Comparison with the table of binomial coefficients in ï¿½ 43 suggests that, if m is any positive integer, (I +x)-m =Sr+Rr (25), where Sr=I -mx+mx2...+(-)rm[r]xr (26), Rr_(_)r+1xr+11m[r] (1Fx) - 1+(m - I[r](I+x) m) (27).
(iv.) To assimilate this to the binomial theorem, we extend the definition of n (r) in (I) of ï¿½ 41 (i.) so as to cover negative integral values of n; and we then have (-m)(r)- iI m- = (-) rm [T] (28), so that, if n=--- -m, Sr1 +n(ox+n(2)x2+...
If other vortices are present, any one may be supposed to move with the velocity due to the others, the resultant stream function being = gy m log r =log IIrm; (9) the path of a vortex is obtained by equating the value of 1P at the vortex to a constant, omitting the rm of the vortex itself.
Blaise, Comptes rendus, 1901, 1 3 2, p. 38), R CN + R'M g I -?
(Slightly altered from Kirkaldy.) rm and lm, Right and left metapleur; at, atriopore; an, anus; e, " eyespot" at anterior end of neurochord projecting beyond the myotomes (my); n, notochord; rgo, gonads of right side only showing through by transparency; go 20, the last gonad; dfr, dorsal fin with fin chambers and fin rays; vfc, ventral fin chambers.