The problem of the best division of pressure ratio between the two spools is investigated by means of simplified expressions for component characteristics. It is found that a unique position of the L.P. compressor operating line (i.e. maximum L.P. flexibility) is obtained when the H.P. compressor operating line is vertical. This arrangement requires a low pressure ratio on the H.P. spool and gives an engine whose power is sensitive to air intake temperature changes, so that the H.P. rotor tends to overspeed at sea level and surge at high altitude. Checks by standard methods show that the algebraic approach is useful for understanding the two-spool matching problem.