The next great advance on the Trigonometria artificialis took place more than a century and a half afterwards, when Michael Taylor published in 1792 his seven-decimal table of log sines and tangents to every second of the quadrant; it was calculated by interpolation from the Trigonometria to 10 places and then contracted to 7.

In The Mystery of Mary Stuart the evidence for an early forged letter was presented with confidence; the interpolation of forgeries based on Crawford's declaration was more dubiously suggested.

The attempts made during the 19th century to disprove the Pauline authorship now possess merely an historic interest, nor have the various hypotheses of more or less extensive interpolation won any serious support.

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Especially Ha,upt's note) and does not involve the interpolation of matter by the later redactor of Colossians and Ephesians (Holtzmann, Hausrath' and Bruckner, Reihenfolge d.

Here the principle of interpolation has reached its maximum.

One method is to construct a table for interpolation of x in terms of u, and from this table to calculate values of x corresponding to values of u, proceeding by equal intervals; a quadrature-formula can then be applied.

The most convenient and accurate formula of interpolation seems to be that discovered by J.

It may be regarded as derived from a wholly dependent sporogonium not unlike that of some of the simpler Bryophyta; the latter are assumed to have arisen from primitive Algal forms, in which, as the first step in the interpolation of the second generation in the life cycle, the fertilized ovum gave rise to a group of swarm spores, each of which developed into a new sexual plant.

In fine, the interpolation of a Median Darius must be regarded as the most glaring historical inaccuracy of the author of Daniel.

If within the range5100-3700A, the constants are determined once for all, the formula seems capable of giving by interpolation results accurate to o 2 A, but as a rule the range to which the formula is applied will be much less with a corresponding gain in the accuracy of the results.