If we assume P Po cos am (~t+e), q =qo sin am (~it+o), r =To~ am (~t-i--~), (7) we find = ~ ~ = 9rp, i = ~0pg~ (8) Hence (5) will be satisfied, provided u~o BC o-qo CA kfi,r0AB
Denoting these convergents by Po/Qo, P1/Q1, P2/Q2, ...
They may be regarded as obtained from a series Po + (Qi - Qo) + (Q2 (P2 - 1:11) +..
If we put qo= Sq' - Vq', then qo is called the conjugate of q', and the scalar q'qo = qoq' is called the norm of q' and written Nq'.
A Similar Theorem Holds In The Case Of Any Number Of Binary Forms, The Mixed Seminvariants Being Derived From The Jacobians Of The Several Pairs Of Forms. If The Seminvariant Be Of Degree 0, 0' In The Coefficients, The Forms Of Orders P, Q Respectively, And The Weight W, The Degree Of The Covariant In The Variables Will Be P0 Qo' 2W =E, An Easy Generalization Of The Theorem Connected With A Single Form.
Ja - u ?I a -a b -u' sh nS2=sh log (Q)=?a - b a - a' b - u' At x where = co, u = o, and q= go, (O n b - a ' a + a -b a' cio) - ?a-a'?b a-a' q In crossing to the line of flow x'A'P'J', b changes from o to m, so that with q = Q across JJ', while across xx the velocity is qo, so that i n = go.
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