Abstract: By using "four shaft concept" a balance system for the second order reciprocating inertia forces of the plane crankshaft eigbt-cylinder V-type internal combustion enr,ines was worked out as reported in the paper[1].In paper[2] we have been able to acquire a "two shaft balance scheme" as a degeneracy of the"four shaft balance system" by pur suiting a far roundabout way.By the way as a mathematical by-product it has been met possibly a new curve which could be named,perhaps,as "The Degenerated hour-Leave.d Rose".which was intended to be discussed in detail with a special paper.