larger for 

 pressure than for tension.* 



20. Systematic Residuals. 



The residuals A,,,,, \ nl have in all cases been plotted on a large scale against A l4l . 

 Three of these diagrams are shown in figs. 7 to 9. The pressure and tension olwerva- 

 tions have l)een plotted to a different base in each case, to avoid the diagrams over- 

 lapping, so that two zero-marks appear on each scale of residuals. Of these the 

 upper zero mark refers to tension ol>servation8. 



Most of them (e.g., fig. 9) are fairly irregular, which is not surprising when we bear 

 in mind that an error of 1 division in the ordinate (10 tenth-metres) is the probable 

 error of the observations. 



Two glasses, however, 3296 and 3453, figs. 7 and 8, appear to show very strongly 

 systematic residuals between 4200 and 5500. If we look at fig. 7 we notice that the 

 curves rise from 4200 to a peak about 4700, after which there is a sharp fall with a 

 trough alxnit 5050. 



AtttT this the curves run fairly horizontal, with indications of another peak at 6300. 



[* Note added April 3r<1, 1907. Later experiments do not confirm the systematic difference between the 

 v.-ilurs of A,, fur tension ;m<l pressure. Very prolwbly the divergence previously noted was due to a change 

 in the adjustments which had to be made when passing from tension to pressure, and which rendered the 

 observations of the two kinds not strictly comparable. 



The true value of A.,, appears to be the mean of the values obtained for tension and pressure.] 



