£>2 
Mr. Knight on the Expansion 
, "-P 
one the exponent of c and changing c into c . Now 
c is either the last quantity or the last hut one in the order of 
the strokes. 
We can then have no difficulty in perceiving the truth of 
the following 
Rule* 
"...(m— s) "...m 
1 st. To fold '4/ take no notice of any terms in but those 
/ 
that are multiplied by the powers of c, in all these diminish the 
exponent of c by one ; and omit the denominators. 
zdly. Diminish the exponent of the last quantity , in these terms, 
by one ; and multiply by the quantity that has the next greater 
number of strokes. 
foly. If the last quantity but one be that which immediately pre- 
cedes the last in the number of strokes, make it vary in the same 
manner as was directed for the last. 
jgthly. All the combinations being thus formed, put the product 
2.3. 4.. ..ju, under every foh power. 
The reader may compare this rule with that given by M. 
Arbogast, p. 36. 
Suppose it were required to find B ; we must begin with 
10 
'...10 
* = 
' I0 "...9 ' 8 
— - — ; from which is derived by the rule, \L = — f— 
2. 3.4... 10 ’ J ^ 2. 3 ...8 
X C , 
"...8 
,7 ,6 ,,2 
, C , c c 
X C 
2 - 3-7 
® =/ w zdzz +M ‘ +/w { Tk* ; + =353 V } 
+ , &c. 
I x—, and so on, whence 
2. 3 ...6 2 
,10 
"...8 
,6 
* See Note I. at the end. 
