pages, there is o degrees, and in the left hand columns are the minutes of a degree. At the head of the next two pages, there is 1°, and fo on to 44° on the head of the two last pages, at the foot of which is 45, from whence they proceed gradually backward unto the first two, where there is 89°; and on each page, the right hand columns contain the minutes of a degree increasing upwards.

13. To find the logarithm fine and tangent of any number of degrees and minutes below 45°. Look for the degrees on the head of the page, and the minutes in the left hand column ; and, oppofité to the minutes, you have their fines and tangents in their respective columns.

14. To find the logarithm fine and tangent of any number of degrees and minutes above 45°.

Look for the degrees at the foot of the page, and the minutes in the right hand column, and opposite to the minutes you have the fine and tangent, each in its proper column, marked at the foot with fine or tangent.

15. To find the fine or tangent of a number of degrees, minutes, and feconds.

Find the fine or tangent of the degrees as before; then find the difference between the fine or tangent found and the next greater, and fay, as 60 is to that difference, fo is the number of feconds to the part to be added for the feconds.

EXAM. Required the fine of 19° 24′ 36′′ ?

The fine of 19° 24' is 9.5213488, which fubtract from 9.5217074, the fine of 19° 25'; the diff. is 3586. Then, as 60": 3586 :: 36′′: 2151, which add to 9.5213488, and the fum 9.5215639 is the fine of 19° 24′ 36′′. Proceed in the fame manner when a tangent is wanted.

16. To find the cofine or cotangent of any number of degrees and minutes.

Look for the fine or tangent of the given number of degrees and minutes, and next it in the column of the fame name you have the cofine or cotangent required.

Thus the cofine of 15° 24' is 9.9841200, which is the fine of 74° 36, and the cotangent of 74° 36' is 9.4400363, or the tangent of 15° 24′.

17. To find the number of degrees and minutes anfwering to a given logarithm fine.

Seek the given logarithm fine in the columns of fines; and, if you find it, or the next lefs in the first column on the left hand, you have the degrees on the head of the page, and the minutes on the left, counting downwards. But, if you find it in the fecond co

tumn, you have the degrees at the foot of the page, and the minutes on the right hand, counting upwards. Proceed in the fame manner with tangents.

18. When the given logarithm fine is not found exactly in the table, and it is required to find seconds, fubtract the logarithm fine found in the table from the given one, also subtract the fame from the next greater in the table, and say,

As the difference of the two tabular fines is to 60", fo is the difference between the given one, and the next less than it, found in the table, to the seconds required.

EXAM. Required the degrees, minutes, and feconds answering to the log. fine 9.9533476 Next lefs in the tables is 63° 54' 9.9532897

19.

To find the natural fine or tangent of any arc by thefe tables.

Find the logarithm, fine, or tangent of the given arc in the table; cancel its index, and find the number answering to it in the table of logarithms to seven figures; it is the answer.

20. To find the log. fecant of any arc. Because the radius is a mean proportional between the cofine of an arc and its fecant; therefore, fubtract the cofine of the given arc from 20.0000000, the remainder is the logarithm fecant.

21. To find the logarithm verfed fine of any arc. Multiply the logarithm fine of half the arc by 2, add •3010300 to the product, and fubtract the radius from the fum; the remainder is the logarithm versed fine of the arc.