110 DIFFRACTION. 



plete, that the computed places of the several bands seldom 

 differ from those observed by more than the 100th part of a 



millimetre. 



\ 



(125) The general circumstances of these phenomena 

 may be deduced by very simple considerations from the 

 principles already laid down ; although the complete de- 

 velopment of these principles demands the aid of a compli- 

 cated analysis. 



Thus, in the case of the fringes produced by a single 



N. 



edge, let be the luminous origin, Mo-N a diverging wave, 

 and E any point at which the illumination is sought. From 

 this point, as centre, let a circle be described, touching the 

 circle MN in #, and let the lines RM, Ita'c, &c., be drawn in 

 such a manner that the intercepts W, cc', dd', &c., are equal 

 respectively to one, two, three, &c., semi-undulations. The 

 effect produced at the point R is then, by the principle of 

 Huygens, the sum of the effects produced by each of the por- 

 tions ab, be, cd, &c., separately. But, the distances of these 

 consecutive portions from the point R differing by half a 

 wave, their effects will be opposed at that point ; so that, if 

 m denote the intensity of the light sent from the portion ab, 

 m' that from be, &c. the light sent from the indefinite wave, 

 #Mor N, being taken as unity the actual light which reaches 

 the point R will be 1, 1 + m, 1 + m - m', 1 + m - m' -f m" , &o., 

 according as the obstacle is placed at the point <?, b, c, d, &c. 



