Abstract. This is an unpublished note, to be read with our article "The Self-Avoiding-Walk and Percolation Critical Points in High Dimensions" (mp_arc, paper# 93-286). Here, we consider in detail (1) the $O(s^6)$ calculation of $\mu$ for the self-avoiding-walk, (2) the calculation of amplitude $A$ and diffusion constant $D$ for the self-avoiding-walk, and (3) detailed $O(s^3)$ calculation of the critical point $p_c$ for bond percolation. Each of these is treated in separate sections, preceded by a brief supplement to Appendix~\ref{sec-AppA} of the archived paper, 93-286. PLEASE NOTE that this note is accompanied with five figures. These figures will also be archived in about a week (i.e. by the middle of November) to this mp_arc.