ON CERTAIN DIFl'KACTiON PHENOIVIENA. oU) 



I shall tirsl pci-l(jrm llie intégrât ion with rcspccl to ^^. 

 We can write 



/* i 6 a' s/«"- (p , /■ / ^ (1 - t-us 2 (f ) , I / ^' /• - / ^' füÄ '2(f> , ,-, , 



/e ^ay^ = je - dç = —p— c - /c ^ a (I if). 



The intégral thus ohtained corresponds to /, Avhicli was already 

 investifTîited in connection with Fraunhofer's (htîVaction ])henoniena. 

 I sh:d], therefore, write ibr simplicity 



(3) p^''''"'''^dir =.K + iU 



Again 



/e ^ " ''"' *^ cos (f d(f = — J -\ cos {a^T~ sin (f)- d {ii ^yi~siii (f) 



+ i I sill {a -y/ Ç sin if)- d {a y/ 5 sin <.ç) I. 



l')ii( /'^'^ ((t a/1~ -s-i/i cr)-(^ (a^/ysmcr) are derivahle in terms of Frcsnel's 

 J sin 



integrals, for whicli the series oljtained by Knochenhaucr, <iilbcrt, 

 Cauchy, or Lommel can be used for calculation. 1 shall, ihereibre, 



})Ut 



( i ) e ^ cos (f dif ^ I + I 1 



Xext [)eriorming the integration with respect to x, we liave to iind 



le ^ '*" dx and c ^ ""^ x dx. 



The ürst is an ordinary Fresnel integral ; and can, therlbre, be 

 written 



( 5 ) p ^ ""' dx = C + i S, 



wliere 



