722 Transactions of the Society. 



image ; tlie rays of different elementary pencils being unable to 

 co-operate. 



For the projection of an image is based on tbe re-collection (into 

 one point) of an undulatory motion which, is derived from one 

 luminous point (one element of the original source of light). Eays 

 which originate from different luminous centres (as is the case with 

 diffracted rays appertaining to the diffraction-pencils of different 

 incident beams) are incapable of interfering — the undulatory motions 

 of those rays are quite independent of one another, " incoherent " ; 

 they cannot add their undulations according to the interference 

 principle ; but can add only their " vis viva," i. e. the intensity of 

 illumination. 



For explanation : In fig. 96 let (a, ai, ag • • • ) and 

 [h, /3i, /32 . . . ) be the cross sections of the diffraction-pencils of 

 any two different incident rays a, h, ui, /3i, a^, /Sg . . . denoting 



Fig. 96. 



corresponding diffracted rays within these pencils, or let the same be 

 a representation of any two elementary spectra at the back of the 

 objective, isolated (mentally) from the whole multitude : then only the 

 rays from the group a, ai, ag • • • act together by way of interference 

 at the plane where the image is projected — and project such an image ; — 

 and also the rays emanating from h, /3i, /Sg . . . in the same way ; 

 but no ray of the first pencil unites with any one of the others. 



Consequently, the image which is obtained by menus of the wide 

 illuminating cone is a mere superposition of a multitude of elementary 

 imao-es, produced quite separately by the various narrow beams ; and 

 this superposition consists of a mere addition of the quantities of 

 light, which the various elementary images obtain at one point of the 

 field, and does not involve an addition of the amplitudes of oscillatory 

 motions according to the interference-principle (as is the case in the 

 formation of every single elementary image). 



(4) The elementary images produced by the various narrow 



