## A treatise on the principal mathematical instruments employed in surveying, levelling and astronomy |

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Treatise on the Principal Mathematical Instruments Employed in Surveying ... Frederick Walter Simms No preview available - 2018 |

### Common terms and phrases

accuracy added adjustment altitude angle appear applied attached axis azimuth bisect called centre circle clamp coincide collimation computed construction correct corresponding declination determined deviation difference direction distance divided divisions double edge effect employed equal error exactly example feet figure fixed former forward give given glass greater half height horizontal inches instrument interval known latitude length limb longitude lower manner mean measured ment meridian method microscope middle minutes moon motion moved nearly object observed obtained operation opposite parallel passing perfect plane plate polar distance position quantity reading reflected remains represents result reversed right ascension round scale screw sextant shown side sidereal space staff star station sun's suppose survey taken telescope theodolite transit true turning upper vernier vertical whole wire zenith zero

### Popular passages

Page 38 - ... 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 31 - ... triangle, of which the perpendicular is the difference of level. It scarcely appears necessary to give the rule for the calculation, but for the sake of uniformity we shall do so.f Add together the logarithm of the measured distance, and the log. sine of the observed angle; the sum, rejecting 10 from the index, will be the log. of the difference of level, in feet or links, efec., the same as the distance was measured in.

Page 22 - The first adjustment is that of the line of collimation ; that is, to make the intersection of the cross wires coincide with the axis of the cylindrical rings on which the telescope turns : it is known to be correct, when...

Page 43 - 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 11 - ... 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 37 - 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 28 - 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 90 - ... We are not aware that a scale of this kind has been put upon the plain scales sold by any of the instrument makers ; but, during the time occupied in plotting an extensive survey, the paper which receives the work is affected by the changes which take place in the hygrometrical state of the air, and the parts laid down from the same scale, at different times, will not exactly correspond, unless this scale has...

Page 23 - ... half the error must be corrected by turning the screw, B, and the other half by the two parallel plate-screws, over which the telescope is placed. Next turn the telescope a quarter round, that it may lie over the other two screws, and make it level by moving them ; and the adjustment will be complete. Before making observations with this instrument, the adjustments should be carefully examined and rectified, after which the screw, B, should never be touched ; the parallel plate-screws alone must...

Page 47 - 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...