114 
ME. W. SPOTTISWOODE ON THE CALCULUS OE SYMBOLS. 
'CD, 
<E>A' 
O. 
'TT 
\ 
2/ I 
'cP- 
^o\' 
O3^+|(P0. 
which agrees with the results found above. 
^ 5. To divide 2“^^g>”(p„(7r) internally by 
The first term of the quotient will be 
n-m ?n(^-M) 
s — M)’ 
and the product of this into the divisor, 
fo(^-M+>«). 
The first term of the remainder will then be 
(pN(’r— 1) \|/m(w— 1), 
and consequently the second term in the quotient will be 
M) 
'livi(’r — M )vl/M (tt — M — 1 ) 
<Pn-i(’*'— M) M) 
<Pn(^— M — 1) M — 1) 
The first term of the second remainder will then be 
c1m-iW 
l)clM(’r— 2) 
CPn-iCtT— 1) 
<Pn(’*'— 2) (^—2) 
,N-2 
I'ivh’f — — 2) 
(PN-2M 0 
<Pn-.(’!- — 1) 4/M(7r — 1) 1) 
^j7r—2) 0 — 2) 
( 1 -) 
( 2 .) 
(3.) 
( 4 .) 
(5.) 
