(425 ) 



In iinler to obtain a somewhat ;4cneral survev of the diffeient 

 pojsiblo cases, which wltc tor us of iniportancL', wc havo uiado 

 concorniuii: the ratio 



« + 6 



the siguificauce of wliicli will bo clear, three hypotheses, viz. 

 Ö — 3, <5=1 and d — 0,6. 



The tirst slit is with the first hypothesij rather wide, with tlie 

 third rather iiarrosv as eonipared with the second slit. The intensity 

 curves for the diHraction iniai^es in the 9 cases are plotted down 

 in fig. 3 a — i. 



Til the same plate are represented also by dotted lines the intensity 

 curves with the s?nie slits and with rectilinear propagation, using 

 the circumstance that th(( areas enclosed between the intensity 

 curves and the axis must he the same with and without diffraction. 



From these figures it appears that already with great values of 

 1%. broadening will be visible, provided that the least perceptible 

 intensity, is reri/ small as com[)ared with tlie greatest intensity, 

 which with given width nccurs in the image of the slit. 



However in our case of the broadenings resembling plumes tiio 

 last condition is certainly not fulfilled ; in the centre of the slit 

 image the intensity is already small, and a high ratio at the edges 

 would be necessary in order to be perceptible. 



In this case Ave see at once from the curves, that with a vaUu^ 

 v., =: 1 there must be in all cases a distinct broadening, witlirs=:2 

 probably never, with i-^. = 1.5 only under favourable circumstances 

 as to the width of the tirst slit, and then only in a small degree. 



It is also clear that, though the influence of the value of ö on 

 the visibility of a broadening exists in general, yet this influence 

 is not great for values of r, between 1 and 1..5. Taking this into 

 account we think to be justified to take Vg =^ 1,3 in every case the 

 slit image is sensibly broadened, that is in the case of every plume. 



Hence we find by means of the relation 



. _ 1 2 (a + t) ., 



29 



Procccdinsrs Roval Acad. Amstecdaiu. Vol. I. 



