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ExAMPLE IV".

Required the Degrees, Minutes, and Seconds, answering to the natural Co-sine 368805.

The natural Co-sine next greater to that given is 368936, to which answers 680 21'; the difference between this natural sine and the given one is 131, to which two cyphers being added, and that divided by 451, the difference found at the bottom of the column, gives the quotient 29". Hence 68° 21'29", or its supplement, 111° 38' 31" are the degrees, &c. required.

To find the natural versed Sine of a given Number of Degrees, JMinutes, - and Seconds.

If the given arch be less than 90°, find its natural co-sine, which subtract from 1000000, and the remainder will be the natural versed sine required. But if the given arch exceed 90°, find the natural cosine of its supplement, which add to 1000000, and the sum will be the natural versed sine required.

EXAMPLE i.

Required the natural versed Sine of 20° 39'. The natural co-sine of 20° 39' is 935752, which subtracted from 1000000, leaves 064248, the natural versed sine of 20° 39'.

EXAMPLE II.

Required the natural versed Sine of 146° 38' 40". The natural co-sine of 33° 21' 20" (the supplement of 146° 38' 40") is 835274, which added to 1000000, the sum 1835274 is the naturai versed sine required.

To find the Degrees, &c. corresponding to a given natural versed Sine.

Take the difference between the given natural versed sine and 1000000, and the remainder will be a natural co-sine; the degrees, &c. corresponding to which, will be those required, if the given natural versed sine be less than 1000000, but if otherwise, it will be their supplement.

EXAMPLE I.

Required the Degrees, &c. answering to the natural versed sine 0.98965. The above subtracted from 1900000, leaves 901035, which taken as a natural co-sine, corresponds to 252 42'20".

EXAMPLE II,

Required the Degrees, &c.answering to the natural versed Sine 1160172. Here 1000000 subtracted from the above, leaves 160172, which ta

ken out as a natural co-sine, corresponds to 80° 46'59"; therefore its

supplement 99° 13'1" are the degrees, &c. required.

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100" 485

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465. 462

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to to 454

390731 42261

451 || 448 445 i 441

699 || 689 679 | 660 659 649 || 639 1629

4.38

619 600 IM

430 in 426 || 422

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