126 



Prof. C. Barus on Elliptic and other 



When there is reinforcement the path difference of the 

 rays L and 1/ from the incident (d) to the diffracted (7i) 



wave front, may be written 



n\ = b — a, 



where b and a are the distances of h and d from the points 

 of incidence of L and U on the grating g and </, respectively. 

 If, finally,/ is the length of the prolongation of U between 

 the gratings we may write in succession 



rf=H"D'cosi, 



/=■ e sec i, 



a = ND sin i — £ sec i, . 



tan 7 = a/rf, 



c = NDcos? sec 7, .... 

 b — c sin (i + # — 7) .... 

 To these should be added 



dN/de= tanz/D 



Hence, after removing 7, arranging and reducing, 



n\=ND (sin 6 — smi) + e secz (l + cos(z + 0)); 



or since sin i — sin — \/D, 



finally, 



1+ cos(i + (9) 2g cos 2 (i + d)/2 



cos i 



(1) 



(2) 

 (3) 

 (4) 

 (5) 

 (6) 



(7) 



(n + N)\=« 



cos» 



(8) 



