Treatise on the principal mathematical instruments employed in surveying, levelling, and astronomy : explaining their construction, adjustments, and use. With an appendix, and tables / By Frederick Walter Simms.

Simms, Frederick Walter, 1803-1865.

Date:: 1844

Credit: Treatise on the principal mathematical instruments employed in surveying, levelling, and astronomy : explaining their construction, adjustments, and use. With an appendix, and tables / By Frederick Walter Simms. Source: Wellcome Collection.

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$B, placed on the stake 6 ; call the two readings, A’ and B’; then, although the instrument be out of adjustment, yet the points read off will be equidistant from the earth’s centre, and conse- quently level. ** Now remove the instrument to a point half way between 6 and c. Again read off the staff B, and read alsoa staff placed on the stake c, which call staff C (the one before, called A, being removed into that situation). Now by adding the difference of the readings on B (with its proper sign) to the reading on C, we get three points, say A’, B’, and C’, equidistant from the earth’s centre, or in the same true level. ** Place the instrument at any short distance, say half a chain beyond A, and, using the bubble merely to see that you do not disturb the instrument, read all three staffs, or, to speak more correctly, get a reading from each of the stakes, a, b,c: call these three readings, A” B”C”. Now, if the stake b, be half way between a and ¢, then ought C’— C’-—(A”—A’) be equal 2 [B’—B’— (A”—A)]; but if not, alter the screws which adjust the diaphragm, and consequently the horizontal spider-line, or wire, until such be the case; and then the instrument will be adjusted for collimation. ** Toadjust the spirit-bubble, without removing the instrument, read the staff, A, say it reads A’’, then adding (A”—A’) withits proper sign to B’ we get a value, say B”. ** Adjust the instrument by means of the parallel plate-screws, to read B” on the staff B. “Now, by the screws attached to the bubble-tube, bring the bubble into the centre of its run. *«‘ The instrument will now be in complete practical adjustment, for level, curvature, and horizontal refraction, for any distance not exceeding ten chains, the maximum error being only z¢5sth of a foot.” EXAMPLE. The instrument being placed half way between two stakes, a and 8, (at one chain from each,) the staff on a or A’ read 6°53, and staff on 6 or B’ read 3°34, placing the instrument half way be- tween the stakes } and c, (three chains from each) the staff on 6 read 4°0], and the staff on c read 5°31. Hence, taking state a as the datum, we have Stake. Above Datum. aor A’ — 0:00 b or B’ = 3:19 ec or C’ ae 1°89 The instrument being now placed at d, (say five feet from a, but the closer the better,) the staff on a or A” read 4°01, on 6 or B”, 1:03, and one, or C”, 3°07. Now had the instrument been D 2$