The image of a source of strength p at S outside a sphere of radius a is a source of strength pa/f at H, where 'OS' =f, OH =a2/f, and a line sink reaching from the image H to the centre 0 of line strength - A la; this combination will be found to produce no flow across the surface of the sphere.
Between H and S, Ar 3 and Ar 2 occur together, as do Ar 2 and Ar l between S and P' and Ar 3, Ar 2 and Ar t at S itself; so that these critical points in these special cases are called Ar 3 _ 2, Ar2_1 and Ar 3 _ 2 _ 1 respectively.
Ay, it's spring again, WI aa the twists an turns that Mother Nature can throw at's.
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