Bakerian Lecture, 1917: The Configurations of Rotating Compressible Masses . ;p(q)\d\dq2 J A. ig2 + wabc ,oc q • 00 1 c(q)\d\dq2 /A. d<f. (24) Both values of E may be regarded as given by a double integration in a plane inwhich A and q are rectangular co-ordinates. Let us first consider fig, 1, let PQ represent the curve whose equation is x V -f z ar + \ b2 + \ c2 + A + <p(q) = q2 (25) VOL. ^A. z 166 ME. J. H. JEANS ON THE CONFIGUKATIONS Clearly, when q = 0, the value of X is oo5 while when q — 1, X has some value \which is the root of x + tf + -? ?7 a2+\ ¥ + \ c2+\ + <
Bakerian Lecture, 1917: The Configurations of Rotating Compressible Masses . ;p(q)\d\dq2 J A. ig2 + wabc ,oc q • 00 1 c(q)\d\dq2 /A. d<f. (24) Both values of E may be regarded as given by a double integration in a plane inwhich A and q are rectangular co-ordinates. Let us first consider fig, 1, let PQ represent the curve whose equation is x V -f z ar + \ b2 + \ c2 + A + <p(q) = q2 (25) VOL. ^A. z 166 ME. J. H. JEANS ON THE CONFIGUKATIONS Clearly, when q = 0, the value of X is oo5 while when q — 1, X has some value \which is the root of x + tf + -? ?7 a2+\ ¥ + \ c2+\ + <p(l) = 1 • (26) The value of E0 is obtained by integrating over the area shaded in fig. the order of integration, we find »GO E, IT abc 1- 90 (q)\dq2 dec dx. (27) in which the lower limit q is the root of equation (25), while the lower limit \ft is theroot of equation (26). The value of E^ is obtained by a double integration in the same plane over an areasuch as that shaded in fig. 2, the different directions of shading distinguishing thephiltrans03687190. 9
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