[ 346 ] 



i 3 



(mj <i2r + I. 2. 3. 2. I AB^j' + i. 2. 3 As cy' = i. a. 3 



^y. 



or 



z _ ; — 1.2 AB^— A ^f . ^ (-. 3 



1.2.3 



Cm) az + 1.2.4. 3. 2. I AC<^j^+ '^-•2.4.3 B^- l>j'^ + x. 2.3.4.3 



4 

 z 



A* Bey" = 4- 3- 2. 1 4>'* or - 



>{-i.2AC^-B'^-3A*Bc ^ 4 

 .2.3.4 '^ 



&c. &c. 



p- h—bk"- , /— 1.2AB-5— Ac 



or sr = — ^ -1 ^^ + ■ ■ — 



a a a 



-y + 



k^\. 2 A C l—h^ b—2, A^ B C 



J"* + &c A, B, C, &c. being thfe 



coefficients of the preceding terms. 



The laws of continuation are readily derived by help of Prob. i. 

 for calling the exponent of tf, i of ^, 2 &c. and of A, i of B, 2 &c. 

 the coefficient of y"" is a fraction the denominator of which is tf, 

 and the numerator the difference between the coefficient of j" in 

 the given equation, and the fum of produdls.of the capital and 

 fmall letters with numeral coefficients derived by the following 

 laws : 



I. To the fmall letter the exponent of which is « are to be 

 affixed n capital letters, fo that the fum of their exponents ffiall 

 be m : this is to be done as often as poffible with each fmall 



letter. 



2. The 



