[ 33^ ] 



ift- 3** + f. « +r = 0. 



!Z\ 3 ;«' + ^. 1 . 2. b-\t a'. 3- 2. X = 0. 



2,^. 3 X» + jr. I. 2. 3 C + 3. 2. I. «i^. 3- 2 .X + <?'. 3. 2 = 0. 



4* 3 X' + y. I. 2. 3. 4 i + 4- $• 2. I «f 



4-3 ^' 



3. 2x + 4.3.tf«<J.3. 2 = 0. 



5*. 3 »' +7. 1. 2. 3. 4. 5<r + 5-4- 3- 2- 1 ''''^ 



5.4.3.2. 1 ^c 



6ec. &o* &c. 



3.2. + ^-^3'^^^ 



3.2 = 



or 



r , _ 3 <** * = — 3" ^ "^'^ "^ ''' // _ _ 



''= ~ J^^T"?' ~ ~ 3^'+7' ''" 3^^ + ?~~' 



3. 2 ^rx +31^' _ Of/ 4- <!'C. 3. 2.A; + 3- flV + ^^' 



&c. &c. 



Calling the exponents of the quantities a, b, c, &c. their 



P P 



places in the feries, and the exponents of a, p: of ^ 2/, &c. 



the law of continuation is eafily had. For the numerator of 



the quantity, the exponent of which is w, confifts of two terms, 



the firil of which is 3. 2. x into a coeff. which is the fum of 



the produdls of every two quantities, the fum of the expo- 



ponents of which is w, and when m is even, ^ the fquare of the 



quantity 



