The responses of systems, whose equations of motion are linear, to arbitrary applied forces are conveniently calculable by the use of impulsive or indicial admittances. Expressions for these admittances are here given explicity for some simple dynamical chains and the procedure for their calculation in chains with more degrees of freedom is outlined. Some general characteristics of the dynamical chains are also examined.

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.

The block diagram representing an aircraft in either its lateral or longitudinal motion is given and is used to explain the aircraft response in the antisymmetric stick-fixed case. A generalised autopilot is added to the aircraft diagram and the method of analysing the combination by conventional servo techniques is indicated. It is shown how an estimate can be made of the effects on stability of non-linearities in the output member of the control system.

This paper is concerned with the drag, at zero lift, of wing-body combinations which are symmetrical about the wing plane. Only two assumptions are made: that surface slopes are sufficiently small for the application of linearised theory, and that it is sufficient to satisfy the body boundary condition on the surface of a circular cylinder.

The configuration is represented entirely by singularities along the body axis, and three drag formulae are derived. The first involves the Laplace transforms of functions representing the strengths of the sources and multisources; the difficult problem of inverting these transforms is thereby avoided. The second involves these strength functions themselves, and is of the form of a series of double integrals of the famous von Kármán type. The third involves functions describing the geometry of a very hypothetical quasi-cylinder which has the same drag as the Whole configuration in question. The convergence of these formulae is established.

These results are then used to make an order-of-magnitude analysis for wing-slender-body combinations: a large number of drag terms are seen to be negligible when the ratio of body radius to wing chord is small, and the dominant terms for smooth bodies are those appearing in Ward's drag formula.

Finally, the geometry of the “ equivalent quasi-cylinder ” is investigated.

This paper concerns the free vibration of linear systems which are subject to damping. The general theory for a system having n degrees of freedom is recalled and illustrated by means of a simple example. Using an analytical method, the approximate theory for small damping is derived, showing the nature of the entrainment of the principal modes; the results are found to confirm those of Southwell (who uses a physical argument) and they are illustrated by an example. The approximate theory is shown to need modification when there are two nearly-equal natural frequencies and the appropriate corrections are found. The analysis is made somewhat complicated by the existence of two criteria of “ smallness ” instead of one; these are the difference between the close natural frequencies and the amount of the damping.