This paper considers the linearised unsteady motion of a lifting surface in a perfect fluid, proceeding from the fluid mechanics equations written in terms of distributions. A singular integral equation which determines the pressure on the lifting surface is deduced. The particular case of the lifting surface which moves over a (fictitious) cylindrical surface along the generatrices is considered. Kussner's equation is given a new derivation without assuming a velocity potential. The particular case of the lifting surface which moves over a helicoidal surface is also analysed. The third section of the paper shows that the integral equation of the lifting line constitutes the first order approximation to Kussner's equations, considered as an asymptotic development, without additional assumptions.