IN FOCAL PLANE OF TELESCOPE. 345 



•drawing the lines <it small intervals, we can obtain a sufficiently large 

 number of such points. The curve obtained by joining these points 

 will be that of equal intensity, and will represent the distribution due 

 to these different sources, The process of drawing the lines of equal 

 intensity is thus analogous to that of drawing equipotential lines. 

 In Fig. 7. PI. XVII., the fine lines are those of equal intensity for a 

 circular disc of radius 40, and an infinite plane with a straight edge ; 

 the combined effect due to the luminous plane and the dark disc is 

 illustrated by the distribution of thick lines, which give the places of 

 equal intensity. The dotted lines show the geometrical boundary of 

 the plane and the disc. 



A problem which has been the subject of long discussion by 

 astronomers comes next under our notice. In the transit of inferior 

 planets over the sun's disc, we observe the phenomenon of drop- 

 formation by the ingress or egress between the rim of the sun and of 

 the planet. 



Suppose now that the luminous source is a circular disc, on 

 which there is a small dark circular space nearly touching the rim of 

 the disc. The image as seen through the telescope will form a drop 

 near the rim, as consideration of the lines of equal intensity will 

 immediately show. We can imagine such a source as produced by the 

 superposition of two different sources, one of which consists of a. 

 circular disc of uniform intensity without any dark space, while the 

 other consists of a circular disc occupying the place of the dark space, 

 and of such an intensity that it is equal but of opposite sign. This 

 consideration gives the solution of the problem either as a mathema- 

 tical formula or as a graphical representation. 



For the latter purpose, we draw the concentric circles represent- 

 ing lines of equal intensity for the luminous source, and similar lines 

 of equal negative intensity for the imaginary source occupying the 



