m THE STUDY OP ANALYSIS. 41'- 



(a.) If there be p syrabols or ekmenti^ viz., m, a's ; e, b's ; 

 i, c's • * • • the number of permutations p together is 



l-2"-m'l-2-e-l'2'"i 



fagfs isyactor di^^-it*. " Five fags is 1*2*3*4*5. 

 (i.) The repeating combinations (of n in p's,) say of 7 in 4*8, 



fr.Q.Q.lA 



are _-.r_r or four-seven-ups by four fiigs. 

 1-2-3-4' ^ '' 



Three-2-ups are 2*3*4. 

 By repeating co/wbination* are meant such as may contain a 

 letter or letters repeated, as 7662, 7744, 7111, 7654, 7777. 

 (c.) Combinations non repeating (of n in />'*,) say of 7 in 

 fours, such as 7654, &c., are in number 



, four-7-backs by four fags. 



Two three backs are 3 '2. 



(<i) iVon-repcating variation* are the non-repeating combi- 

 nations permuted : thus the repe. vars. of 7 in 4*8 will 

 include 7654, 7645, 7564, &c., being in number 

 7-6-5-4. 

 («.) The repeating tjariation-s of 7 in 4's include 7777, 7767, 

 7776, 6777, &c., and are in number 7* : n to jo*** power. 

 (12.) In the theory of numbers most students find difficulty 

 in retaining both the results and the demonstrations. Here 

 follows an example of a mnemonic to aid in remembering both: 

 Make dissyllables of em, etol, etom ; 



If mups are e'm and 'm is pri 



vi dm has the rem. of etol vi ; 



(A.) You piit eto'm Suto'm (un 'd) 



The two extre. will have the re } 

 Then put dtom Suto'm (un 'c) ; &c. 



I (over 'g) is g-int 

 (B.) if e*°» IS e«m-int ; 



and e if there -is no 'g 

 a prim root of 'm will be; 



