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 -m[1]x+m[2]x2...+(-)**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.

- anp, Anterior neural pore; be, rudiment of buccal skeleton; c, cilia; cb, ciliated band; cc, ciliated groove; cm, cilia at margin of mouth; gl, external opening of club-shaped gland; Hn, Hatschek's nephridium; lm, left metapleur; n, notochord; pp, praeoral pit; ps, primary gill-slits, I, 5, and 13; **rm**, right metapleur showing through.

- a, Atrium; al, alimentary canal; y blood-vessel; cv, cerebral vesicle; df, dorsal section of myocoel (= fin spaces); e, " eyespot"; end, endostyle; gl, club-shaped gland; lm, edge of left metapleur; m, lower edge of mouth; n, notochord; nt, pigmented nerve tube; ps, primary gill-slits, I, 9, and 14; rc, renal cells on atrial floor; **rm**, edge of right metapleur; so, sense organ opening into praeoral pit; ss, thickenings, the rudiments of the row of secondary gill-slits.

Are intersected by the lines RK, **RM**, RN, we have SA/AX = TP/PQ = SP/PQ, since the angle PST = angle PTS.