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. 1915 Excerpt: ...of the parts. Evidently the fewer the parts, the smaller will be R, and the greater the precision. Also the longer the chain, the fewer will be the parts, and the greater the precision. It must be carefully noted, however, that the preceding reasoning only applies to the accidental errors (Art. 7) of observation, and ...
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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. 1915 Excerpt: ...of the parts. Evidently the fewer the parts, the smaller will be R, and the greater the precision. Also the longer the chain, the fewer will be the parts, and the greater the precision. It must be carefully noted, however, that the preceding reasoning only applies to the accidental errors (Art. 7) of observation, and that all constant errors must be investigated, and removed from the results, before the formulas (37) and (39) are used. The effects of temperature on the length of the chain or tape, for instance, may be removed by reading the thermometer, and applying the proper computed corrections, and the effects of side deviations may be removed by making the chain sufficiently longer at the start. In general, the constant errors of linear measurements increase directly as the length of the line; while only the accidental errors increase as the square root of the length. Angle Measurements. 94. The measurement of an angle is in general effected by taking the difference of readings from a graduated limb; and these readings, in their turn, may be the means of readings on two or more verniers. By the use of the principle expressed in formula (25) it is possible to determine the precision of these readings from the probable errors of observed results. As an example, the following measurements of an angle made with a transit having two verniers reading to minutes will be discussed. The angle was chosen at about 35 in order that eleven readings might approximately go around the circle, and each reading is the mean of the two verniers. By the method of the last chapter it is easy to find that the probable error of a single observation of an angle is nearly 20." Let r, represent the probable error of a reading on one vernier, and r2 that of the mean of the t...
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Add this copy of A Textbook on the Method of Least Squares. 8th Ed., Rev to cart. $43.00, new condition, Sold by Revaluation Books rated 4.0 out of 5 stars, ships from Exeter, DEVON, UNITED KINGDOM, published 2009 by Cornell University Library.
