Dawn Stars

Cover Dawn Stars
Dawn Stars
Trent, Lucia, 1897-1977
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Then form H (m) from these modified equations by the rule already given in Art. 366 and finally multiply me constitu- ents of the first column by the same power of S. If this modified operator be called 11' (wi), we see that FI (m; and 11' (m) differ by some multiple of A (m). If A (S) = have a roots each equal to m, it follows tnat all the differential coefficients of 11 (m) and 11' (m) up to the (a — l)th are equal each to each.
372. Thus let the equations be (AuS" + BuS + Cn) x + iA^-^ B^,8
...+ C,,) y = 01 taking only two variables to shorten the results. We divide each equation by 8, then to form 11 (m) we divide bv S — m and reject the remainders. Finally we multiply again by o. We thus have n(m): AuSx+A^^^^^^^^"^, A^m^ + B^m^C^ m m In this form the constituents of the first column (when the equa- tions are of the second degree) may be vrritten down by copying them from the equation.
The advantage of this form is that the forces of resistance which depend on the potential B (Art.


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