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In the second he not only enlarges his matter and gives multiplied applications of his ideas, but also follows the synthetic method, first expounding the laws he had discovered and then proving them by the facts to which they are applied.

Pigs and goats, however, with cattle, horses, asses and dogs, have been introduced, have multiplied, and in considerable numbers run wild.

The population of Victoria was doubled in the first twelvemonth of the gold fever, and the value of imports and exports was multiplied tenfold between 1851 and 1853.

Thus, if x= horned and y = sheep, then the successive acts of election represented by x and y, if performed on unity, give the whole of the class horned sheep. Boole showed that elective symbols of this kind obey the same primary laws of combination as algebraical symbols, whence it followed that they could be added, subtracted, multiplied and even divided, almost exactly in the same manner as numbers.

I harp (multiplied quant.

in such forms as Velella, Porpita, &c., the ancestor was an eight-rayed medusa (Disconula) which acquired a pneumatophore as an ectodermal pit on the ex-umbrella, and in which the organs (manubrium, tentacles, &c.) became secondarily multiplied, just as they do in Gastroblasta as the result of incomplete fission.

These images take the place of the coloured fragments of glass, and they are symmetrically multiplied by the mirrors.

Such quotations were multiplied, as theologians learnt to depend increasingly upon their predecessors, until the testimony of "our holy father" Athanasius, or Gregory the Divine, or John the Golden-mouthed, came to be regarded as decisive in reference to controverted points of faith and practice.

To check this courts were multiplied (there were five, six or more instances), which only multiplied the evil.

After his death in 1054 the process of disintegration went on apace and the family feuds multiplied at an alarming rate.

Moreover, the prohibitions are strengthened and multiplied.

The situation went from bad to worse, the deficit in the budget increased, the gendarmery, which received no pay, became insubordinate, and crime multiplied.

Meanwhile his academic honours from home and foreign universities multiplied, and he became a fellow of the Royal Society in 1894.

Among the ruder or savage tribes they possess but one form; but the ingenuity of man has devised many inventions to increase his comforts; he has varied and multiplied the characters and kinds of domestic animals for the same purpose, and hence the various breeds of horses, cattle and dogs.

Thus all that was shocking in the barbarism of Africa was multiplied and intensified by this foreign stimulation.

After the field preaching began converts multiplied.

The expenses were met by collections made in the Calvinistic Methodist Societies, and as the funds increased masters were multiplied, until in 1786 Charles had seven masters to whom he paid £io per annum; in 1787, twelve; in 1789, fifteen; in 1794, twenty.

And similar records might be multiplied almost to any extent.

Shirazi (f9o5); but the literature in new translations and imitations has recently multiplied exceedingly.

Hence_li y ` A 1n where A li and A li, are minors of the complete determinant (a11a22...ann)ï¿½ an1 ant ï¿½ï¿½ï¿½an,n-1 or, in words, y i is the quotient of the determinant obtained by erasing the i th column by that obtained by erasing the n th column, multiplied by (-r)i+n.

The discriminant of the product of two forms is equal to the product of their discriminants multiplied by the square of their resultant.

and take therein the coefficient of the function (mi t tm7t t m 31 t ...), we obtain the same result as if we formed the separation function in regard to the specification (mï¿½ It t'tm2 32tm"`l3t...), multiplied by Alt!!

If u, a quantic in x, y, z, ..., be expressed in terms of new variables X, Y, Z ...; and if, n,, ..., be quantities contragredient to x, y, z, ...; there are found to exist functions of, n, ?, ..., and of the coefficients in u, which need, at most, be multiplied by powers of the modulus to be made equal to the same functions of E, H, Z, ...

the i t " power of that appertaining to a x and b x multiplied by the j t " power of that appertaining to a x and c x multiplied by &c. If any two of the linear forms, say p x, qx, be supposed identical, any symbolic expression involving the factor (pq) is zero.

Every symbolic product, involving several sets of cogredient variables, can be exhibited as a sum of terms, each of which is a polar multiplied by a product of powers of the determinant factors (xy), (xz), (yz),...

1 And The Actual Forms For The First Three Weights Are 1 Aobzo, (Ao B 1 A 1 B O) Bo, (A O B 2 A 1 2 0 Bo, Ao(B2, 3 A1B2 A2B1 A O (B L B 2 3B O B 3) A I (B 2 1 2B 0 B 2); Amongst These Forms Are Included All The Asyzygetic Forms Of Degrees 1, 1, Multiplied By Bo, And Also All The Perpetuants Of The Second Binary Form Multiplied By Ao; Hence We Have To Subtract From The 2 Generating Function 1Z And 1 Z Z2, And Obtain The Generating Function Of Perpetuants Of Degrees I, 2.

The sum of the corresponding numbers multiplied by 332600 gives Log.

When P is the neutral point, H is equal and opposite to R; therefore M = Hd 3, or the moment is numerically equal to the cube of the distance from the neutral point to a pole, multiplied by the M.

Then if a known change of induction SB a inside the standard coil is found to cause a throw of d scale-divisions, any change of induction SB through the experimental coil will be numerically equal to the corresponding throw D multiplied by snRBa/SNrd.

When the magnetizing current is twice reversed, so as to complete a cycle, the sum of the two deflections, multiplied by a factor depending upon the sectional area of the specimen and upon the constants of the apparatus, gives the hysteresis for a complete cycle in ergs per cubic centimetre.

Thus the magnetization which the sample of Swedish iron received in a field of 1490 was not increased (beyond the limits of experimental error) when the intensity of the field was multiplied more than thirteen-fold, though the induction was nearly doubled.

At the temperature of liquid air (-185°) the application of a field of 21,800 multiplied the resistance of the bismuth no less than 150 times.

In opposition to this Nominalistic view, which implied the reversal of his whole position, William may have meant to say that, instead of the universal being multiplied, it is rather the individuals which are reduced to unity in the universal.

Matthias laboured strenuously to develop and protect the towns, multiplied municipal charters, and materially improved the means of communication, especially in 1 We know actually of fifteen, but there may have been many more.

it means that i lb is to be multiplied by 7, the result by 3, and the new result by 5.

If it is intended that the first number is to be multiplied by the second, a special sign such as X should be used.

The number by which an algebraical expression is to be multiplied is called its coefficient.

Later, in his article " Chromatics " in the supplement to the 5th edition of this encyclopaedia, he shows that the colours " lose the mixed character of periodical colours, and resemble much more the ordinary prismatic spectrum, with intervals completely dark interposed," and explains it by the consideration that any phasedifference which may arise at neighbouring striae is multiplied in proportion to the total number of striae.

Put for short- do d{- +ply+dz (1), and represent by v2E the quantity multiplied by b 2.

New corms are produced at the end of the season, and by these the plant is multiplied.

The Boer leaders definitely decided upon a guerrilla and a wearing policy, deliberately dispersed their field army, and then swelled and multiplied the innumerable local commandos.

Garments were multiplied, and the cape and long mantle, which had previously been uncommon, were now usual.

multiplied by the total rubbing or friction surface of the air-ways in square feet and by the coefficient of friction.

high, obviously act as efficient mercury-traps; but the already considerable height of the pump is thus multiplied by two.

the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

Even before the Reformation, however, signs of decay had already begun to appear, and these multiplied in the 16th and 17th centuries.

While Berlin and Budapest have made the most rapid progress of all European cities, having multiplied their population by nine in the period 1800-90, Vienna - even including the extensive annexations of 1892 - only increased sevenfold.

four series of "Researches on Heat," in the course of which he described the polarization of heat by tourmaline, by transmission through a bundle of thin mica plates inclined to the transmitted ray, and by reflection from the multiplied surfaces of a pile of mica plates placed at the polarizing angle, and also its circular polarization by two internal reflections in rhombs of rock-salt.

Infirmities multiplied upon him, until his death at Washington on the 22nd of October 1900.

With him the unit is termed "digitus"; when multiplied by ten it becomes the "articulus"; while the combination of the articulus and the digitus is the "numeras compositus."

Yahweh's judgments are multiplied against the land, and the issue can be nothing else than its total desolation.

Throughout the whole of this period, embracing about a hundred years, there still continued to work, altogether apart from the men who were making the success of popular art, a large number of able painters of the Kano, Tosa and Chinese schools, who multiplied pictures that had every merit except that of originality.

(I) The heat, H, absorbed in isothermal expansion (latent heat of expansion) from p to p" is equal to the diminution of pressure (p' - p”) multiplied by the absolute temperature and by the expansion per degree (v" - v')/(o' - o") at constant pressure.

(2) The heat, H, absorbed in isothermal expansion from v to v" is equal to the increase of volume (v" - v') multiplied by the absolute temperature, and by the increase of pressure per degree (p' - p")/(o' - o"), at constant volume.

With the aid of the Jesuits, whose privileges he multiplied, he conducted a vigorous propaganda.

The result is that although the forms of apparatus utilized for this purpose are all based on the one fundamental principle of bringing about the contact of the carbide with the water which is to enter into double decomposition with it, they have been multiplied in number to a very large extent by the methods employed in order to ensure control in working, and to get away from the dangers and inconveniences which are inseparable from a too rapid generation.

To the oldtime belief that languages multiplied by splitting and colonizing, must be added the theory that languages were formerly more numerous, and that those of the Americans were formed by combining.

The census of 1871 obtained for the first time a return of persons of unsound mind not confined in asylums. During the next ten years, the separate areas for which population returns had to be prepared were seriously multiplied by the creation of sanitary districts, to the number of 966.

area should be treated not only as length multiplied by length, but also as volume divided by thickness.

The formula, in the above case, is 3h{ *k(uo,o + 3 where u 0, 0 denotes the ordinate for which x=xo+Oh, y=yo+c¢k The result is the same as if we multiplied lk(vo 3v1+3v2 + v 3) by lh(uo 4u1 +u2), and then replaced uovo, uov1, ..

can be calculated before it is multiplied by 3h .

During the next twenty years the gold discoveries, the public works expenditure, and the development of agriculture; multiplied the number of colonists five times to 498,000 in April 1881.

In algebra, the "cube" of a quantity is the quantity multiplied by itself twice, i.e.

The amplitudes of these tones are proportional to the products of a and b multiplied by X or µ.

Misunderstandings and movements at cross-purposes multiplied on the Russian side, and at midnight Kuropatkin at last obtained information of events on the side of Yentai Mines.

Among certain Gnostic sects Amen became the name of an angel, and in post-biblical Jewish works exaggerated statements are multiplied as to the right method and the bliss of pronouncing it.

In Germany, their original home, both training schools and societies have multiplied and developed.

All his life long Spener had been exposed to the attacks and abuse of the orthodox Lutheran theologians; with his years his opponents multiplied, and the movement which he had inaugurated presented increasingly matter for hostile criticism.

Ultimately, indeed, as sanctuaries were multiplied and the priests all over the land came to form one well-marked class, " Levite and legitimate priest became equivalent expressions, as is explained in the article Levites.

As time went on the Cossacks multiplied exceedingly.

3 by the height AH, such that the rectangle Ahkb is equal to the area Apdb; and the M.E.P. multiplied by 41rd 2, the cross-section of the bore in square inches, gives in tons the mean effective thrust of the powder on the base of the shot; and multiplied again by 1, the length in inches of the travel AB of the shot up the bore, gives the work realized in inch-tons; which work is thus equal to the M.E.P. multiplied by 41+-d 2 l = B -C, the volume in cubic inches of the rifled part AB of the bore, the difference between B the total volume of the bore and C the volume of the powder-chamber.

The system of Marshal Valee had been the defensive: he multiplied the fortified posts in order to draw the enemy to a spot chosen beforehand.

Paulo in Brazil supplied Sars with representatives of all the three in his Norwegian aquaria, in some of which the little Macrothrix elegans " multiplied to such an extraordinary extent as at last to fill up the water with immense shoals of individuals."

The principle on which the instrument works is as follows: Suppose any circuit, such as an electric motor, lamp or transformer, is receiving electric current; then the power given to that circuit reckoned in watts is measured by the product of the current flowing through the circuit in amperes and the potential difference of the ends of that circuit in volts, multiplied by a certain factor called the power factor in those cases in which the circuit is inductive and the current alternating.

In 797 Charlemagne commissioned Alcuin to prepare an emended text of the Vulgate; copies of this text were multiplied, not always accurately, in the famous writingschools at Tours.

It should be borne in mind that in early times the larger values, such as minae, would be transmitted by commerce, while after the introduction of coinage the lesser values of shekels and drachmae would be the units; and this needs notice, because usually a borrowed unit was multiplied or divided according to the ideas of the borrowers, and strange modifications thus arose.

Seeing the good reasons for this digit having been exported to the West from Egypt--from the presence of the 18.23 cubit in Egypt, and from the 0.729 digit being the decimal base of the Greek long measures--it is not surprising to find it in use in Italy as a digit, and multiplied by 16 as a foot.

As a unit of 1.013, decimally multiplied, is most commonly to be deduced from the ancient Persian buildings, we may take 25.34 as the nearest approach to the ancient Persian unit.

Among them (29) the two contiguous groups can be discriminated by the 129 being multiplied by 30 and 60, while the 67 or 134 is differently x 25, 40, 50 and l00.

It is evident that Wittich's prosthaphaeresis could not be a good method of practically effecting multiplications unless the quantities to be multiplied were sines, on account of the labour of the interpolations.

0.00000 00000 00000 0 73 18 5593 6 90623 9336, which multiplied by 2 47 gave 0.01029 995 66 39811 95 265277444, the logarithm of 1.024, true to 17 or 18 places.

If the logarithms are to be Briggian all the series in the preceding formulae must be multiplied by M, the modulus; thus, log i o(I +x) = M(x-2x2+3x3-4x4+&c.), and so on.

If the logarithm required is Briggian, the value of the series is to be multiplied by M.

In all the communities schools have multiplied, but the new seminaries are of the old non-progressive type.

Not only has the number of known forms been greatly multiplied, but the study of the biology and life-history of the parasites has been attended in some cases with remarkable and unexpected results.

As the frame has the same linear expansion as the wire, external changes of the temperature will not affect their relative length, but if the fine wire is heated by the passage of an electric current, its expansion will move the indicating needle over the scale, the motion being multiplied by the gear.

In the Hartmann and Braun form of hot-wire voltmeter, the fine wire is fixed between two supports, and the expansion produced when a current is passed through it causes the wire to sag down, the sag being multiplied by a gear and made to move an indicating needle over a scale.

The result was that, despite the numbers who entered the army or emigrated to Canada, the standard of civilization sank lower, and the population multiplied in the islands.

Urban and Rural Population.The five cities of the country that had 8000 or more inhabitants in 1790 had multiplied to 548 in 1900.

Minnesota alone produces more than half of the same total, having multiplied her product since 1889 by more than 33 times.

Songbirds are plentiful, especially in wooded regions, and include the American robin, oriole, thrushes, the cat-bird and various sparrows; while the English sparrow, introduced years ago, has multiplied excessively and become a nuisance in the towns.

In The Reformed Calendar The Intercalary Period Is Four Hundred Years, Which Number Being Multiplied By Seven, Gives Two Thousand Eight Hundred Years As The Interval In Which The Coincidence Is Restored Between The Days Of The Year And The Days Of The Week.

The specific gravity of any sample of spirits thus determined, when multiplied by ten, gives the weight in pounds per imperial gallon, and the weight of any bulk of spirits divided by this number gives its volume at once in imperial gallons.

The scale is so arranged that the reading multiplied by 5 and added to 1000 gives the specific gravity with reference to water as 1000.

Among the archives, kept in the sacristy of the church, are several banners captured by the Appenzellers in former days, among them one taken in 1406 at Imst, near Lanedeck, with the inscription Hundert Teufel, though popularly this number is multiplied a thousandfold.

As a result of their isolation, the proportion of endemic plants is greater here than in any other region, and the great elevation of the mountains, with the consequent variation in temperature, moisture and barometric pressure, has multiplied the number of species.

In the half-century from 1830 to 1880 the cloisters likewise prospered and multiplied fivefold.

- Six families of Orthoptera are here recognized, but most special students of the order consider that these should be rather regarded as super-families, and the number of families greatly multiplied.

Such examples might be multiplied unendingly, but enough has been said to show that the attitude of civilized man towards the sphinx-riddle of his end has been in part dictated and is even still influenced by the savage belief that to die is unnatural.

The proofs of this which Schultz and Gautier adduce from the Chansons de Geste might be multiplied indefinitely.

When the work was recommenced it was found that the native Christians had multiplied and developed during the harsh treatment of the 25 years.

Having an easy task in defending himself against Hobbes's trivial criticism, he seized the opportunity given him by the English translation of the De corpore to track Hobbes again step by step over the whole course, and now to confront him with his incredible inconsistencies multiplied by every new utterance.

Anti-slavery societies were greatly multiplied throughout the North, and many men of influence, both in the church and in the state, were won to the cause.

Books were in demand and were multiplied.

When the stand on which w rests is shaken, a multiplied representation of this movement takes place at h, and any small body resting on that point, as for example a small screw s standing on its head, may be caused to topple over.

consists of a weight of 300 kilos suspended by a wire 25 metres in length, the movements of which by means of writing indexes are multiplied 12.5 times.

Vicentini of Padua, will yield excellent diagrams of the gentle undulations of earthquakes which have originated at great distances, but for local disturbances, even if the bob of the pendulum acts as a steady point, the highly multiplied displacements are usually too great to be recorded.

Their political influence, again, which arises from the fusion of private and political law in Koran and Sunna, is highly inconvenient to the state, and often becomes intolerable now that relations with Western states are multiplied.

Instances might be multiplied.

They multiplied exceedingly, and by the time of Theodosius were reckoned by Chrysostom at about 10o,000 souls.

Both capitals multiplied their population by nine in the first nine decades of the century.

The seed thus sown rapidly germinated and multiplied.

Collegiate honours accompanied the issue of its successive volumes, which, however, at the same time multiplied his foes and stimulated their hatred.

flows through the spiral coolers N and M, and finally through the box H, where it is well mixed before passing the outflow thermometer P. As soon as a steady state is reached, the difference of temperature between the outflow and inflow thermometers, multiplied by the current of water in grammes per minute gives the heat per minute supplied by combustion.

The progress of Protestant missions was very slow for some years, but from 1895 converts multiplied.

Thus, applied to a potential, it gives the direction and magnitude of the force; to a distribution of temperature in a conducting solid, it gives (when multiplied by the conductivity) the flux of heat, &c.

p. 173) that the increase of the total heat of a saturated vapour between any two temperatures should be equal to the specific heat S of the vapour at constant pressure multiplied by the difference of temperature, provided that the saturated vapour behaved as an ideal gas, and that its specific heat was independent of the pressure and temperature.

But the development has been rapid; the value of products multiplied seven times, the wages paid nine, and the capital invested twelve, in the years 1880-1900; and the increase in the same categories from 1900-1905 was 35, 42.8 and 82.4% respectively.

Shares that at first represented so many dollars per foot in a tangible mine were multiplied and remultiplied until they came to represent paper thicknesses or almost nothing, yet still their prices mounted upward.

In the meantime, however, agreements of this nature between one power and another have multiplied rapidly within the last few years (see Arbitration).

Hence if H varies the magnet will rotate in such a way that the couple due to torsion is equal to the new value of H multiplied by M.

But in the interval their duties vastly multiplied.

Analytically, it is convenient to put Q~ equal to eirt multiplied by a complex coefficient; owing to the linearity of the equations the factor e~ni will run through them all, and need not always be exhibited.

If, therefore, the screw has several equidistant threads, the true pitch is equal to the divided axial pitch, as measured between two adjacent threads, multiplied by the number of threads.

Variable Effort and Resistance.Jf an effort has different magnitudes during different portions of the motion of its point of application through a given distance, let each different magnitude of the effort P be multiplied by the length Lts of the corresponding portion of the path of the point of application; the sum ~.

When several couples act on one piece, the resultani of their moments is to be multiplied by the common angular velocit) of the whole piece.

If that velocity is different for different portions of the rubbing surfaces, the velocity of each portion is to be multiplied by the friction of that portion, and the results summed or integrated.

The product wp/g, by which the half-square of the angular velocity is multiplied, is called the moment of inertia of the revolving body.

The actual energy due to the rotation of the fly, with its mean angular velocity, is equal to one-half of the periodical excess of energy multiplied by the steadiness.

Each year has multiplied the produce of the preceding, and for thirty years it is this rice which has been served at my table.

Some seeds were obtained from China; but they proved to be of small importance, as it was clearly ascertained by the members of the Assam deputation that both the black and the green tea plants were indigenous here, and might be multiplied to any extent; another result of the Chinese mission, that of procuring persons skilled in the cultivation and manufacture of black tea, was of more material benefit.

Impediments multiplied at every step; the cry was raised: " The constitution is in danger "; and on the 30th of January 1770 the Reaction Riksdag, after a barren ten months' session, rose amidst chaotic confusion without accomplishing anything.

They had also rapidly multiplied, so that by 1 9 04 they were more numerous than the whites in the colony.

Since 0(o) is finite, proportional to K, the integrated term vanishes at both limits, and we have simply f 0(z)dz f: (z)dz, (34) and T= ref: z1,1,(z)dz (35) In Laplace's notation the second member of (34), multiplied by 27r, is represented by H.

Resolving vertically we find that the weight of the liquid raised above the level must be equal to T(sin 0 2 - sin 01), and this is therefore equal to the area P 1 P 2 A 2 A 1 multiplied by gp. The form of the capillary surface is identical with that of the " elastic curve," or the curve formed by a uniform spring originally straight, when its ends are acted on by equal and T 2 opposite forces applied either to the ends themselves or to solid pieces attached to them.

The analytical expression for the motion in the latter case involves exponential terms, one of which (except in case of a particular relation between the initial displacements and velocities) increases rapidly, being equally multiplied in equal times.

The coefficient (q) of the time in the exponential term (e at) may be considered to measure the degree of dynamical instability; its reciprocal 1 /q is the time in which the disturbance is multiplied in the ratio I: e.

Thus, if d= 1, q -1 -= -115; or for a diameter of one centimetre the disturbance is multiplied 2.7 times in about one-ninth of a second.

If the disturbance be multiplied 1000 fold in time, t, qt=3log e 10=6.9, so that t= 79d a.

For example, if the diameter be one millimetre, the disturbance is multiplied 1000 fold in about one-fortieth of a second.

From (3) it appears that the time in which a disturbance is multiplied in a given ratio varies, not as d, but as d z.

As everybody knows, however, books could be and were multiplied by the process of copying tolerably freely, and a copy at first or second hand which belonged to the fiddler king Rene of Provence in the 15th century was used for the first printed edition in 1547.

In Wales, for instance, the rivalry of the sects has multiplied chapel accommodation out of all proportion to the population; while everywhere it happens that churches, at one time crowded every Sunday, have been emptied by the shifting of population or other causes.

A fact is nothing except in its relations to other facts; and as these relations are multiplied in the progress of knowledge the nature of the so-called fact is indefinitely modified.

The line n shows the factor by which the index of refraction of the transmitted vibration is multiplied, and the curve p the intensity of the absorbed vibration for that wave-length.

No exact comparison can be made showing the increase in the native population owing to the varying areas of the colony, but the natives have multiplied more rapidly than the whites; the increase in the numbers of the last-named being due, in considerable measure, to immigration.

the power is applied at the end of the long arm of the steelyard and multiplied by levers from loo to 500 times, so that the weights used are small and handy.

In the present article a+b will mean that a is taken first, and b added to it; but a X b will mean that b is taken first, and is then multiplied by a.

When this new unit has been multiplied by a number, we can again take the product as a unit for the purpose of another multiplication; and so on indefinitely.

If this unit is A, then what we are really considering is - 4A; and this means, not that A is multiplied by - 4, but that A is multiplied by 4, and the product is taken negatively.

Thus "-4 of A " no longer means two of the units, three of which make up A; it means that A is multiplied by the fraction 3, i.e.

Hence the digits are multiplied in pairs, and grouped according to the power of io which each product contains.

When a mixed quantity or a mixed number has to be multiplied by a large number, it is sometimes convenient to express the former in terms of one only of its denominations.

The lower clergy were more amenable; the two hundred who alone are said to have been ejected should perhaps be multiplied by five; but even so they were not one in seven, and these seven were clergy who had been promoted in Marys reign, or who bad stood the celibate and other tests of 1553-1554.

on the values of the coefficients in the terms multiplied by 0, 0 2, ...; they are thus in some measure arbitrary points as regards the ultimate curve P1 It may be added that we have summits only on the component curves P 1 = o, of a multiplicity a l > 1; the number of summits on such a curve is in general = (a 1 2 - a,)m 1 2.

While a number of ferns can be multiplied vegetatively, by buds formed on the leaves and in other ways, the regular mode of propagation is by sowing the spores shed from the ripe sporangia.

Clubs were multiplied and pamphlets came forth every hour.

Join to the original equations the new equation ax+(33'+yz=8; a like process shows that, the equations being satisfied, we have a,a,'Y,S a,b,c,d a' b ' c ' d'a",, b", c", or, as this may be written, a,13,y - 8a,b,c =07 a,b,c,d a',b'c' a' b r c r d'a", b N c" a", b", c", d",, , which, considering b as standing herein for its value ax+0y+yz, is a consequence of the original equations only: we have thus an expression for ax+/3y+yz, an arbitrary linear function of the unknown quantities x, y, z; and by comparing the coefficients of a, /3, y on the two sides respectively, we have the values of x, y, z; in fact, these quantities, each multiplied by a,b,c a' b ' c',, a N b r/ c", b", are in the first instance obtained in the forms a,b,c,d a 'b' c' d'a", b N' c N' dN,, , respectively.

This solution being reached, the additional terms were found, which were multiplied by the first power of the several eccentricities and of the inclination.

One of them, Simon Brec, proceeded to Greece, where his posterity multiplied to such an extent that the Greeks grew afraid and reduced them to slavery.

Unable to rise, the wretched people multiplied on their potato plots with perfect recklessness.

Perquisites, offices, frced loans were multiplied to such a point that a critic of the times, Guy Patin, facetiously declared that duties were to be exacted from the beggars basking in the sun.

The Company of the Indies became the grantee for the farming of.tobacco, the coinage of metals, and farming in general; and in order to procure funds it multiplied the output of shares, which were adroitly launched and became more and more sought for on the exchange in the rue Quincampoix.

playing the Roman senate: all these causes, added together and multiplied, assisted in setting a general fermentation to work.

Clubs were openly organized, pamphlets and journals appeared, regardless of administrative orders; workmens unions multiplied in Paris, Bordeaux and Lyons, in face of drastic pro hibition; and anarchy finally set in with the defection of the army in Paris on the 23rd of June, at Nancy, at Metz and at Brest.

The Girondins, discredited in Paris, multiplied their attacks upon Danton, now the master: they attributed the civil war and the disasters of the foreign campaign to the ?I~ despotism of the Paris Commune and the clubs; they the corn- accused Marat of instigating the September massacres; mane and they began the supreme struggle by demanding the a~d the election of a committee of twelve deputies, charged with ron e.

The existing species of things having thus been transferred, with all their specialities, to the prehistoric stage, they were multiplied endlessly in number, by reducing their size through continued subdivision; at the same time each one thing is so indissolubly connected with every other that the keenest analysis can never completely sever them.

In Australia, as in America, horses imported by European settlers have escaped into unreclaimed lands and multiplied to a prodigious extent, roaming in vast herds over the wide and uncultivated plains.

l/y = i/f = V.1; (2) it is thus equal to the magnifying power multiplied by the distance of distinct vision, or the number of times that the focal length is contained in Io in.

The value of the clearness of an image-point in a median section is the sine of the semi-aperture of the pencil multiplied with the refractive index of the medium.

Petals multiplied at the expense of the stamens, which are reduced in number.

The floral envelopes are rarely multiplied.

m.; its revenue had multiplied sevenfold; and its small army was unsurpassed for efficiency.

From the above instances, which could be multiplied, we have no hesitation in postulating a Hebrew original of i.

atm m " which needs multiplied by to convert to Joules.

Thu 26 January 2006 @ 02:51 Comment from: Unity [Member] Is there a word that means clueless multiplied several millions times?

An entrant's score is the sum of each driver's points multiplied by the entrant 's rating of the driver.

So that means that the value of x is given by cos( q) multiplied by the hypotenuse.

Privately multiplied debt issuances are the currency of the global corporate gang's control.

William of Occam, a 14th century logician, wrote " Entities should not be multiplied unnecessarily.

matrixtransformation matrices that apply to a given model object are multiplied together when the object is rendered.

multiplyaid, the expectation for an outcome is its probability multiplied by its utility value for you.

multiplyount you win or lose depends on the size of your stake multiplied by how correct or how wrong you are.

multiplyould be multiplied by a factor of around 16.

multiplyrant's score is the sum of each driver's points multiplied by the entrant 's rating of the driver.

multiplyto calculate the grid-box mean, the output ﬁelds should be multiplied point-wise by the coverage fraction.

multiplys multiplied by the probability estimates in the third layer, and the class with lowest estimated cost is selected.

multiplyage size is multiplied by the width and height percentages to obtain the final image dimensions.

multiplyes might be multiplied indefinitely were design in nature our only subject.

multiplyould be multiplied by a factor of around 16.

stake multiplied by the SP of the horse.

Law of If we know the weights a and b of two elements that are reciprocal found in union with unit weight of a third element, then proporwe can predict the composition of the compounds which the first two elements can form with each other; either the weights a and b will combine exactly, or if not, these weights must be multiplied by integers to obtain the composition of a compound.

In the second he not only enlarges his matter and gives multiplied applications of his ideas, but also follows the synthetic method, first expounding the laws he had discovered and then proving them by the facts to which they are applied.

Pigs and goats, however, with cattle, horses, asses and dogs, have been introduced, have multiplied, and in considerable numbers run wild.

The first to attempt to define pitch would seem to have been Arnold Schlick (Musica ausgeteutscht and ausgezogen, Heidelberg, 1 511), who gives a measure, a line of 4s Rhenish inches, which, he says, multiplied sixteen times, should be the lowest F of a small organ.

It will be noticed that the rods only give the multiples of the number which is to be multiplied, or of the divisor when they are used for division, and it is evident that they would be of little use to any one who knew the multiplication table as far as 9 X9.

On p. 8, 10.502 is multiplied by 3.216, and the result found to be 33.77443 2; and on pp. 23 and 24 occur decimals not attached to integers, viz.

The new settlement, however, continued to prosper, and the cattle and horses brought from Europe multiplied and spread over the plains of the Pampas.

The population of Victoria was doubled in the first twelvemonth of the gold fever, and the value of imports and exports was multiplied tenfold between 1851 and 1853.

Thus, if x= horned and y = sheep, then the successive acts of election represented by x and y, if performed on unity, give the whole of the class horned sheep. Boole showed that elective symbols of this kind obey the same primary laws of combination as algebraical symbols, whence it followed that they could be added, subtracted, multiplied and even divided, almost exactly in the same manner as numbers.

Extending his investigations to the currents produced by batteries, he found that the total voltaic heat generated in any circuit was proportional to the number of electrochemical equivalents electrolysed in each cell multiplied by the electromotive force of the battery.

I harp (multiplied quant.

If the insulation per mile, i.e., the total insulation multiplied by the mileage of the wire loop, is found to be less than 200,000 ohms, the wire is considered to be faulty.

nut and screw are rotating at the same speed, the position - of the former will remain fixed; and as the nut is driven by friction from the surface of the cone, this equality of speed will obtain only when the product of the diameter (d) of the cone at that position multiplied into its speed of rotation (n) equals the product of the diameter (a) of the disk multiplied into the speed of rotation (N) of the screw, or N/n = d/a, and thus the ratio of cable paid out to that of wire paid out is continuously given by a pointer controlled 1 See Sir W.

The tentacles are primarily four in number, perradial, alternating with four interradial tentaculocysts, but both tentacles and sense-organs may be multiplied and the primary perradii may be six instead of four (fig.

in such forms as Velella, Porpita, &c., the ancestor was an eight-rayed medusa (Disconula) which acquired a pneumatophore as an ectodermal pit on the ex-umbrella, and in which the organs (manubrium, tentacles, &c.) became secondarily multiplied, just as they do in Gastroblasta as the result of incomplete fission.

The grey and white poplars are usually multiplied by long cuttings; the growth is so rapid in a moist loamy soil that, according to Loudon, cuttings 9 ft.

These images take the place of the coloured fragments of glass, and they are symmetrically multiplied by the mirrors.

Such quotations were multiplied, as theologians learnt to depend increasingly upon their predecessors, until the testimony of "our holy father" Athanasius, or Gregory the Divine, or John the Golden-mouthed, came to be regarded as decisive in reference to controverted points of faith and practice.

To check this courts were multiplied (there were five, six or more instances), which only multiplied the evil.

After his death in 1054 the process of disintegration went on apace and the family feuds multiplied at an alarming rate.

Moreover, the prohibitions are strengthened and multiplied.

The situation went from bad to worse, the deficit in the budget increased, the gendarmery, which received no pay, became insubordinate, and crime multiplied.

Meanwhile his academic honours from home and foreign universities multiplied, and he became a fellow of the Royal Society in 1894.

The order of Friends was organized in a hierarchy of ranks, which were multiplied as time went on.

Among the ruder or savage tribes they possess but one form; but the ingenuity of man has devised many inventions to increase his comforts; he has varied and multiplied the characters and kinds of domestic animals for the same purpose, and hence the various breeds of horses, cattle and dogs.

Thus all that was shocking in the barbarism of Africa was multiplied and intensified by this foreign stimulation.

After the field preaching began converts multiplied.

The expenses were met by collections made in the Calvinistic Methodist Societies, and as the funds increased masters were multiplied, until in 1786 Charles had seven masters to whom he paid £io per annum; in 1787, twelve; in 1789, fifteen; in 1794, twenty.

And similar records might be multiplied almost to any extent.

Shirazi (f9o5); but the literature in new translations and imitations has recently multiplied exceedingly.

- The value of a determinant is unchanged if we add to the elements of any row or column the corresponding elements of the other rows or other columns respectively each multiplied by an arbitrary magnitude, such magnitude remaining constant in respect of the elements in a particular row or a particular column.

From the equations a11xi+ a12x2+ a13x3 +Ã¯¿½Ã¯¿½Ã¯¿½ = El, a21x1+a72x2+ a23x3+Ã¯¿½Ã¯¿½Ã¯¿½ = 2, a3lxl+a32x2+a33x3+Ã¯¿½Ã¯¿½Ã¯¿½ = 53, 0x1 =A111+A21E2+A31Er3+Ã¯¿½Ã¯¿½Ã¯¿½ 0x2 = Al2E1 + A22E2+ A32Srr3+Ã¯¿½Ã¯¿½Ã¯¿½ AX3 =A13E1+A23E2+A33E3+Ã¯¿½Ã¯¿½Ã¯¿½ A n 1 E1 = B110x1 + B12Ax2+ B13Ax3+Ã¯¿½Ã¯¿½Ã¯¿½, On - lt2 = B 21Ax1+ B220x2+ B230x3+Ã¯¿½Ã¯¿½Ã¯¿½ An-15513 = B31Ax1 + B 32Ax2+B330x3+Ã¯¿½Ã¯¿½Ã¯¿½ and comparison of the first and third systems yields B = An-2a rs = rsÃ¯¿½ In general it can be proved that any minor of order of the adjoint is equal to the complementary of the corresponding minor of the original multiplied by the h power of the original determinant.

Hence_li y ` A 1n where A li and A li, are minors of the complete determinant (a11a22...ann)Ã¯¿½ an1 ant Ã¯¿½Ã¯¿½Ã¯¿½an,n-1 or, in words, y i is the quotient of the determinant obtained by erasing the i th column by that obtained by erasing the n th column, multiplied by (-r)i+n.

The discriminant of the product of two forms is equal to the product of their discriminants multiplied by the square of their resultant.

and take therein the coefficient of the function (mi t tm7t t m 31 t ...), we obtain the same result as if we formed the separation function in regard to the specification (mÃ¯¿½ It t'tm2 32tm"`l3t...), multiplied by Alt!!

If u, a quantic in x, y, z, ..., be expressed in terms of new variables X, Y, Z ...; and if, n,, ..., be quantities contragredient to x, y, z, ...; there are found to exist functions of, n, ?, ..., and of the coefficients in u, which need, at most, be multiplied by powers of the modulus to be made equal to the same functions of E, H, Z, ...

the i t " power of that appertaining to a x and b x multiplied by the j t " power of that appertaining to a x and c x multiplied by &c. If any two of the linear forms, say p x, qx, be supposed identical, any symbolic expression involving the factor (pq) is zero.

Every symbolic product, involving several sets of cogredient variables, can be exhibited as a sum of terms, each of which is a polar multiplied by a product of powers of the determinant factors (xy), (xz), (yz),...

1 And The Actual Forms For The First Three Weights Are 1 Aobzo, (Ao B 1 A 1 B O) Bo, (A O B 2 A 1 2 0 Bo, Ao(B2, 3 A1B2 A2B1 A O (B L B 2 3B O B 3) A I (B 2 1 2B 0 B 2); Amongst These Forms Are Included All The Asyzygetic Forms Of Degrees 1, 1, Multiplied By Bo, And Also All The Perpetuants Of The Second Binary Form Multiplied By Ao; Hence We Have To Subtract From The 2 Generating Function 1Z And 1 Z Z2, And Obtain The Generating Function Of Perpetuants Of Degrees I, 2.

The sum of the corresponding numbers multiplied by 332600 gives Log.

When P is the neutral point, H is equal and opposite to R; therefore M = Hd 3, or the moment is numerically equal to the cube of the distance from the neutral point to a pole, multiplied by the M.

Then if a known change of induction SB a inside the standard coil is found to cause a throw of d scale-divisions, any change of induction SB through the experimental coil will be numerically equal to the corresponding throw D multiplied by snRBa/SNrd.

When the magnetizing current is twice reversed, so as to complete a cycle, the sum of the two deflections, multiplied by a factor depending upon the sectional area of the specimen and upon the constants of the apparatus, gives the hysteresis for a complete cycle in ergs per cubic centimetre.

Thus the magnetization which the sample of Swedish iron received in a field of 1490 was not increased (beyond the limits of experimental error) when the intensity of the field was multiplied more than thirteen-fold, though the induction was nearly doubled.

At the temperature of liquid air (-185Ã‚°) the application of a field of 21,800 multiplied the resistance of the bismuth no less than 150 times.

In opposition to this Nominalistic view, which implied the reversal of his whole position, William may have meant to say that, instead of the universal being multiplied, it is rather the individuals which are reduced to unity in the universal.

Matthias laboured strenuously to develop and protect the towns, multiplied municipal charters, and materially improved the means of communication, especially in 1 We know actually of fifteen, but there may have been many more.

The whole burden of taxation rested on their shoulders, and so ground down were they by ingeniously multiplied exactions, that thousands of them were reduced to literal beggary.

it means that i lb is to be multiplied by 7, the result by 3, and the new result by 5.

If it is intended that the first number is to be multiplied by the second, a special sign such as X should be used.

The number by which an algebraical expression is to be multiplied is called its coefficient.

- (i.) An expression such as a.2.a.a.b.c.3.a.a.c, denoting that a series of multiplications is to be performed, is called a monomial; the numbers (arithmetical or algebraical) which are multiplied together being its factors.

Later, in his article " Chromatics " in the supplement to the 5th edition of this encyclopaedia, he shows that the colours " lose the mixed character of periodical colours, and resemble much more the ordinary prismatic spectrum, with intervals completely dark interposed," and explains it by the consideration that any phasedifference which may arise at neighbouring striae is multiplied in proportion to the total number of striae.

Put for short- do d{- +ply+dz (1), and represent by v2E the quantity multiplied by b 2.

New corms are produced at the end of the season, and by these the plant is multiplied.

The Boer leaders definitely decided upon a guerrilla and a wearing policy, deliberately dispersed their field army, and then swelled and multiplied the innumerable local commandos.

Garments were multiplied, and the cape and long mantle, which had previously been uncommon, were now usual.

multiplied by the total rubbing or friction surface of the air-ways in square feet and by the coefficient of friction.

high, obviously act as efficient mercury-traps; but the already considerable height of the pump is thus multiplied by two.

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.