This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1875 Excerpt: ...are divided by 2. How are the values of the co-efficients determined from eight points 1 Answer. We arc now enabled to form an opinion as to the degree of approximation of the several results. A B C D B Do the co-efficients A, B, C, D, E, as denoted by Eoman letters, represent the exact value of the deviations observed under all circumstances i A. No; the formula? from which they are derived are only approximate, and though the approximation is close when the deviations are moderate in amount, the errors increase as the square of the deviations. Thus, if with a maximum deviation of 7, they are 10' in error, with a deviation of 21, they will be about 1 30' in error; hence, when the maximum deviation on any course much exceeds 20, it is necessary to use instead of A, B, C, D, E, what are known as the exact co-efficients--the exact co-efficients being distinguished by the German letters 91, 55, 6, 3), (S, and being nearly the natural sines of the angles A, B, C, D, E. How are the exact co-efficients 81, S3, Q, 35, @, determined 1 A. When A, B, C, D, E, are known by the ship being completely swung, the exact co-efficients may be derived from the following simple formula and calculation, which are sufficiently exact for deviations not exceeding 40. 9I = sin A 58 = sin B X(i+$ sin D-f-T'5 versin B--J versin C)+J sin Cxsin E 6 =sin C X(i--i sin D--£ versin B-f-TV versin C)-f£ sin Bxsin E 2 = sin Dx(i+1 versin D) (5=sinE--sin Ax sin D D cannot be determined from deviations observed on the four cardinal points, o E from deviations observed on the four inter-cardinal points, t Found as follows:--Ship's I. Ship's II. III. IV. V. head,, head „, „,,, „ N.E. +24 10 S.W.-10 30 I +6 50 +17 20 S4 +12 J5SumCol. V.=B +21 16, S.E. +'6 o N.W.--19 301...

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