Let t be the time it takes standard ¿-dimensional Brownian motion, started at a point inside a cone T in R¿ which has aperture angle 6 , to leave the cone. Burkholder has determined the smallest p , denoted p(6, d), such that Etp = oo . We show that if y e dF then the smallest p , such that E(rP\Bz = y) = oo , is p = 2p{6, d) + (d -2)/2 . We will be working with spherical coordinates in Rd , d > 2. Let, for a point x = (xx, ... , xd) £Rd, \x\ = (Y^xf)x/2, and let tp be the angle that the line

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... gment connecting the origin 0 and x makes with the line segment connecting the origin and 1 = (0, 0, ... ,0,1). Let, for 0 < d < n, Y = T(d, 0)