We study the image of a transfer homomorphism in the stable homotopy groups of
spheres. Actually, we show that an element of order 8 in the 18 dimensional stable
stem is in the image of a double transfer homomorphism, which reproves a result due
to P J Eccles that the element is represented by a framed hypersurface. Also, we
determine the image of the transfer homomorphism in the 16 dimensional stable
stem.
