His intention of killing Napoleon and his calculations of the cabalistic number of the beast of the Apocalypse now seemed to him meaningless and even ridiculous.
It was late day-three by our calculations when we broke through.
Between Betsy's internet searching and Quinn's calculations the location we sought was found.
It took us all the following day and part of next, though our calculations of time were suspect, to finish our ladder.
Windows have a chilling effect on a room, and in calculations extra allowance should be made for window areas.
(The calculations are mad in both cases on the total of births and deaths of both sexes.) The result is that, while in 1871 there was an excess of 143,370 males over females in the total population, in 188f the excess was only 71,138, and in I90f there were 169,684 more females than males.
Their calculations proved erroneous.
The value of is variable, but is between 7 and 8, and for approximate calculations may be taken equal to unity.
Now, however, the use of his remaining eye had been reduced to an hour a day, divided into portions at wide intervals, and he was driven to the conclusion that whatever plans he made must be formed on the same calculations as those of a blind man.
- For thermochemical calculations it is of great importance to know the heat of formation of compounds from their elements, even when the combination cannot be brought about directly.
When her brother accepted the office of astronomer to George III., she became his constant assistant in his observations, and also executed the laborious calculations which were connected with them.
Provision was thus made for 600,000 yeomen, assigning (according to different calculations) from sixteen to twenty-five acres of land to each.
It was only the chronologists and historians of the church who, following Julius Africanus, made use of apocalyptic numbers in their calculations, while court theologians like Eusebius entertained the imperial table with discussions as to whether the dining-hall of the emperor - the second David and Solomon, the beloved of God - might not be the New Jerusalem of John's Apocalypse.
In calculations the latter hypothesis is made because of its mathematical simplicity.
Working out the calculations, Pettersson finds that the favourable constellation occurred and will occur in 3500 B.C., 1900 B.C., 250 B.C., 1433 A.D., 3300 A.D., and so on.
Before the days of the "higher criticism" and the rise of the modern scientific views as to the origin of species, there was much discussion among the learned, and many ingenious and curious theories were advanced, as to the number of the animals and the space necessary for their reception, with elaborate calculations as to the subdivisions of the ark and the quantities of food, &c., required to be stored.
1 - z 2.1 -z 3.1 - z4' The series may be continued, but the calculations soon become very laborious.
We get therefore M 2 = MH X M/H = 27r 2 A(d 2 - l 2) 2 tan 0/t 2 d (42) s H 2 =Mhxh/M = 87r 2 Ad/tt 2 (d 2 -1 2) 2 tan B} (43) When a high degree of accuracy is required, the experiments and calculations are less simple, and various corrections are applied.
He had not attempted to include in his calculations the orbital variations of the disturbing bodies; but Lagrange, by the happy artifice of transferring the origin of coordinates from the centre of the sun to the centre of gravity of the sun and planets, obtained a simplification of the formulae, by which the same analysis was rendered equally applicable to each of the planets severally.
The development of railway construction in Brazil has been impeded to a great extent by two unfavourable conditions-by the chain of mountains or plateau escarpments which follow the coast line and obstruct communication with the interior, and by the detached positions of the settlements along the Atlantic, which compel 1 The areas are reduced from the planimetrical calculations made at Gotha and used by A.
Thus the concrete fact required to enable us to pass arithmetically from the conception of a fractional number to the conception of a surd is the fact of performing calculations by means of logarithms.
Advantage can be taken of this, when n is large, to make approximate calculations, by omitting terms that are negligible.
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.
In the application to sound, where we know what we are dealing with, the matter is simple enough in principle, although mathematical difficulties would often stand in the way of the calculations we might wish to make.
This is necessarily a question of degree; but it does not require detailed calculations in order to show that the discrepancy first becomes conspicuous when the phases corresponding to the various secondary waves which travel from P to B range over a complete period.
It may be remarked that these calculations apply to the rays in the primary plane only.
Calculations taking this into account have been made by J.
It is not worth while to refer to all the wild guesses that were made by various writers, but Dr Creighton shows the absurdity of one of these calculations made in 1554 by Soranzo, the Venetian ambassador for the information of the doge and senators of Venice.
Following on his calculations from 1509, when the population may be supposed to have been about 50,000, Dr Creighton carries on his numbers to the Restoration The same causes that operated to bring about these changes in the whole kingdom were of course also at work in the case of the City of London.
These numbers were arrived at with much care and may be considered as fairly accurate although some other calculations conflict with a few of the figures.
And another reason for their calculations resulting in so high a figure is suggested by the recent discoveries: they may in all good faith have reckoned as consecutive a number of early dynasties which were as a matter of fact contemporaneous.
Logarithms were originally invented for the sake of abbreviating arithmetical calculations, as by their means the operations of multiplication and division may be replaced by those of addition and subtraction, and the operations of raising to powers and extraction of roots by those of multiplication and division.
Thus in arithmetical calculations if the base is not expressed it is understood to be io, so that log m denotes log n m; but in analytical formulae it is understood to be e.
Calculations he had made, and suggested to Napier the advantages) that would result from the choice of io as a base, an improvement which he had explained in his lectures at Gresham College, and on which he had written to Napier.
It seems to be due to Wittich of Breslau, who was assistant for a short time to Tycho Brahe; and it was used by them in their calculations in 1582.
Some valuable notes are added by the translator, in one of which he shows the accuracy of the method employed by Napier in his calculations, and explains the origin of a small error which occurs in Napier's table.
Accounts, of Sang's calculations are given in the Trans.
Direct material for answering the question when and how far astronomical calculations replaced simple observations as the basis of the Jewish calendar is not forthcoming.
But in one of the two empirical tests of the value of these calculations that he was able to obtain (loc. cit.
- The birth of Christ took place before the death of Herod, and the evidence of Josephus fixes the death of Herod, with some approach to certainty, in the early spring of 4 B.C. Josephus, indeed, while he tells us that Herod died not long before Passover, nowhere names the exact year; but he gives four calculations which serve to connect Herod's death with more or less known points, namely, the length of Herod's own reign, both from his de jure and from his de facto accession, and the length of the reigns of two of his successors, Archelaus and Herod Philip, to the date of their deposition and death respectively.
The various calculations are not quite easy to harmonize, but the extent of choice for the year of Herod's death is limited to the years 4 and 3 B.C., with a very great preponderance of probability in favour of the former.
After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.