A much better approximation to the heat of combustion of such substances is obtained by deducting the oxygen together with the amount of carbon necessary to form C02, and then ascertaining the amount of heat produced by the residual carbon and hydrogen.
Is approximately equal to -J(27rn).(nle) n; the approximation may be improved by Stirling's theorem log e 2 +log e 3 +...
Mansi, Hardouin, Hefele and Dale are in substantial agreement upon 305 or 306, and this is probably the closest approximation possible in the present state of the evidence.
They were five-toed, bunodont Condylarthra, with a decided approximation to the perissodactyle type in the structure of the feet.
A pair of cones having a semi-vertical angle of 45° were considered to combine high concentrative power with a sufficient approximation to uniformity of field.
Subsequently to the floating off of the entosternite the approximation of the nerve cords took place in the prosoma, and thus they were able to take up a position below the entosternite.
In the mesosoma the approximation had occurred before the entosternites were formed.
Scelidotherium is another genus of large South American Pleistocene ground-sloths, characterized, among other features, by the elongation and slenderness of the skull, which thus makes a decided approximation to the anteater type, although retaining the full series of cheek-teeth, which were, of course, essential to an herbivorous animal.
The approximation was mutual.
They are not exact, but may be taken as representing an approximation correct within one per cent.
With increase of speeds this matter has become important as an element of comfort in passenger traffic. As a first approximation, the centre-line of a railway may be plotted out as a number of portions of circles, with intervening straight tangents connecting them, when the abruptness of the changes of direction will depend on the radii of the circular portions.
Every hypothesis must be tested by an appeal to the facts of life, and modified or abandoned if it will not bear examination, unless we are convinced on genuine evidence that it may for a time be employed as a useful approximation, without prejudice to the later stages of the investigation we are conducting.
They show again the closer approximation and better understanding with the Mahom.medans, which marks this Crusade.
In others there is an approximation of the lateral stems towards the median ventral line (Drepanophorus); in a genus of Heteronemertines (Langia), on the other hand, an arrangement occurs by which the longitudinal stems are no longer lateral, but have more or less approached each other dorsally.
In the article Crystallography the nature and behaviour of twinned crystals receives full treatment; here it is sufficient to say that when the planes and axes of twinning are planes and axes of symmetry, a twin would exhibit higher symmetry (but remain in the same crystal system) than the primary crystal; and, also, if a crystal approximates in its axial constants to 'a higher system, mimetic twinning would increase the approximation, and the crystal would be pseudo-symmetric.
The result is an approximation, for inequalities of the ground bounded by the two contours have not been considered.
But the point which is important is that there was a certain approximation between the condition of the colonus and the slave which tended towards the fusion of both in a single class.
Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers.
The outcome has been that in the Church of England, and in many of her daughter Churches, there exists a bewildering variety of "uses," varying from that of Sarum and that of Rome down to the closest possible approximation to the Geneva model.
In such experiments the narrowness of the zones renders necessary a pretty close approximation to the geometrical conditions.
In spite of any inequality between p and p', the definition will be good to this order of approximation, provided a and y vanish.
226) has shown that success may be attained by a variety of processes, including bichromated gelatin and the old bitumen process, and has investigated the effect of imperfect approximation during the exposure between the prepared plate and the original.
If we write p = 27rR/A (6), we must regard p as a function of f, and we may take with sufficient approximation under any ordinary circumstances where p' denotes the value of p at 0, and is a constant, which is positive when the retarding plate is held at the side on which the blue of the spectrum is seen.
With sufficient approximation we may regard BQ and b as rectangular co-ordinates of Q.
Perhaps a closer approximation would be to rate the creole element (whites of European descent) at 10%, as in Colombia, and the mixed races at 70%, the remainder consisting of Africans, Indians and resident foreigners.
The approximation to square roots in Hero has been the subject of papers too numerous to mention.
The first step in this process is that of grinding the surface down until all projections are removed and a close approximation to a perfect plane is obtained.
Estimates of the population of Arabia vary enormously, and the figures given in the following table can only be regarded as a very rough approximation: 4,825,000 Communications.
It is found by experiment that the change of pv with pressure at moderate pressures is nearly proportional to the change of p, in other words that the coefficient d(pv)/dp is to a first approximation a function of the temperature only.
(17) in which c is a small quantity (expressing the defect from the ideal volume V =Re/p due to co-aggregation of the molecules) which varies inversely as the nth power of 0, but is independent of p to a first approximation at moderate pressures.
Zeuner's formula for steam), but they cannot be made to represent with sufficient approximation the deviations from the ideal state at moderate pressures and generally lead to erroneous results.
In working to a first approximation, the small term nc/V may be omitted in the expression for s.
2) differ from the corresponding organs of allied species in great breadth of the crown as compared with the length, the narrowness and crowding or close approximation of the ridges, the thinness of the enamel, and its straightness, parallelism and absence of " crimping," as seen on the worn surface or in a horizontal section of the tooth.
There must be considerable dissociation of molecules, and as a first approximation it may be taken that of io molecules of most of the components about 9 (or in the case of magnesium sulphate 5) have been separated into their ions, and that it is only during slow concentration as in a natural saline that the ions combine to produce the various salts in the proportions set out in the above table.
While Gelocus exhibits a marked approximation to the Tragulidae, Prodremotherium comes nearer to the FIG 2.
Thus, to within the degree of approximation to which our theory is accurate, the value of y for every gas ought to be one of this series.
The vibrations of certain sources of sound may be represented, at least as a first approximation, as consisting of stationary waves, and from a consideration of the rate of propagation of waves along these sources we can deduce their frequency when we know their length.
At the open end, as a first approximation to be corrected later, there are no pressure changes, for any tendency to excess can be relieved by immediate expansion into the outer air, and any tendency to defect can be filled up by an inrush from the outer air.
Now µx 2 is very small compared with Ax, so that x is nearly equal to F/X, and as an approximation, F=Ax+µF 2 /A 2, or x=F/A - µF 2 /A 3.
The closest approximation of actual to theoretical dimensions of the parts.
Empirical formulas based on practical experience are employed for an approximation to the result.
44-64 can thus be fixed with a fair approximation to certainty, it is unfortunately otherwise with the events of A.D.
Besides this, all their evidence is but approximate, often only stating quantities to a half or quarter of the amount, and seldom nearer than 5 or 10%; hence they are entirely worthless for all the closer questions of the approximation or original identity of standards in different countries; and it is just in this line that the imagination of writers has led them into the greatest speculations, unchecked by accurate evidence of the original standards.
Found in Asia Minor and northern Greece, it does not appear unreasonable to connect it, as Hultsch does, with the Belgic foot of the Tungri, which was legalized (or perhaps introduced) by Drusus when governor, as 1/8 longer than the Roman foot, or 13.07; this statement was evidently an approximation by an increase of 2 digits, so that the small difference from 13.3 is not worth notice.
In order to render an 'account of Tyndall's "residual blue" it is necessary to pursue the approximation further, taking for simplicity the case of spherical shape.
Their form, however, is not sufficiently characteristic to warrant this identification, though it may be noted that the nearest approximation to phallic worship is found amongst the most typical of African peoples, viz.
The Arab astronomers measured a degree on the plains of Mesopotamia, thereby deducing a fair approximation to the size of the earth.
Thus the best approximation to the average depth of the ocean is little more than an expert guess; yet a fair approximation is probable for the features of sub-oceanic relief are so much more uniform than those of the land that a smaller number of fixed points is required to determine them.
A mean degree of the meridian being assumed to be 69-09 statute miles of 5280 ft., the nautical mile (A l b - degree) is taken as 6080 ft., which is a sufficiently close approximation for practical purposes, and the distances between the knots are made to bear the same relation to 6080 ft.
The people, though remarkable for their intelligence whilst Europe was in a state of barbarism, made no approximation to the mechanical operations of modern times, nor was the cultivation of cotton either improved or considerably extended.
Thus the prominent school of criticism which appraised Wagner in the 10th century by his approximation to Darwin and Herbert Spencer, appraises him in the aoth by his approximation to Bernard Shaw; with the absurd result that Gatterdammerung is ruled out as a reactionary failure.
But though a formula of this type has no physical significance, and cannot be accepted as an equation to the actual curve of W and B, it is, nevertheless, the case that by making the index e =1.6, and assigning a suitable value to r t, a formula may be obtained giving an approximation to the truth which is sufficiently close for the ordinary purposes of electrical engineers, especially when the limiting value of B is neither very great nor very small.
The latter gives values of the constants a and b for different samples of iron and steel, some of which are shown in the following table :- K=a+bH For most samples of steel the straight-line law was found to hold approximately up to H=3; in the case of iron and of soft steel the approximation was less close.
1470 grains), which agrees well to the weight; but this was probably an approximation, and not derivative, as there is (14) a weight called shet of 4.70 or 4.95 uten, and this was perhaps the actual weight of a hon.
And without considering the multiplicity and complexity of the conditions any one of which taken separately may seem to be the cause, he snatches at the first approximation to a cause that seems to him intelligible and says: "This is the cause!"