SCALES OF NOTATION 57

we have, following the plan of the first formula,

4 X ¥3 = 14443
L 606
axXY 156

8 11

Hence 4398(f) = 15552(7)

Or, using the second formula, we may proceed as follows:
4(7)

X 13
15
4
55

+ 3
61

X 13

243
61

3 1153
-+~ %2

1165
X 13

3561
1165

15541
+ 11

15552(7)

i

The third method is that of the rule given in § 102.

Suppose that the radix of the new notation is #’ and that
the new digits, which we are searching for, are a,’, a,—/, - - -,
a), a/, ay'.