What is the cube-root of 10648?

10648 log.

3)4.02726

Root is 22, log= 1.34242

To find the Root of a Decimal Fraction.

For the square-root, add 10 to the index before it is divided; and for the cube-root, add 20, &c.

To find the Logarithm of the Sines, Tangents, and Secants, belonging to any number of degrees and minutes.

RULE.

the

If the degrees be less than 45, seek them on the top of page, and the minutes in the left hand column marked M, against which, in the column signified at the top with the proposed name, stands the sine, tangent, or secant required; but when the degrees given, be more than 45, seek them at the bottom, and the minutes in the right hand column, marked M, against which, and over the proposed name, stands the sine, tangent, or secant required.

Observe, that the degrees at the top, and minutes in the left hand column, added to the degrees at the bottom, and minutes in the right hand column, always make 90°; hence, if a sine be looked for, the co-sine or complement will be found in the adjoining column. Observe the same of tangents and secants.

EXAMPLES.

Required the logarithm sine of 28° 37′?

Under 28°, and opposite 37', in the left hand column, as above, and under the word Sine, stands 9.68029, the logarithm of the sine of 28° 37', as required.

Required the logarithm tangent of 67° 45′?

Find 67° at the bottom of the page, and 45′ in the right hand column, opposite to which, and over the word Tangent, stands 10.38816, the log. required.

The logarithm of any number of degrees above 90, is found by subtracting the given degrees from 180°, and taking the logarithm of the remainder.

To find the Degrees, Minutes, and Seconds, to any given Logarithm.

Find the degrees and minutes corresponding to the nearest logarithm, which is exact enough for common business; but if seconds be wanted, they are thus found: take the difference between the given log. and the next less; also between the next less and greater; then say,

As the difference between the next less and greater log. Is to 60";

So is the difference between the next less and given log. To the seconds required.

But if they be required to a given log. co-sine, then say,

As the difference between the next less and greater log. Is to 60";

So is the difference between the given and next greater log.

EXAMPLES.

Find the degrees, minutes, and seconds, corresponding

to the logarithm sine, 9.61405.

As 29.. 60" :: 23 48", to be annexed to the degrees and minutes corresponding to the next loss log. gives 24° 16′ 48′′, as required.

Find the degrees, minutes, and seconds corresponding to the logarithm co-sine 9.43297.

As 45 60" :: 26 34", to be annexed to the degrees and minutes corresponding to the next less log. gives 74° 16′ 34′′, as required.

To find the Logarithm Sine or Co-Sine, for Degrees, Minutes, and Seconds.

Find the logarithm to the degrees and minutes; take the difference between this and the next greater, if a sine; but if a co-sine, the next less; then say,

As 60

Are to this difference ;

So are the given seconds,

To the correction, to be added to the first logarithm, if a sine; but subtracted, if a co-sine.

EXAMPLES.

Required the logarithm sine of 24° 16' 48"?

Next greater log. is 9.61411

The log. of 24° 16′, is 9.61382

29

As 60".. 29:: 48" 23, to be added to 9.61382, gives 9.61405, the log. of 24° 16′ 48", as required.

What is the logarithm co-sine of 74° 16′ 34′′ ?

leaves 9.43297, the log. co-sine of 74° 16′ 34′′, as required.