378 Trans. Acad. Sci. of St. Lows. 
TABLE IV 
a2 all 
I | =_e 
19 | 36—= 2X18 
21 57 = 3X19 
23 s0=—= 4X 20 
a | jon 6 CO 
7 | 1392— 6X 22 
99° |-- 161 = 798 
31 | 199 8X24 
33 | 995 == 9% 95 
35 | 260—10X 26 
37 | 997—11 & 27 
39 | 336=12 X28 
41 | 377=13 X29 
43 | 490=14 X30 
45 | 46515 31 
47 | 512—16X32—2° 
some integral number, the value of v® may be represented 
by either of the systems above described. For example 
of «= 25 and n= 2 and the first term of the series be 
taken as unity, the final term will be 
2 
ow 0 te 
The sum of the series will be 625. The number of terms 
will be 25. The sum of the series is equal to the square 
of the number of terms, as is shown in Hq. (3). 
If the second method above diseussed be adopted, equa- 
tions (4) give as the first and last terms 
3 
— 25% + 1—=121 
+ 25% — 1129 
The number of terms will then be 
2—1 
N = 25 *=5. 
