Advantage can be taken of this, when n is large, to make approximate calculations, by omitting terms that are negligible.
His ancestors had been members of the community of the Bohemian Brethren, and had secretly maintained their Protestant belief throughout the period of religious persecution, eventually giving their adherence to the Augsburg confession as approximate to their original faith.
To 2300 (the approximate mean level of 2x00 i the land), and highlands, from 2300 upwards, might 20000 y also be distinguished.
It has been mentioned in ï¿½ 41 (ix.) that the binomial theorem can be used for obtaining an approximate value for a power of a number; the most important terms only being taken into account.
As the approximate date of Hero's activity.
It should be noted that the figures for area and population are, as a rule, only estimates, but in most instances they probably approximate closely to accuracy.
Their approximate form was only arrived at by excavations made during the later years of the 19th century.
Him succeeded, not only in showing that such a difference exists, but in measuring it, and hence determining a tolerably approximate value of the mechanical equivalent of heat.
Owing to the high price of gutta-percha the tendency, of recent years, has been to approximate more closely to the theoretical dimensions, x xvl.
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.
The approximate revenue for 1906 was £65,000, and the expenditure about £60,000, but some of the revenue was still collected in paper of uncertain value.
(iii.) From (21) of ï¿½ 43 (iv.) we see that I R r l is less than m[r+l]xr+1 if x is positive, or than 1 m [r+1] x m+1 (I+x)- m I if x is negative; and it can hence be shown that, if 1 x I < 1, 1 R r I can be made as small as we please by taking r large enough, so that we can make S r approximate as closely as we please to (r +x)-1n.
These figures include not only the categories of income and expenditure proper, but also those known as movement of capital, railway constructions and part ite di giro, which do not constitute real income and expenditure.i Considering only income and expenditure proper, the approximate totals are:
The following approximate figures are taken from the American Jewish Year-Book for1909-1910and are based on similar estimates in the English Jewish Year-Book, the Jewish Encyclopedia, Nossig's Jiidische Statistik and the Reports of the Alliance Israelite Universelle.
The first is a ventral flexure in the antero-posterior or sagittal plane; the result of this is to approximate the two ends of the alimentary canal.
1 Approximate values of the atomic weights are employed here.
Identity, or approximate identity, of crystal form is not in itself sufficient to establish true isomorphism.
His doctrine was rooted in the old Iranian - or Aryan - folk-religion, of which we can only form an approximate representation by comparison with the religion of the Veda.
The distribution of magnetism and the position of the poles in magnets of other shapes, such as cylindrical or rectangular bars, cannot be specified by any general statement, though approximate determinations may be obtained experimentally in individual cases.'
His method for determining approximate values of the roots of equations is far in advance of the Hindu method as applied by Cardan, and is identical in principle with the methods of Sir Isaac Newton and W.
The advantage of approximate bisection lies in the superior brilliancy of the surviving spectra; but in any case the compound grating may be considered to be perfect in the longer interval, and the definition is as good as if the bisection were accurate.
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.
Occupations.The following table, which shows the approximate numbers of persons engaged in the various manufacturing industries of France, who number in all about 5,820,000, indicates their relative importance from the point of view of employment:
The study of the evolution of faunas and the comparison of the faunas of distant regions have furnished a trustworthy instrument of pre-historic geographical research, which enables earlier geographical relations of land and sea to be traced out, and the approximate period, or at least the chronological order of the larger changes, to be estimated.
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.
If x and y be co-ordinates in the plane of the wave-surface, the axis of y being parallel to the lines of the grating, and the origin corresponding to the centre of the beam, we may take as an approximate equation to the wave-surface -- -} z =+Bxy 2, +ax 3 13x2 2pp p y+-yxy2-?-Sy3+..
The temperatures at the head of the Persian Gulf approximate to those of northern India, and those of Aden to Madras.
Among the contents of this book we simply mention a trigonometrical chapter, in which the words sinus versus arcus occur, the approximate extraction of cube roots shown more at large than in the Liber abaci, and a very curious problem, which nobody would search for in a geometrical work, viz.
Laurent tells us that the present government having found it absolutely impossible to arrive at even an approximate estimate of this " occult debt," recourse was had, in order to fix it, to the creditors themselves, and a short act of parliament was passed declaring all debts prescribed which should not be claimed by a fixed date.
Even in the higher flowering plants, in which the processes of the absorption of substances from the environment has been most fully studied, there is a stage in their life in which the nutritive processes approximate very closely to those of the group last mentioned.
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.