# A Treatise on the Principal Mathematical Instruments Employed in Surveying, Levelling, and Astronomy: Explaining Their Construction, Adjustments, and Use

Lucas, 1844 - 134 pages
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Page 51 - ... fixing the index, and altering the position of the instrument to make the objects appear on the other wire ; if the contact still remains perfect, the axis of the telescope is in proper adjustment ; if not, it must be altered by moving the two screws which fasten, to the up-and-down piece, the collar into which the telescope screws. This adjustment is not very liable to be deranged.
Page 15 - ... any deviation in it is easily rectified, by releasing the screws by which it is held, and tightening them again after having made the adjustment ; or, what is perhaps better, note the quantity of deviation as an index error, and apply it, plus or minus, to each vertical angle observed. This deviation is best determined by repeating the observation of an altitude or depression in the reversed positions, both of the telescope and the vernier plate : the two readings will have equal and opposite...
Page 26 - The whole is mounted on parallel plates, and three legs, the same as a theodolite. It is evident, from the nature of this instrument, that three adjustments are necessary. First, to place the intersection of the wires in the telescope, so that it shall coincide with the axis of the cylindrical rings, on which the telescope turns ; secondly, to render the level parallel to this axis ; and lastly, to set the telescope perpendicular to the vertical axis, that the level may preserve its position while...
Page 59 - But what is still of more consequence, the error of the centre is perfectly corrected, by reading the three branches of the index; while this property combined with that of observing both ways, probably reduces the errors of dividing to one-sixth part of their simple value. Moreover, angles may be measured as far as one hundred and fifty degrees, consequently the sun's double altitude may be observed when his distance from the zenith is not less than fifteen degrees ; at which altitude, the head...
Page 50 - The amount of the index error may be found in the following manner: clamp the index at about 30 minutes to the left of zero, and looking towards the sun, the two images will appear either nearly in contact or overlapping each other ; then perfect the contact, by moving the tangent-screw, and call the minutes and seconds denoted by the vernier, the reading on the arc. Next place the index about the same quantity to the right of zero, or on the arc of excess, and make the contact of the two images...
Page 36 - Now, if the stake 6 be half way between a and c,f then ought c" — c' — (A" — A) to be equal to 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. " To adjust the spirit-bubble without removing the' instrument, read the staff A, say it reads A'", then adding (A'"— A') with its proper sign to B
Page 41 - The difference, it is evident, is always equal to the excess of the secant of the arc of distance above the radius of the earth.
Page 41 - AC 2AC nearly ; that is, the difference between the true and apparent level is equal to the square of the distance between the places, divided by the diameter of the earth ; and consequently it is always proportional to the square of the distance.
Page 62 - Various natural, as well as artificial, reflecting surfaces have been made by mechanical arrangements, to afford the means of obtaining double angles ; such as pouring water, oil, treacle, or other fluid substances into a shallow vessel ; and to prevent the wind giving a tremulous motion to its surface, a piece of thin gauze, talc, or plate-glass, whose surfaces are perfectly plane and parallel, may be placed over it, when used for observation. But the most accurate kind of artificial horizon is...
Page 68 - ... telescope, need only carry two cross wires, but in this instrument it has five vertical and two horizontal wires. The centre vertical wire ought to be fixed in the optical axis of the telescope, and perpendicular with respect to the pivots of the axis. It will be evident, upon consideration, that these wires are rendered visible in the daytime by the rays of light passing down the telescope to the eye ; but at night, when a very luminous object, as the moon, is observed, they cannot be seen.