# A Manual of Modern Surveying Instruments, and Their Uses; Together with a Catalogue and Price List of Scientific Instruments ... Made by the A. Liet

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## Description

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1911 edition. Excerpt: ...in the diagram, figure 2: (3) o, = a cos n + /2 sin n tan (n + m) + tan (n--m) Now, since the angle m in an instrument rated 1: 100 only amounts to 17 minutes, it is evident that the expression y2 sinn tan ( + m) + tan (--m) is almost the same as sin n tan n, the difference being so small that it will not be noticeable at all in any of the stadia requirements, and writing sin n tan n in terms of the cosine, we have S and substituting in formula (3), it will reduce to the simple expression (4) at = i cos n. This, then, is the normal rod reading, which, by applying the constant K, gives the distance K a cos n, representing the hypothenuse h of a right-angled triangle, of which the horizontal distance d and the difference in elevation e are the co-ordinates. Their values in turn are proportional to the cosine and sine of the angle n, so that the distance (5) d = K a cos 2 n, and the elevation e = K a cos n sin n, which is (6) e--Ka y2 sin 2 n. (It is understood, in the case of the difference in elevation between the two points (e), that the middle hair touches the rod at a mark corresponding to the height of the instrument, as shown in figure 2.) Introducing, now, our constant c, which causes corrections also dependent upon the angle n, we must add to the horizontal distance d the value c cos n; and to the elevation e the value c sin n, so that the corrected horizontal distance is (7) D = c cos n-Ka cos 2 n, and the corrected elevation (8) E = c sin n--K a y2 sin 2 n; or, if the constant K--100, and the constant c = 1.15, then D = 1.15 cos n-j-100 a cos2 n, and E = 1.15 sin n-f-100a jsin2. If, for example, the rod reading a be 2.22 feet, and the vertical angle = 20, then D = (1.15 X cos 20 = 1.08) + (222 X cos2 20 =...show more

## Product details

• Paperback | 60 pages
• 189 x 246 x 3mm | 127g
• Miami Fl, United States
• English
• black & white illustrations
• 1236509366
• 9781236509369