Page:The Construction of the Wonderful Canon of Logarithms.djvu/37

CONSTRUCTION OF THE CANON. 13

First table.

10000000.0000000

1.0000000

9999999.0000000

.9999999

9999998.0000001

.9999998

9999997.0000003

.9999997

9999996.0000006

to be
continued
up to

9999900.0004950

Thus from radius, with seven cyphers added for greater accuracy, namely, 10000000.0000000, subtract 1.0000000, you get 9999999.0000000; from this subtract .9999999 you get 9999998.0000001; and proceed in this way, as shown at the side until you create a hundred proportionals, the last of which, if you have computed rightly, will be 9999900.0004950.

17.The Second table proceeds from radius with six cyphers added, through fifty other numbers decreasing proportionally in the proportion which zs easiest, and as near as possible to that subsisting between the first and last numbers of the First table.

Second table.

10000000.0000000

100.000000

9999900.0000000

99.999000

9999800.0010000

99.998000

9999700.0001000

99.997000

9999600.006000

Thus the first and last numbers of the First table are 10000000.00000000 and 9999900.0004950, in which proportion it is difficult to form fifty proportional numbers. A near and at the same time an easy proportion is 100000 to 99999, may be continued with sufficient exactness by adding six cyphers to radius and continually subtracting from each number its own 109900^th part in the manner shown at the side; and this table

contains