IX FOCAL PLANE OF TELESCOPE. 



331 



The foregoing table enables us to integrate (II) mechanically for 

 a source of given geometrical shape. About a point at which the 

 intensity is sought describe a number of concentric circles dividing 

 the region of integration into a series of zones, whose breadth will be 

 equal to the difference between the successive roots of J l (x)=0. If 

 the angle subtended at the point by these zones be known, we can by 

 summation of the separate effects find the intensity at the required point. 



If the luminous source subtend several seconds of arc, the value 

 of r would be a large quantity. Thus, if the boundary does not show 

 great irregularities, we can approximate!) 7 assume it to be straight for 

 contiguous zones. Calculating the mean angle x„ subtended by the 

 zone at the point, we get approximately 



i-^Z^h-h-,). 



(Ill) 



We notice that for the first zone, I I — 1 =0.8378, while for all the 

 rest I œ — J 1 = 0.1622 ; it is thus necessary to subdivide the first zone 

 into a series of subsidiary zones and sum their effect as for the other 

 zones, provided a is different from 2~. In addition to this, we shall 

 have to add a small correction for a few successive zones, inasmuch 

 as we multiply the height of the step by the arithmetical mean of the 



