to the proportion of a hundred to one; and the triple of the same, namely 69077527.02, will be the difference of all logarithms whose sines are in the ratio of a thousand to one; and so of the ratio ten thousand to one, and of the others as below.
53.Whence all sines in a ratio Sea of the ratios two to one and ten to one, have the difference of their logarithms formed from the differences 6931469.22 and 23025842.34 in the way shown in the following
Short Table.
Given Proportions of Sines.
Corresponding Differences of Logarithm.
Two
to one.
6931469.22
Four
to one.”
13862938.44
Eight
to one.”
20794407.66
Ten
to one.”
23025842.34
20
to one.”
29957311.56
40
to one.”
36888780.78
80
to one.”
43820250.00
A hundred
to one.”
46051684.68
200
to one.”
52983153.90
400
to one.”
59914623.12
800
to one.”
66846092.34
A thousand
to one.”
69077527.02
2000
to one.”
76008996.24
4000
to one.”
82940465.46
Given Proportions of Sines.
Corresponding Differences of Logarithm.
8000
to one.
89871934.68
10000
to one.”
92103369.36
20000
to one.”
99034838.58
40000
to one.”
105966307.80
80000
to one.”
112897777.02
100000
to one.”
115129211.70
200000
to one.”
122060680.92
400000
to one.”
128992150.14
800000
to one.”
135923619.36
1000000
to one.”
138155054.04
2000000
to one.”
145086523.26
4000000
to one.”
152017992.48
8000000
to one.”
158949461.70
10000000
to one.”
161180896.38
54.To find the logarithms of all sines which are outside the limits of the Radical table.
This is easily done by multiplying the given sine by 2, 4, 8, 10, 20, 40, 80, 100, 200, or any other proportional number you please, contained in the short table, until you obtain a number within the limits of the Radical table. By 50
