Propeller theory has always been a subject of extreme difficulty, and those who riginated the screw propeller as a means of propulsion and developed itduring the latter half of last century were in most part guided by common senseand empiricism. Without much in the way of theory to guide them the results thus achieved in connection with marine propulsion were remarkable—but little short of the best possible. The designers of the early experimental aircraft were able to make use of the wealth of experience thus placed at their disposal; nevertheless, some new aspects of the problem presented themselves—fortunately the vortex theory, newly developed to deal with the problem of sustentation in flight came to their aid, though the manner of its application was not obvious or easy. The writer's first attempt consisted in treating the propeller blade as an aerofoil connected to the boss by an arm of spar section, geometrically related to a helical surface, in which the tracks of the blades relatively to the fluid follow these surfaces.

If A, B, C,… be the successive bending- moments involved, the equations to find them have the following characteristics : The first involves A and B only, the second A, B and C only, the third (if more than three) B, C and D only, and so on for all intermediate equations; finally, the last equation contains only the last two unknowns.

The method to be considered applies more generally, however, when each equation in succession contains only one additional unknown, so that the third may contain A, B, C and D, the fourth A, B,C, D and E, and so on.

It often happens that in a plane truss all joints are not transversely stiffened. If one joint of the compressed girder of a beam is free, the girder is liable to fail by buckling perpendicular to the plane of the truss, between the adjacent joints. The chart given here enables a rapid determination of the critical loading to be made. The compression and moment of inertia are assumed constant along the length of each bay, but may be different in the two bays.