Semi-Annual Bulletin of the Colorado College Observatory Volume 16-19

Semi-Annual Bulletin of the Colorado College Observatory Volume 16-19

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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. 1905 edition. Excerpt: ...of the chord coincide with those of the corresponding tangent-ordinate, they are correct also for the intermediate value of the ordinate of the curve. The approximation made in this way will not, however, in the first instance be very close. A second calculation is based upon the first, by taking for values of y, and y, two successive values of the curve-ordinate as just found--or, if it be more convenient, two numbers that differ but little from these--and assuming a new series of values of x, with a common difference much smaller than before, for instance, one-tenth as large. By repeating this procedure, the computation may be carried to whatever degree of approximation may be desired. The compactness of the tables and the consequent facility of their use requires that the rate of change of the function as compared with that of the argument be slow. To secure this, it would probably be well to break up the tables into three parts, the range of value of the argument (the abscissa) in one part being from + 3 (or thereabout) indefinitely toward + co, in another part between + 3 and--3, while still another (overlapping the preceding by a little) comprises the negative values below--=--1.88988. In the first-named section, the tabulated function should be the ordinate of the curme as just described; in the next, it should be the difference between that ordinate (that is, that of the upper branch) and the ordinate of the inflectional tangent; while the remaining section, dealing with those abscissas which furnish three real roots, should contain tabulated values of the difference between the ordinates of the curve and those of the parabolic asymptote. If this plan were to be carried out, the most rapid change in the function would occur in more

Product details

  • Paperback | 36 pages
  • 189 x 246 x 2mm | 82g
  • United States
  • English
  • black & white illustrations
  • 1236793706
  • 9781236793706