. Carnegie Institution of Washington publication. 102 THE TIDAL PROBLEM. The derivative of (68) is dw K k{M—wy (70) It depends only upon w and is negative for all w>M. For w = M it is infinite. For w less than, but near to, M it is positive; when M is large it vanishes and becomes negative and again vanishes and becomes positive, as w decreases from M to 0. It is positive for all wEi>E^>E^.. Fio. 13. From equation (69) and fig. 13 the equi-energy curves in fig. 14 are drawn, the corresponding curves being similarly lettered. There are two points of particular interest, A and B. As the
. Carnegie Institution of Washington publication. 102 THE TIDAL PROBLEM. The derivative of (68) is dw K k{M—wy (70) It depends only upon w and is negative for all w>M. For w = M it is infinite. For w less than, but near to, M it is positive; when M is large it vanishes and becomes negative and again vanishes and becomes positive, as w decreases from M to 0. It is positive for all wEi>E^>E^.. Fio. 13. From equation (69) and fig. 13 the equi-energy curves in fig. 14 are drawn, the corresponding curves being similarly lettered. There are two points of particular interest, A and B. As the energy decreases, the energy curves descend to a point at A. That is, on a section through A approxi- mately parallel to the vE'-plane the point A is a minimum. With decreas- ing E the energy curves separate at A and recede in opposite directions nearly parallel to the liJ-axis. Hence a section by a plane through A approxi- mately parallel to the ly^E^-plane has the point A as a maximum. Therefore A. is a minimax point of the surface. The minimax point A, fig. 14, corresponds to the point A, fig. 13, at which/(w)=0. Therefore, by (69), for this point v = K K+l W (71). Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Carnegie Institution of Washington. Washington, Carnegie Institution of Washington
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