There are extensions of the binomial theorem, by means of which approximate calculations can be made of fractions, surds, and powers of fractions and of surds; the main difference being that the number of terms which can be taken into account is unlimited, so that, although we may approach nearer and nearer to the true value, we never attain it exactly.

As the approximate date of Hero's activity.

The following are the approximate wave-lengths of the most brilliant lines: When the discharge passes through helium at a pressure of several millimetres, the yellow line 5876 is prominent.

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The chief experimental basis for supposing that a train of longitudinal waves with displacement curve of this kind arouses the sensation of a pure tone is that the more nearly a source is made to vibrate with a single simple harmonic motion, and therefore, presumably, the more nearly it sends out such a harmonic train, the more nearly does the note heard approximate to a single pure tone.

This is shown by the following observations of Riihlmann on water, the light used being the D line of the spectrum: Eykmann's observations also support the approximate constancy of the Lorenz-Lorentz formula over wide temperature differences, but in some cases the deviation exceeds the errors of observation.

For the Algol variables it is possible to form even more direct calculations of the density, for from the duration of the eclipse an approximate estimate of the size of the star may be made.

If on each occasion he himself made the observations his voyage must have extended over six years; but it is not impossible that he ascertained the approximate length of the longest day in some cases by questioning the natives.

Standard solutions are prepared by weighing out the exact amount of the pure substance and dissolving it in water, or by forming a solution of approximate normality, determining its exact strength by gravimetric or other means, and then correcting it for any divergence.

The Nannosciurinae, or second sub-family of Sciuridae, are represented only by the pigmy squirrels (Nannosciurus), characterized by their very short-crowned molars (which approximate to those of dormice in structure) and small premolars, of which the first upper pair is often deciduous, while the upper molars have only three oblique ridges.

Statistical inquiries as to the incidence of taxation or of particular taxes, though ideal or even approximate equality of a palpable arithmetical kind is practically unattainable by governments, are not altogether to be put aside.