On the attractions of homogeneous ellipsoids / [Sir James Ivory].

  • Ivory, James, Sir, 1765-1842.
Date:
1809
Catalogue details

Licence: Public Domain Mark

Credit: On the attractions of homogeneous ellipsoids / [Sir James Ivory]. Source: Wellcome Collection.

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    cos. 4<p . sin. O . dtp . d-^ A = a x zkk'k x ff - - ^ A* + e1 sin. cos. ^ -f e'2 sin. 2<p sin. ^ [ f B =i X aW' X ff-(-cos. - j kz + ez sin. zq> cos. 24> 4- e'z sin. z<p sin. ^ f C = C x MV X ff,-«ln-V «in.. N> - ■ *l>- . •J ’* -x k1 4- ez sin. z$ cos. 4i|/ 4- e'x sin. z<p sin. > -| the several fluents to be taken from <p = o>.to <p = and from 2 = 0 tO ij/ = 2”ZT. Let „ r P sin. <p . dtp . ^4” | Aa 4- e2 sin. z<p cos. *-4/ 4- en sin. 2ip sin. ^ j §• then the last values of A, B, and C will be expressed by the partial fluxions of Q, as follows : A = a x akk'k x { - T (tt) + T (tt) + 7 (17) } B = b x att* x-■£-(-£) C=cx sikk'k x — 7/ [-^r] • For the sake of brevity, let pa = <?* cos.+ en sin.: then I (id \ _ rrk sin. Q . dtp . d-b m ■\ir/ J J ( (£a 4- p1 sin. *■£)-!■ * and, by integrating relatively to <p, / den_r_^L_ y_*cos- ? 7. \dT J J A* 4- P* * t (** + pa sin. 3 ' and, by taking the whole fluent from (p = o to <p = ~, and restoring the value of p% [nr) Jkz 4- ex cos. 24i 4- «'a sin. * Let T = (FT7 * 5$: then> hy substitution, __ / <*qa_j_r (/t._ l ^ I ““ («2 + Of (*a + Of j »+ t15 and, by integrating from t]/ = o to = 2^, E 2
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