with the Aid of a Grating. 429 



These results show that the distance apart o£ fringes on 

 the two sides of the centre of ellipses is not very different, 

 though they are somewhat closer together in the hlue than 

 in the red end of the spectrum, as observed. There is thus 

 an approximate symmetry of ovals, and dO/dn falls off very 

 fast on both sides of the infinite value at the centre. 



The observed angle between the Fraunhofer lines D and E 

 for the given grating was 4380". The number of fringes 

 between D and E would thus be even less than 4380"/638" 

 = 6*7 only, which is itself about 4 times too small. The 

 cause of this is then finally to be ascribed to the assumed 

 constancy of — a=(dfi/fi)/(d\/X) J a discrepancy still to be 

 remedied. We may note that a does not now enter as 

 directly as appeared in equation (16). 



By replacing a by its equivalent, equation (18) takes the 

 form 



1 • • (19) 



dn 2D cos 6 e 



(*-*S) 



and a definite series of values may be obtained by computing 

 dfijdK ; but as all experimental reference here is, practically, 

 not to path differences but to displacements of the movable 

 opaque mirror N, the form of the equation applicable is 



d ± = _* 1 (9 ) 



dn 2D cos ( ^ X dfi\ ' v J 



e\ uu cos R ^ -&) — -N 



(^ cosR -^iR7a) 



To make the final reduction, I have supposed that for the 

 present purposes a quadratic interpolation of /ul between 

 the B and the y lines of the spectrum would suffice. Taking 

 the E line as fiducial, I have therefore assumed an equation 

 for short ranges, corresponding to Cauchy's in simplified 

 form, 



in preference to the more complicated dispersion equations. 

 From the above data for light crown glass we may then put 

 roughly, Z> = '456 x 10" 20 and dfi/dX= -2b/\\ Thus I found 

 the remaining data of Table III. The results for dO/dnsLgree 

 as well with observations as may be expected. The ovals 

 resemble ellipses, but are somewhat coarser on the red side, 

 as is the case. 



The centres of ellipses are thus defined by the semi air- 

 path equation 



y= *L-x^) = — ,s (p + Zb/X*), nearly, (21) 



