14 J. B. CHERRIMAN : APPLICATION OF A SPECIAL DETERMINANT. 
This curious relation can be readily verified by an independent process, as follows :— 
Denoting tm BE ....:-1...:., + D, by f(a), we have 
T 

hg, ae ou El AS APT ae Se 
Ff (x) 
also 
af’ (x) =n+s, 01+ s 2° + + s, a + 
#@) i ; ; 
therefore, 
Cl Se 6, Gig tine se nena Yer (CE) 
= is aa sy ees ances a OG gaa Rr ee 
or, substituting for f’ (x) its value # 2° + n-1 p, Detar , and equating co-efficients of 
az", there is 
By — NO SS On ie re eee + nr p, 
7 {a+ CPS Pa) Oe RP OUEN DC +p, 
— Py 0,1 — 2 Pa Oo — «+--+ sHononec 0000000 po o Poe o —7 pr 
but the quantity between the is equal to zero, and therefore 
— S, = Py Or, + 2 Pro Oy Re ete eee + Tr Pre 
