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The fundamental solution of the gravity waves due to a two‐dimensional point singularity submerged in a steady free‐surface flow of a stratified fluid is investigated. A linearized theory is formulated by using Love's equations. The effect of density stratification p_0(y) and the gravity effect are characterized by two flow parameters σ = −(dp_0∕dy)∕p_0 and λ = gL∕U^2, where λ^(1/2) may be regarded as the internal Froude number if L assumes a characteristic value of σ^(−1). Two special cases of σ and λ are treated in this paper. In the first case of constant σ (and arbitrary λ) an exact mathematical analysis is carried out. It is shown that the flow is subcritical or supercritical according as λ > or < (1/2), in analogy to the corresponding states of channel flows. In addition to a potential surface wave, which exists only for λ > (1/2), there arises an internal wave which is attenuated at large distances for λ > (1/4) and decays exponentially for λ < (1/4). In the second example an asymptotic theory for large λ is developed while σ(y) may assume the profile roughly resembling the actual situation in an ocean where a pronounced maximum called a seasonal thermocline occurs. Internal waves are now propagated to the downstream infinity in a manner analogous to the channel propagation of sound in an inhomogeneous medium.

The diffraction of a plane electromagnetic wave by an infinitely long, perfectly conducting cylinder has been treated by a variational method (see the two papers by H. Levine and J. Schwinger). The incident field is assumed to be polarized in the direction of the cylinder axis, and thus the entire field is of two‐dimensional nature. This formulation yields an expression for the diffracted cylindrical wave amplitude, at distances from the cylinder large compared to its transverse dimension and the wave‐length, which is stationary relative to small independent variations of the surface currents arising from plane‐wave excitation along a pair of directions in space; furthermore, the stationary form of the diffracted amplitude is independent of the scale of the surface currents. In accordance with a theorem of Levine and Schwinger, the total plane‐wave scattering cross section is simply related to the diffracted cylindrical wave amplitude in the direction of incidence. To examine the high frequency behavior of the cross section, the surface current induced by a plane wave is taken different from zero only on the illuminated part of the cylinder, where its value is derived from the tangential component of the incident magnetic field. The resulting cross section is obtained and is shown to approach 4a when ka approaches infinity (k=2π÷wave‐length, a equals the radius of cylinder).