A scale for the approximate transformation for the curves in fig.
This ratio, termed by Guye the critical coefficient, has the following approximate values: C. H.
Advantage can be taken of this, when n is large, to make approximate calculations, by omitting terms that are negligible.
The value of is variable, but is between 7 and 8, and for approximate calculations may be taken equal to unity.
Trade is carried on almost entirely with the United Kingdom; the approximate annual value of exports is £120,000, and of imports a little more than half that sum.
The approximate weights of some of the principal bales on the English market are as follows: United States.
Thus if s be known, an approximate value of W is determinate.
The figures obtainable with respect to shipping are approximate, the statistical data not being altogether complete.
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.
As the approximate date of Hero's activity.
He also determined a roughly approximate value for the mechanical equivalent of heat from the results of these experiments.
The deficiency on the working for the year ended 31st March 1907 was £54,924, and the approximate number of messages transmitted during the year was 96,783 with 1,126,940 words.
To 2300 (the approximate mean level of 2x00 i the land), and highlands, from 2300 upwards, might 20000 y also be distinguished.
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.
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.
But not to speak of the intrinsic quality of histories of this kind (which may possibly even be of use to someone for something) the histories of culture, to which all general histories tend more and more to approximate, are significant from the fact that after seriously and minutely examining various religious, philosophic, and political doctrines as causes of events, as soon as they have to describe an actual historic event such as the campaign of 1812 for instance, they involuntarily describe it as resulting from an exercise of power--and say plainly that that was the result of Napoleon's will.
(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.
In this case there is approximate periodicity in the half interval, but complete periodicity only after the whole interval.
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 first maximum in fact occurs when 6=2A-0046X, and the first minimum when 5 = 8X- oo16X, the corrections being readily obtainable from a table of G by substitution of the approximate value of V.
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.
The main body of his works belongs, so far as can be ascertained from the scanty evidence which we have, to the latter half of his life; 206 B.C. is the approximate date of the Miles gloriosus; cf.
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.
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:
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.
He wished the institutions of the present to approximate more closely to those of the past, and devised for the new French constitution a body of reforms which reflected the opinions he had formed upon the democracy at Rome and in ancient France.
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.
The results may be seen in the approximate estimates below of cotton grown more or less directly under the auspices of the association.
1 Approximate values of the atomic weights are employed here.
The second method possesses greater advantages, for rings of approximate stability come in one group, and, consequently, their derivatives may be expected to exhibit considerable analogies.
He applied himself more particularly to the oxygen compounds, and determined with a fair degree of accuracy the ratio of carbon to oxygen in carbon dioxide, but his values for the ratio of hydrogen to oxygen in water, and of phosphorus to oxygen in phosphoric acid, are only approximate; he introduced no new methods either for the estimation or separation of the metals.
An approximate normal sulphuric acid is prepared from 30 ccs.
Identity, or approximate identity, of crystal form is not in itself sufficient to establish true isomorphism.
The question as to the total number of slaves at Rome or in Italy is a very difficult one, and it is not, perhaps, possible to arrive with any degree of certainty at an approximate estimate.
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.
With regard to a great many rivers we know only the position of their mouths and their approximate lengths estimated by natives in terms of a day's march.
There are no figures from which even an approximate idea can be gained as to the value of the internal trade of Siberia, but it is certainly considerable.
The following approximate figures for small magnetizing forces are deduced from Hopkinson's curves: 9 Proc. Roy.
These four stars, in the order a, 13, 7, rc, form an approximate rectangle.
£59,118,895 stg.) Approximate total indebtedness..
With approximate certainty may be ascribed also to Tamas and Balint the original of the still extant transcript, by George Nemeti, of the Four Gospels, the Jciszay or Munich Codex (finished at Tatros in Moldavia in 1466).
(v.) Permutations and Combinations may be regarded as arithmetical recreations; they become important algebraically in reference to the binomial theroem (ï¿½ï¿½ 41, 44)ï¿½ (vi.) Surds and Approximate Logarithms. - From the arithmetical point of view, surds present a greater difficulty than negative quantities and fractional numbers.
Their approximate form was only arrived at by excavations made during the later years of the 19th century.
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.
The geography of the island is still very imperfectly known, and all figures are approximate only.
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.
With an approximate date—or at least a year—and a first name, the chore would be infinitely easier than scouring decades for a nameless individual.
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:
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 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.
The temperatures at the head of the Persian Gulf approximate to those of northern India, and those of Aden to Madras.
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.
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.
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.
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.
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.