Many hydrophilous insects recognize water by the polarization of the reflected light [1]. When the water is illuminated by diffuse, nonpolarized sky light, the animals have a relatively simple polarization pattern to identify: all the e vectors in the reflected light are horizontal. But when the sky is clear and visibility good, very complicated polarization patterns can develop due to superposition of the polarization characteristics of the water surface and the partially reflected polarization pattern of the sky light. We have calculated such patterns for an ideal water surface, and present them here. We also present a revised picture of the polarization of sky light. The drawing of the sky polarization pattern published in 1959 by Stockhammer [2], which has been reproduced in many review articles and textbooks (e.g. [3-6]), and the two-dimensional representation of the sky polarization pattern published by Wehner [7,8] contain an error in the directions of the e vectors. Here we correct this error. For the calculations of reflection polarization the sky polarization pattern was slightly idealized; the lines of equal polarization were assumed to form exact circles around the position of the sun, as in Wehner's [9] three-dimensional polarization pattern, and the e vectors were assumed to be exactly aligned with these circles. Departures from this regular pattern in the vicinity of the sun (Babinet and Brewster neutral point) were disregarded. These departures are negligible because here the stronger polarization of the water surface predominates. The degree of polarization was approximated by d = dmax-Sin 2 cd(l+cos2c0 (see [10], p. 288; a is the angular distance from the sun). For sun elevations of 0 ° (sun at the horizon), 30 ° , 60 ° , and 90 ° , dma~ was taken to be 77, 70, 63, and 56%, respectively (see [10], p. 295). To calculate the reflection of the sky polarization pattern the appropriate Fresnel formulas were used ([11], p. 332). With an ideal water surface under diffuse, unpolarized sky light, all the e vectors in the reflection-polarization pattern are arranged concentrically around the center of the pattern; that is, from the viewpoint of an observer they appear horizontal (Fig. la). Polarization is maximal at the Brewster angle 0 = 5 3 ° (dotted line representing a degree of polarization d=100 %). The relative intensity of the reflected light is not shown in the figures. For unpolarized incident light it is 2% at ®=0 ° (in the center of the pattern) and 7.6 % at the Brewster angle; the amount of light reflected rises rapidly for ® > 60 °, reaching 100 % at ®=90 ° (at the edge of the pattern). With a clear, cloudless sky the polarization pattern visible over the water surface is considerably more complicated, because the polarization pattern of the sky itself contributes, to some extent,