On the Motion of a Homogeneous Spheee Oe Spheeical Shell on an Inclined Plane, Taking into Account the Eotation of the Eaeth

is continuous and as is readily seen single-valued. Thus the first term on the right taken along any closed path of the region is 0. As to the second term, consider any closed path not including c. Then F (z) and F'(z)—f(z) are both continuous throughout the enclosed region and hence the integral along the boundary of the region is 0.* Finally let the path include c and surround c by a small circle. Then ƒ F(z) dz extended in the usual way over the path and the circle will vanish. But the contribution that the circle yields is readily seen to be null; and thus ƒ F(z) dz along any closed path whatever vanishes. Hence <p(z) is analytic at c too. I ts derivative at c is