IN THE STUDY OF ANALYSIS. 43 



(B.) If n is a fraction having e for dfewominator, say n : e, you 

 put r : e ^vtre) for r : writing out (r : e)° -f- (r : e)^ -|- (r : e)* &c. : 

 num dits wed e ; i. e., the numeraior digits are affected by the 

 factor e ; tved meana, are multiplied by : so that the co-efficient 

 of (r : e)' is (n • n — e 'n — 2e • • • • (n — (i — 1) e)j : l*2-3*-i' 

 And 6 may be of either sign. The tyro who has this mnemonic 

 at his tongue's end, and understands it, will see no difficulty in 

 the expansion of ani/ binomial a" ( 1 -f- (l> : a)} " :rz (a -j- b)™. 



"We say multiply with in (A) ; bt/ should always denote divi- 

 sion. 



(C.) golt is fr" tong. 



This means .* zi t" + y + i^ + p^ + &c. 



I call g*, or log"^ t, golt j g" is gol(ax) ; gol is log read back- 

 wards : fru t on vid (A) above, t ong differs from t on, in that 

 every power is divided in the former by ^^fags of that power : 

 the zero power is unity in both of course. There is no ambiguity 

 in pronouncing t ong here as one syllable tong. 



(D.) a'"^ le one 's vi ong {y mod) ^^ ^'^^ ^^''^ ^^*-> 



and mod is ci loga: i.e. 



y :^ , (y • »») ' , (y-mf 



ay-^lz=:-^ + -Y^ +172^ + "* '' 

 this is vi ong^ or a quote ong ; the quote of y and m, m being 

 modulus of the system: and the mod. m is (log.a)-i ; the 

 re«procal of hyp. log.a. 



(E.) If ii be loga 



vi (A>i niod)'s pin inca.** on by — dex. i. e., 

 If M ir log a, and h be the increment of a ; and Wj zi 

 log (a + A) ; 



mod — mod a 2a* •" 3a* 4a* 



pin vid. (7 c). incaths is the fraction — zz - 

 *^ a a 



vi (Au mod) (8, g\ is this fraction pin on by index of the power. 

 (F.) N"* val is n-'bino fun obp. 



(G.) Ator u *s r-bin fun up repm ; (pron. Deitteoo.) 



