Appendix to Mr. Drach's Paper on Epicyclic Curves, 521 

 the general or 5th term of ( -r j 's bracketed factor is 



1.2. 3. ..25 



. {q^^i){q^j^8^ X)(^q^j-s^2) . . (g-2; + 1) ' 

 1.2.3..(i-5) 



and of (Q-^ai)?-=y-' is 



(bY. (P-l)(P-2)..(P-25) 

 -\a) ' 1.2.3..(2s+l) 



(g->25-l).(g~7-5-g).(y-i-5-3)..(g-2;') 

 1.2.3.J-S 



+ as stated, so that both series end always with §' — 2;+ 1 or 

 q—%j'i two consecutive terms being in the ratio of 



b^ P— 25 P — 25— 1 <7— 25 — 2 j—s 



1 to -^ X 



a2'^25+l 25 + 2 j-25 q-j—s—V 



and 



i^ p_2s—i P-25— 2 q-2s—B J—s 

 ^°a2 X 25 + 2 25 + 3 ' q — 2s—l' q—j—s — 2 



respectively. 



Mr. Perigal's finite syphonoids, strongly resembling a di- 

 stiller's * worm,' are expressed by 



Hence 



2 cosj9.g'<p=SAJ cos 5-^= -j = 2 cos 5' . j»<p 



=2B/(cosj9f ="^j. 



The nodal or lemnoid curves of a finite number of knots 

 are comprised in 



x=^acosq<^i y=bs\np<p. 

 Hence 



2cos;).(2gf)==2A,.(cos2g^=-^-lj ==2cosg(2pf) 

 = SB^(cos2;,^ = l-^y. 



