From Horners book, some quotes without comment. (excuse typing mistakes) From here to bottom all quotes, not by me:-)

At the location of lifting line or wing, the flow is deflected by an average angle which is half the final theoretical downwash angle. that angle is the induced angle of attack ..............the force "F" originating in a direction normal to the average direction of the flow in the vicinity of the wing, is therefore tilted backward by the incuded angle

alphai - CL / pi A

In this manner, the force exhibits a component in the direction of flow, which is the induced-drag, represented by the minimum coefficient

CDi = CL tan alphai = CL CL / pi A..........

Any deviation from the elliptical distribution results in a certain increase of the average or effective induced angle of attack. There are other effects of wing shape (sweep, dihedral) that make the induced drag larger.........

In low aspect-ratio wings, the lateral edges have an important influence upon lift and drag...... A similar but smaller effect of wing tip shape is also found in other aspect ratios. .........

A series of shapes has, therefore, been investigated on a basically rectangular wing............ Shapes with sharp lateral edges are seen to give the widest effective spans, while rounded edges result in a loss of effective span or aspect ratio. ......

It is seen that the shapes having the widest vortex spans, are generally the ones exhibiting the least drag due to lift.............

In conclusion, the shape of the tips can be more important for the performance of an airplane than the plan form of the wing.......