. Carnegie Institution of Washington publication. CASE VII. 103 At the point A, fig. 13, we have also Kdfjw) ^ (/c+l)m^^ 2 dw ^'^(M-wy which becomes by virtue of (71) and (66) --H[M-(/c + l)wP=0 u agreeing with (61), the condition for a maximum or minimum (or minimax).. Fig. 14. The point B of fig. 14 corresponds to the point B of fig. 13. At the point B, fig. 13, we have Aw)=0 dfiw) dw = 0 which lead again to equation (61). Therefore the smaller real root of (61) belongs to a minimum and the larger to a minimax. However the system may change under loss of energy the w and v of fig. 14 must al
. Carnegie Institution of Washington publication. CASE VII. 103 At the point A, fig. 13, we have also Kdfjw) ^ (/c+l)m^^ 2 dw ^'^(M-wy which becomes by virtue of (71) and (66) --H[M-(/c + l)wP=0 u agreeing with (61), the condition for a maximum or minimum (or minimax).. Fig. 14. The point B of fig. 14 corresponds to the point B of fig. 13. At the point B, fig. 13, we have Aw)=0 dfiw) dw = 0 which lead again to equation (61). Therefore the smaller real root of (61) belongs to a minimum and the larger to a minimax. However the system may change under loss of energy the w and v of fig. 14 must always go from a curve of higher to one of lower energy. When the energy is greater than that for which the point A appears in fig. 14, the curves give us no positive knowledge regarding the series of changes the system may undergo, except that if at any time w = u + v<M it has always been, and will always be, less than M, and the opposite. But if the energy is less than that for which A appears in fig. 14, then, if at any. 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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