L916] MEMBRANES, BARS, AND PLATES 431 Added August 21. The accompanying tables show the form of the curves of deflexion defined by (39), (40). V (39) y (39) 0° oooo 50 7416 10 1594 60 8574 20 3162 70 9530 30 4675 80 1-0217 40 6104 90 T0518 X (40) X (40) o-o 1-0518 3-0 1992 0-5 9333 4-0 0916 i-o 7435 5-0 0404 2-0 4066 10-0 0005 In a second communication* Mesnager returns to the question and shows by very simple reasoning that all points of a rectangular plate supported at bhe boundary move in the direction of the applied transverse forces. If z denote V2w, then V2^, = V4'jy, is positive over the plate if the applied forces are everywhere positive. At a straight portion of the boundary of a supported plate z = 0; and this is regarded as applicable to the whole boundary Df the rectangular plate, though perhaps the corners may require further consideration. But if V2# is everywhere positive within a coutour and z vanish Dn the contour itself, z must be negative over the interior, as is physically obvious in the theory of the conduction of heat. Again, since V2w is negative throughout the interior, and w vanishes at the boundary, it follows in like manner that w is positive throughout the interior. It does not appear that an argument on these lines can be applied to a rectangular plate whose boundary is clamped, or to a supported plate whose boundary is in part curved. P.S. In connexion with a recent paper on the "Flow of Compressible Fluid past an Obstacle" (Phil. Mag. July 1916)I, I have become aware that :he subject had been treated with considerable generality by Prof. Cisotti of Milan, under the title " Sul Paradosso di D'Alembert" (Atti R. Istituto Veneto, 'j. Ixv. 1906). There was, however, no reference to the limitation necessary yhen the velocity exceeds that of sound in the medium. I understand that ;his matter is now engaging Prof. Oisotti's attention. * G. R. July 24, 1916, p. 84. t [This volume, p. 402.]n the former w is proportional to , , ,.