£)r. Waking's Obfervatiom 
72 
r 
y pin 1 
&c. 
1 — ir 1—3^ I— 4r Ql 
y ' “ "pin 
I— r 1 — 2r 1 1 — r 
+ — " • • — — - “P — • • 
2 r y p 3 r ~ 1 r 2 r 
- &C. = =±= M) Xy/-I = ±L±M 
\/ — 1 , in which cafe the two feriefes =♦= L and ±M converge, 
and (r + Av/ — 1) x (±L±Mv/ - 1) will be a value or root 
of the given quantity. 
In the fame manner the remaining roots may be deduced. 
2. Let ±P be - P, multiply (- 1) into — r, 
and it becomes PrpQ^^/ (—1) a quantity of the fame for- 
mula as the preceding; let r' + A\/ (-1) be a root of the 
equation x r 4- 1 = o, then will (r / + aV — i ) (±L±M s/ - 1 ) 
= ±H -K'y ( - 1) be a root of the given quantity : other- 
wife; the root may be deduced from the above-mentioned feries 
1 ir 
byfubftitutinginitfor — (P) r its value P r x ( - 1)' , and it will 
become the fame as the preceding. 
3. Let P be lefs than and the value of (ntPrtQ 
v/— 1 ) r may be deduced from the preceding feries by fubfli- 
tuting in it —Q, V - 1 for P, and =^P for Qy. otherwife, fince 
(— P^=Q v/ ( " >)) r = *&■( - 0 * (Q.-P ✓ ( - ' L = and 
the root of (Q =pP </ (— i)}' can be deduced by the pre- 
ceding method, which fuppofe L / ( - 1) ; multiply this 
root into 11 =^ 0 ^ ( - r), where H + 0 v /(— 1) denotes a 
value of the root \Z ( - 1), and the quantity refulting will 
be 
