1888 - 89 .] Prof. Tait on a Geometrical Problem. 
317 
we have 
9\ ~ A i + fii9o ; 
2 2 = A 22o + A#l 
9z — A 32l + {$2,92 \ 
&C. 
(1) 
We have also, generally, 
Pm~ <*7 
9 m - 1 
9m— 2 
or 
_ 2m-l + a m9m - 2 _ A m-l2m-3 + a m-l9m-2 _P m - 2 „ 11tinADfl /Q\ 
pm = = = - — 5 suppose. . (i). 
2m— 2 2 m— 2 i/m— 2 
Prom (1), and the value of 2o> we see that all the values of q are 
linear functions of /q of the form 
2rn = r m + S mPl (3). 
By (2) Pm —1 = % 2 m -2 + «m2m-l 
= (1 + ali)q m _ 2 + a m {A m _ 1 g m _ 3 + (a m _ x - a m )g w _ 2 } 
9m— 2 P l9m— 3 P ^m— l2m— 2 ) 
9m— 2 P ^mPm—2 1 
Similarly 2m-i = j9 m _ 2 - a m q m _J 
But the first equations in (1) give at once 
1+ “iPi j. whence 
20 ~ “ a i P Pi ' Po~ ~ 9oPi 1 
2 h = a 2 — a i P P a 2 a l)Pl ) 
2 1 = l + a 2 a l — ( a 2 — a l)Pl J 
2i= -PiPi 
(• 
This suggests that 
} 
2» = (-)”2V>i 
Pm=(~ T +1 imPl 
By (4) we have 
Pm — 1 = 9m— 2 P a mPm— 2 > 
9m— \ Pm— 2 ®m2m— 2 • 
Let m he odd, then we should have by (5) 
j? m _2 = ApBp 1? 
9m— 2 = B — Ap^ j 
(5). 
whence 
Pm- 1 = B - A Pl + a m (A + Bp x ) , 
9 m- 1 = A + Bp : - a m (B - A Pl ) ; 
