(J6 Mr. Jarrett on Algebraic Notation. 



Example 1. x'"-' + i 



,(/ 2m-l /— - . 2m-l \ 



= (a; + 1) . P,„"- ■[(:«- cos ^^—j- . TT - V - 1 • sin ^^—^ . tt; 



/ 2m-l / — - ■ 2m-l \) 



Pv •> rosa; = P ^1 — — ), and sin x=a; . P,,, I 1 J. 



4. Prop. To invert the order of the factors in a given 

 factorial, 



P",„ • («m) = fli . Wa • «3 • • • a» 



= a„ . a„_i . a„-2 . flij taking the factors in an inverted 

 order 



^ * 7« • ^Ai — jn + l- 



5. Prop. To separate any number of the factors from the rest, 



= P^„.(aJ.P„r'.K+J. 



Ex. 1. If -^^^^=c„„ »i being any positive integer, then shall 



a, = aj.P;»-'.(c,). 



i> or. i-, . (c^) - p^^_, ^^^^ = ^^ ^ „._, ^^^^^^ ^^ , 

 .-. a„, = a,.P,"-» (c). 



Ex. 2. If ?^^ = c,„, then a.„,_._ = a, . P;— (c^..^), 

 and a2„_i = a^ . Pr""' . {car-\)- 



