Equal to sentence examples

  • Her arms were crossed, and though she smiled at Lon, Sofia could see her level of comfort was equal to hers among the giants that towered even above a supermodel.

    0
    0
  • Only this was equal to a hundred thunderstorms.

    0
    0
  • Sometimes, a night in the underworld was equal to seconds in the mortal world, sometimes a night and sometimes, a few nights.

    0
    0
  • The life insurance World Wide provided its employees was equal to one year's pay, hardly enough to leave a rich widow.

    0
    0
  • Yully, the third woman who would become her sister, was just as unique with a heart equal to that of any of the women.

    0
    0
  • Her wealth made it certain that he would be the richest man in France, and he determined to play a part equal to that of his great-grandfather, the regent, whom he resembled in character and debauchery.

    0
    0
  • The distance between the centres of the two spectrographs shall be equal to the distance between the optical axes of the two viewing microscopes.

    0
    0
  • AMICABLE NUMBERS, two numbers so related that the sum of the factors of the one is equal to the other, unity being considered as a factor.

    0
    0
  • In 1831, from a study of the specific heats of compounds, he formulated "Neumann's law," which expressed in modern language runs: "The molecular heat of a compound is equal to the sum of the atomic heats of its constituents."

    0
    0
  • But the day showed the ' B attle of Macedonian army equal to the task.

    0
    0
  • To secure election a candidate must at the first voting poll an absolute majority and a number of votes equal to one-fourth of the number of electors.

    0
    0
  • From the receveur is demanded a security equal to five times his total income.

    0
    0
  • Their length is nearly equal to that of the longest pair of the ordinary form hitherto recorded, while the tip-to-tip interval is nearly double that of any other known specimen.

    0
    0
  • This is equal to 1 m.

    0
    0
  • For the period of thirty years during which the mine was worked the production of ore amounted to 234,648 tons, equal to 51,622 tons of copper, valued at £4,749,924.

    0
    0
  • Several companies are devoting all their energies to zinc extraction, and the output is now equal to about 5% of the world's production.

    0
    0
  • per inhabitant, from indirect taxation £2: 4: 6, and the total revenue from all sources £35,699,782, equal to £8: 16: 2 per inhabitant.

    0
    0
  • The federal government has no public debt, but each of the six states has contracted debts which aggregate £237,000,000, equal to about £58, 8s.

    0
    0
  • Such was the growth of infant Victoria in five years; that of Adelaide or South Australia, in the same period, was nearly equal to it.

    0
    0
  • In him Orange was to find an adversary who was not only a great general but a statesman of insight and ability equal to his own.

    0
    0
  • The wood is hard, heavy and of fine grain, quite equal to the best British oak for indoor use, but of very variable durability where exposed to weather.

    0
    0
  • Thus if the instrument depends on the pressure or suction effect alone, and this pressure or suction is measured against the air pressure in an ordinary room, in which the doors and windows are carefully closed and a newspaper is then burnt up the chimney, an effect may be produced equal to a wind of io m.

    0
    0
  • Rumford then turned up a hollow cylinder which was cast in one piece with a brass six-pounder, and having reduced the connexion between the cylinder and cannon to a narrow neck of metal, he caused a blunt borer to press against the hollow of the cylinder with a force equal to the weight of about ro,000 lb, while the casting was made to rotate in a lathe.

    0
    0
  • He shows that the amount of work obtainable is equal to that which can be done by the first gas in expanding into the space occupied by the second (supposed vacuous) together with that done by the second in expanding into the space occupied by the first.

    0
    0
  • If the looped lines are both in good condition and free from leakage, the current sent out on line r will be exactly equal to the current received back on line 2; and as these currents will have equal but opposite effects on the galvanometer needle, no deflection of the latter will be produced.

    0
    0
  • 23, representing the " differential " method, B is the sending battery, B 1 a resistance equal to that of the battery, R a rheostat and C an adjustable condenser.

    0
    0
  • Thus for a dash the interval between the positive and the negative current is equal to the time the paper takes to travel over twice the space between two successive holes.

    0
    0
  • If, then, a long copper bar which forms part of this circuit is placed in proximity to the transmitting antenna and the handle moved, some position can be found in which the natural time period of the cymometer circuit is made equal to the actual time period of the telegraphic antenna.

    0
    0
  • Pupin showed that by placing inductance coils in circuit, at distances apart of less than half the length of the shortest component wave to be transmitted, a non-uniform conductor could be made approximately equal to a uniform conductor.

    0
    0
  • In 1906 there were 30,551, equal to 7.2 per cent., more telephone stations in the United Kingdom than in the ten European countries of Austria, Hungary, Belgium, Denmark, Holland, Italy; Norway, Portugal, Russia, Sweden and Switzerland, having a combined population of 288 millions as against a population of 42 millions in the United Kingdom.

    0
    0
  • Hence this part of the country has a cold winter climate, so that while the mean summer temperature of Milan is higher than that of Sassari, and equal to that of Naples, and the extremes reached at Milan and Bologna are a good deal higher than those of Naples, the mean winter temperature of Turin is actually lower than that of Copenhagen.

    0
    0
  • Taking into account the variations in wages and in the price of wheat, it may be calculated that the number of hours of work requisite to earn a sum equal to the price of a cwt.

    0
    0
  • Although in some industrial centres the working-class movement has assumed an importance equal to that of other countries, there is no general working-class organization comparable to the English trade unions.

    0
    0
  • The Italian sees (exclusive of Rome and of the suburbicarian sees) have a total annual revenue of 206,000 equal to an average of 800 per see.

    0
    0
  • A race was formed strong enough to keep the empire itself in check, strong enough, except for its own internecine contests, to have formed a nation equal to its happier neighbors.

    0
    0
  • Meanwhile the podest still subsists; but he is no longer equal to the task d maintaining an equilibrium of forces.

    0
    0
  • But DAzeglio was not equal to the situation, and he, too, resigned in November 1852; whereupon the king appointed Cavour prime minister, a position which with short intervals he held until his death.

    0
    0
  • It may be asked, Why can God not create a triangle whose three angles shall not be equal to two right angles?

    0
    0
  • The subject of patent medicines is but little understood by the general public. Any medicine, the composition of which is kept secret, but which is advertised on the label for the cure of diseases, must in Great Britain bear a patent medicine stamp equal to about one-ninth of its face value.

    0
    0
  • The Dutch nation, as soon as it was emancipated from Spanish tyranny, displayed an amount of enterprise, which, for a long time, was fully equal to that of the British.

    0
    0
  • m., the volume of water below sea-level 323,800,000, and the total volume of the water equal to about hth of the volume of the whole globe.

    0
    0
  • Eight times the mean motion of Venus is so nearly equal to thirteen times that of the earth that the difference amounts to only the 2.

    0
    0
  • It is customary to ascribe to Offa a policy of limited scope, namely the establishment of Mercia in a position equal to that of Wessex and of Northumbria.

    0
    0
  • In several university towns there are free teaching establishments for women, supported by subscription, with programmes and examinations equal to those of the universities.

    0
    0
  • The number killed (811) is equal to about three in every thousand trainmen employed.

    0
    0
  • The number of passengers (36) killed in train accidents in 1907 was equal to o 0759 per million passengers carried and o o024 per million kilometres travelled by passengers, or 0.1503 per million kilometres travelled by trains.

    0
    0
  • An endeavour is made so to plan the works of a railway that the quantity of earth excavated in cuttings shall be equal to the quantity required for the embankments; but this is not always practicable, and it is sometimes advantageous to obtain the earth from some source close to the embankment rather than incur the expense of hauling it from a distant cutting.

    0
    0
  • Thus if R is equal to 10,000 lb when the velocity is 44 ft.

    0
    0
  • If there are several driving-axles in a train, the product Tw must be estimated for each separately; then the sum of the products will be equal to RV.

    0
    0
  • Also let l be the length of the stroke in feet and let a be the area of one cylinder in square inches, then, assuming two cylinders of equal size, I.H.P. =2 planl550 (8) The I.H.P. at any instant is equal to the total rate at which energy is required to overcome the tractive resistance R.

    0
    0
  • The sum of all these components of resistance is at any instant equal to the resistance represented by R.

    0
    0
  • per hour, is equal to 58.6 ft.

    0
    0
  • per hour, which is equal to 22 ft.

    0
    0
  • 465)/32 = 28,720 ib, and the corresponding horse-power which must be developed in the cylinders is, from (20), f V/550, and this is with f and V equal to the above values, 1149.

    0
    0
  • The value of is variable, but is between 7 and 8, and for approximate calculations may be taken equal to unity.

    0
    0
  • This high mean pressure cannot be maintained for long, because as the speed increases the demand for steam per unit of time increases, so that cut-off must take place earlier and earlier in the stroke, the limiting steady speed being attained when the rate at which steam is supplied to the cylinders is adjusted by the cut-off to be equal to the maximum rate at which the boiler can produce steam, which depends upon the maximum rate at which coal can be burnt per square foot of grate.

    0
    0
  • If h is the water heat at the lower temperature, h l the water heat at the higher temperature, and L the latent heat at the higher temperature, the heat supply per pound of steam is equal to h1 - h2+L1, which, from the steam tables, with the values of the temperatures given, is equal to 1013 B.Th.U.

    0
    0
  • Thar equal to 148930 foot pounds 4 2.37 cubic feet.

    0
    0
  • It is doubtful whether even the genius of Valdemar would have proved equal to such a stupendous task.

    0
    0
  • It can be shown that unless a quantity of meteors in collective mass equal to our moon were to plunge into the sun every year the supply of heat could not be sustained from this source.

    0
    0
  • Berthelot, on the other hand, assumed that the heat-capacity of an aqueous solution is equal to that of an equal volume of water, and calculated his results on this assumption, which involves much the same uncertainty as that of Thomsen.

    0
    0
  • of water from o° C. to C., and is approximately equal to ioo cal.

    0
    0
  • The oxygen contained in the compound was deducted, together with the equivalent amount of hydrogen, and the heat of combustion of the compound was then taken to be equal to the heats of combustion of the elements in the residue.

    0
    0
  • The Senate is composed of fifty members elected biennially by senatorial districts as nearly as possible equal to one another in population, and the House of Representatives (in the Constitution of 1776 called the House of Commons) of one hundred and twenty, elected biennially and chosen by counties' according to their population, each county having at least one representative, no matter how small its population.

    0
    0
  • five slaves to be counted equal to three whites.

    0
    0
  • His character is perhaps best described by a writer who says "his strength was not equal to his goodness."

    0
    0
  • The interior of the province is also thickly sprinkled with lakes, the combined area of which is equal to about one-twentieth of the entire surface.

    0
    0
  • But his pride was equal to his abilities.

    0
    0
  • The bark and young cones afford a tanning material, inferior indeed to oakbark, and hardly equal to that of the larch, but of value in countries where substances more rich in tannin are not abundant.

    0
    0
  • Were his powers, physical as well as mental, equal to the task ?

    0
    0
  • Oscines, equal to Miiller's group of the same name; 2.

    0
    0
  • The lemniscate of Bernoulli may be defined as the locus of a point which moves so that the product of its distances from two fixed points is constant and is equal to the square of half the distance between these points.

    0
    0
  • They are in almost continuous motion, their power of endurance being equal to the rapidity of their motions.

    0
    0
  • But under the Statute of Frauds (1677), ss., 1, 2) leases, except those the term of which does not exceed three years, and in which the reserved rent is equal to two-thirds at least of the improved value of the premises, were required to be in writing signed by the parties or their lawfully authorized agents; and, under the Real Property Act 1845, a lease required by law to be in writing is void unless made by deed.

    0
    0
  • 1818); (iii.) cheptel given to a farmer (fermier) or participating cultivator (colon partiaire) - in the cheptel given to the farmer (also called cheptel de fer) stock of a value equal to the estimated price of the stock given must be left at the expiry of the lease (Art.

    0
    0
  • Though it is probably destined to be used even more extensively as a fertilizer before the demand for it as a feeding stuff becomes equal to the supply, practically all the cotton seed meal of the south will ultimately be used for feeding.

    0
    0
  • For a long time these shells or hulls, as they are called, were burned at oil mills for fuel, 22 tons being held equal to a cord of wood, and 43 tons to a ton of coal.

    0
    0
  • In Germany, the law prescribes a close-test of 21° C., equal to about 70° F., whilst in Russia the standard is 28° C., equal to 84.4° F., by the close-test; in both these countries the weights of petroleum which may be stored in specified buildings are determined by law.

    0
    0
  • When a current is passed through the wire, continuous or alternating, it creates heat, which expands the air in the bulb and forces the liquid up one side of the U-tube to a certain position in which the rate of loss of heat by the air is equal to the rate at which it is gaining heat.

    0
    0
  • an angle equal to that of the torsion head.

    0
    0
  • Many ingenious devices for forming bars have been produced; but generally a strong frame is used, across which steel wires are stretched at distances equal to the size of the bars to be made, the blocks being first cut into slabs and then into bars.

    0
    0
  • He burned phosphorus in air standing over mercury, and showed that (1) there was a limit to the amount of phosphorus which could be burned in the confined air, (2) that when no more phosphorus could be burned, one-fifth of the air had disappeared, (3) that the weight of the air lost was nearly equal to the difference in the weights of the white solid produced and the phosphorus burned, (4) that the density of the residual air was less than that of ordinary air.

    0
    0
  • He also showed that on heating mercury calx alone an " air " was liberated which differed from other " airs," and was slightly heavier than ordinary air; moreover, the weight of the " air " set free from a given weight of the calx was equal to the weight taken up in forming the calx from mercury, and if the calx be heated with charcoal, the metal was recovered and a gas named " fixed air," the modern carbon dioxide, was formed.

    0
    0
  • Unfortunately, the term normal is sometimes given to solutions which are strictly decinormal; for example, iodine, sodium thiosulphate, &c. In technical analysis, where a solution is used for one process only, it may be prepared so that I cc. is equal to.

    0
    0
  • Recent researches have shown that the law originally proposed by Kopp - " That the specific volume of a liquid compound (molecular volume) at its boiling-point is equal to the sum of the specific volumes of its constituents (atomic volumes), and that every element has a definite atomic value in its compounds " - is by no means exact, for isomers have different specific volumes, and the volume for an increment of CH 2 in different homologous series is by no means constant; for example, the difference among the esters of the fatty acids is about 57, whereas for the aliphatic aldehydes it is 49.

    0
    0
  • only contain single carbon linkages, then the number of such linkages is 2n - m, and if the thermal effect of such a linkage be X, then the termAisobviously equal to (2n - m)X.

    0
    0
  • it is equal to the sum of the thermal effects of the aldehyde and carbonyl groups.

    0
    0
  • molecular weight, is constant for isomers, and that two atoms of hydrogen were equal to one of carbon, three to one of oxygen, and seven to one of chlorine; but these ratios were by no means constant, and afforded practically no criteria as to the molecular weight of any substance.

    0
    0
  • The piece was warmly received at Dresden on the 2nd of January 1843; but its success was by no means equal to that of Rienzi.

    0
    0
  • Fears were entertained, and even the friends of the viceroy to some extent shared them, that he was not equal to the crisis.

    0
    0
  • In the male the right tooth usually remains similarly concealed, but the left is immensely developed, attaining a length equal to more than half that of the entire animal.

    0
    0
  • The scale of that map, as determined by the equator or centre meridian, we will suppose to be i: 125,000,000, while the encircling meridian indicates a scale of i: 80,000,000; and a " mean " scale, equal to the square root of the proportion which the area of the map bears to the actual area of a hemisphere, is r: 112,000,000.

    0
    0
  • Dorpfeld, we assume an Attic stadium of 200 steps (500 ft.) to be equal to 164 metres, a degree of 700 stad.

    0
    0
  • would be equal to 114,800 metres, its actual length according to modern measurement being I Io,808 metres.

    0
    0
  • Si-ngan-fu), the capital of China, was equal to 225 °, which Ptolemy reduced to 177°, but which in reality only amount to 126°.

    0
    0
  • The errors due to an exaggeration of distances were still further increased on account of his assuming a degree to be equal to Soo stadia, as determined by Posidonius, instead of accepting the 700 stadia of Eratosthenes.

    0
    0
  • Nor can Idrisi's map of the world, were drawn at intervals of zams, supposed to be equal to three hours' sail.

    0
    0
  • These miles, however, were not the ordinary Roman miles of l000 paces or 5000 ft., but smaller miles of Greek or Oriental origin, of which six were equal to five Roman miles, and as the latter were equal to 1480 metres, the Portolano miles had a length of only 1233 metres, and 75 2 of the former, and 90 3 of the latter were equal to a degree.

    0
    0
  • A trigonometrical survey of British India was begun in 1800 and the country can now boast of a survey which in most respects is equal to those of most European states.

    0
    0
  • But a day of God is equal to a thousand years (Ps.

    0
    0
  • The largest of all, however, was the macrocollon, probably of good quality and equal to the hieratic, and a cubit or nearly 18 in.

    0
    0
  • The patriarch of Constantinople is the nominal head of the Orthodox priesthood; but by an arrangement concluded in 1879, his authority was delegated to the Austrian emperor, in exchange for a revenue equal to the tribute previously paid by the clergy of the provinces; and his nominations for the metropolitanate of Serajevo, and the bishoprics of Dolnja Tuzla, Banjaluka and Mostar require the imperial assent.

    0
    0
  • The copper money was in pieces of a nominal value of 40, 20, TO, 5 and i paras, 40 paras being equal to 1 piastre.

    0
    0
  • He himself tried versification, and some of his lines which have come down to us appear quite equal to the average work of his contemporaries.

    0
    0
  • His hasidas are almost equal to his ghazels; for, while they rival those of Nef `i in brilliancy, they surpass them in beauty of diction, and are not so artificial and dependent on fantastic and farfetched conceits.

    0
    0
  • In cavalry they were weak, for the Russian does not take kindly to equitation and the horses were not equal to the accepted European standard of weight, while the Cossack was only formidable to stragglers and wounded.

    0
    0
  • Had the Austrians possessed mobility equal to that of the French the latter should have been overwhelmed in detail, but whilst the French covered 17 and 19 m.

    0
    0
  • In his position at Bautzen he felt himself equal to all his enemy's combinations.

    0
    0
  • The actual working of his mind towards that strategic and tactical ascendancy that rendered his presence on the battlefield, according to the testimony of his opponents, equal to a reinforcement of 40,000 men, was entirely undiscernible.

    0
    0
  • Faraday found that the mass of substance liberated at the electrodes in the cell C was equal to the sum of the masses liberated in the cells A and B.

    0
    0
  • The mean result of the best determinations shows that when a current of one ampere is passed for one second, a mass of silver is deposited equal to o ooi i 18 gramme.

    0
    0
  • If we assume that no other cause is at work, it is easy to prove that, with non-dissolvable electrodes, the ratio of salt lost at the anode to the salt lost at the cathode must be equal to the ratio of the velocity of the cation to the velocity of the anion.

    0
    0
  • The velocity with which the ions move past each other is equal to the sum of their individual velocities, which can therefore be calculated.

    0
    0
  • (I) In very dilute solutions of simple substances, where only one kind of dissociation is possible and the dissociation of the ions is complete, the number of pressure-producing particles necessary to produce the observed osmotic effects should be equal to the number of ions given by a molecule of the salt as shown by its electrical properties.

    0
    0
  • In the case of substances like ammonia and acetic acid, where the dissociation is very small, I - a is nearly equal to unity, and only varies slowly with dilution.

    0
    0
  • This is fully borne out by the experiments of Julius Thomsen, who found that the heat of neutralization of one gramme-molecule of a strong base by an equivalent quantity of a strong acid was nearly constant, and equal to 13,700 or 13,800 calories.

    0
    0
  • Let an electromotive force exactly equal to that of the cell be applied to it in the reverse direction.

    0
    0
  • Thus, if L denote the heat corresponding with the chemical changes associated with unit electric transfer, Le will be the heat corresponding with an electric transfer e, and will also be equal to the change in internal energy of the cell.

    0
    0
  • If secondary effects are eliminated, the deposition of metals also is a reversible process; the decomposition voltage is equal to the electromotive force which the metal itself gives when going into solution.

    0
    0
  • Their representation in the states general was exactly equal to that of the Dutch, though their population was in the proportion of seven to five.

    0
    0
  • " Plantation " Para rubber from Ceylon and the Malay States has brought prices equal to and often exceeding those of fine Para rubber from Brazil.

    0
    0
  • It is therefore to be expected that as time goes on the quality of " plantation " rubber will improve, and there would seem to be no reason why it should not eventually be fully equal to that of the " wild " rubber.

    0
    0
  • Proselytes are still not allowed, in Orthodox circles, to become the wives of reputed descendants of the priestly families, but otherwise marriage with proselytes is altogether equal to marriage between born Jews.

    0
    0
  • In 1824 the settled indigenes had to pay the very heavy rate of 11 roubles (about 1) per head, and the arrears, which soon became equal to the sums levied, were rigorously exacted.

    0
    0
  • In the same address he called attention to the conditions of the world's food supply, urging that with the low yield at present realized per acre the supply of wheat would within a comparatively short time cease to be equal to the demand caused by increasing population, and that since nitrogenous manures are essential for an increase in the yield, the hope of averting starvation, as regards those races for whom wheat is a staple food, depended on the ability of the chemist to find an artificial method for fixing the nitrogen of the air.

    0
    0
  • Similarly, by putting one or more of the deleted rows or columns equal to rows or columns which are not deleted, we obtain, with Laplace, a number of identities between products of determinants of complementary orders.

    0
    0
  • Hence the product determinant has the principal diagonal elements each equal to A and the remaining elements zero.

    0
    0
  • Its value is therefore O n and we have the identity D.0 = A n or D It can now be proved that the first minor of the adjoint determinant, say B rs is equal to An-2a�.

    0
    0
  • the sum of the suffixes in each term of the resultant is equal to mn.

    0
    0
  • It is the resultant of k polynomials each of degree m-I, and thus contains the coefficients of each form to the degree (m-I)'-1; hence the total degrees in the coefficients of the k forms is, by addition, k (m - 1) k - 1; it may further be shown that the weight of each term of the resultant is constant and equal to m(m-I) - (Salmon, l.c. p. loo).

    0
    0
  • and, dividing by y1y2...ym, the discriminant of f is seen to be equal to the product of the squares of all the differences of any two roots of the equation.

    0
    0
  • The discriminant of the product of two forms is equal to the product of their discriminants multiplied by the square of their resultant.

    0
    0
  • p, taking n equal to 00, we may write 1 +aix +a2x2 +...

    0
    0
  • being subsequently put equal to a, a non-unitary symmetric function will be produced.

    0
    0
  • In the theory of forms we seek functions of the coefficients and variables of the original quantic which, save as to a power of the modulus of transformation, are equal to the like functions of the coefficients and variables of the transformed quantic. We may have such a function which does not involve the variables, viz.

    0
    0
  • 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, ...

    0
    0
  • This will be recognized as the resultant of the two linear forms. If the two linear forms be identical, the umbral sets a l, a2; b l, b 2 are alternative, are ultimately put equal to one another and (ab) vanishes.

    0
    0
  • are equal to a x, x, c x, ...

    0
    0
  • The degree of the covariant in the coefficients is equal to the number of different symbols a, b, c, ...

    0
    0
  • and the weight' of the coefficient of the leading term xi +Q+T+.�� is equal to i+j+k+....

    0
    0
  • The process of transvection is connected with the operations 12; for?k (a m b n) = (ab)kam-kbn-k, (x y x y or S 2 k (a x by) x = 4))k; so also is the polar process, for since f k m-k k k n - k k y = a x by, 4)y = bx by, if we take the k th transvectant of f i x; over 4 k, regarding y,, y 2 as the variables, (f k, 4)y) k (ab) ka x -kb k (f, 15)k; or the k th transvectant of the k th polars, in regard to y, is equal to the kth transvectant of the forms. Moreover, the kth transvectant (ab) k a m-k b: -k is derivable from the kth polar of ax, viz.

    0
    0
  • and that thence every symbolic product is equal to a rational function of covariants in the form of a fraction whose denominator is a power of f x.

    0
    0
  • The discriminant of f is equal to the discriminant of 0, and is therefore (0, 0') 2 = R; if it vanishes both f and 0 have two roots equal, 0 is a rational factor of f and Q is a perfect cube; the cube root being equal, to a numerical factor pres, to the square root of A.

    0
    0
  • we find that Di must be equal to p x g x for then t x (p x) 3 +, u (g x) 3, Hence, if px, qx be the linear factors of the Hessian 64, the cubic can be put into the form A(p x) 3 +�(g x) 3 and immediately solved.

    0
    0
  • Hesse's canonical form shows at once that there cannot be more than two independent invariants; for if there were three we could, by elimination of the modulus of transformation, obtain two functions of the coefficients equal to functions of m, and thus, by elimination of m, obtain a relation between the coefficients, showing them not to be independent, which is contrary to the hypothesis.

    0
    0
  • Putting n equal to co, in a generating function obtained above, we find that the function, which enumerates the asyzvgetic seminvariants of degree 0, is 1 1-z2.1-z3.1-z4....1-z0 that is to say, of the weight w, we have one form corresponding to each non-unitary partition of w into the parts 2, 3, 4,...0.

    0
    0
  • In every magnet the strength of the south pole is exactly equal to that of the north pole, the action of the same magnetic force upon the two poles being equal and oppositely directed.

    0
    0
  • terminate outside the magnet or inside, have a resultant, equal to the sum of the forces and parallel to their direction, acting at a certain point N.

    0
    0
  • The line through the given point along which the potential decreases most rapidly is the direction of the resultant magnetic force, and the rate of decrease of the potential in any direction is equal to the component of the force in that direction.

    0
    0
  • The force in the interior is uniform, opposite (6) (II) [[[Terminology And Principles]] to the direction of magnetization, and equal to 3rI.

    0
    0
  • If the magnetization is parallel to the major axis, and the lengths of the major and minor axes are 2a and 2C, the poles are situated at a distance equal to 3a from the centre, and the magnet will behave externally like a simple solenoid of length 3a.

    0
    0
  • The internal force F is opposite to the direction of the magnetization, and equal to NI, where N is a coefficient depending only on the ratio of the axes.

    0
    0
  • Kohlrausch 2 the distance between the poles of a cylindrical magnet the length of which is from io to 30 times the diameter, is sensibly equal to five-sixths of the length of the bar.

    0
    0
  • Hence if the induction per square centimetre at any point is denoted by B, then in empty space B is numerically equal to H; moreover in isotropic media both have the same direction, and for these reasons it is often said that in empty space (and practically in air and other nonmagnetic substances) B and H are identical.

    0
    0
  • Suppose the whole space in which induction exists to be divided up into unit tubes, such that the surface integral of the induction over any cross-section of a tube is equal to unity, and along the axis of each tube let a line of induction be drawn.

    0
    0
  • Where the induction is high the lines will be crowded together; where it is weak they will be widely separated, the number per square centimetre crossing a normal surface at any point being always equal to the numerical value of B.

    0
    0
  • (26) Also A = B = H H4?rI _ I +41K, (27) and (28) 471 Since in empty space B has been assumed to be numerically equal to H, it follows that the permeability of a vacuum is equal to i.

    0
    0
  • Hence, whatever the position of the body, if the field be resolved into three components parallel to the 1 For all except ferromagnetic substances the coefficient is sensibly equal to See W.

    0
    0
  • 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.

    0
    0
  • The distance between the poles may with sufficient accuracy for a rough determination be assumed to be equal to five-sixths of the length of the magnet.

    0
    0
  • If the distance of the mirror from the scale is equal to n scale divisions, and if a deflection 0 of the needle causes, the reflected spot of light to move over s scale divisions, we shall have s/n = tan 20 exactly, s/2n = tan 0 approximately.

    0
    0
  • Since the induction B is equal to H 47rI, it is easy from the results of experiments such as that just described to deduce the relation between B and H; a curve indicating such relation is called a curve of induction.

    0
    0
  • 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.

    0
    0
  • When a current of strength i is suddenly interrupted in the primary, the increment of induction through the secondary is sensibly equal to 47rin/l units.

    0
    0
  • With these arrangements there is no demagnetizing force to be considered, for the ring has not any ends to produce one, and the force due to the ends of a rod 400 or 500 diameters in length is quite insensible at the middle portion; H therefore is equal to Ho.

    0
    0
  • If a transverse cut is made through a bar whose magnetization is I and the two ends are placed in contact, it can be shown that this force is 27r I 2 dynes per unit of area (Mascart and Joubert, Electricity and Magnetism, § 322; and if the magnetization of the bar is due to an external field H produced by a magnetizing coil or otherwise, there is an additional force equal to HI.

    0
    0
  • 23 should have a common vertex in the middle of the neck with a semi-vertical angle of 54° 44', while the condition for a uniform field is satisfied when the cones have a semivertical angle of 39° 14'; in the latter case the magnetic force in the air just outside is sensibly equal to that within the neck.

    0
    0
  • Further, Maxwell's stress is a tension along the lines of force, and is equal to B 2 /87r only when B = H, and there is no magnetization.

    0
    0
  • Heusler 2 in 1903 that certain alloys of the non-magnetic metal manganese with other non-magnetic substances were strongly magnetizable, their susceptibility being in some cases equal to that of cast iron.

    0
    0
  • The tranverse electromotive force is equal to KCH/D, where C is the current, H the strength of the field, D the thickness of the metal, and K a constant which has been termed the rotatory power, or rotational coefficient.

    0
    0
  • If V is the volume of a ball, H the strength of the field at its centre, and re its apparent susceptibility, the force in the direction x is f= K'VH X dH/dx; and if K',, and are the apparent susceptibilities of the same ball in air and in liquid oxygen, K' Q -K'o is equal to the difference between the susceptibilities of the two media.

    0
    0
  • The strength of the induced current is - HScosO/L, where 0 is the inclination of the axis of the circuit to the direction of the field, and L the coefficient of self-induction; the resolved part of the magnetic moment in the direction of the field is equal to - HS 2 cos 2 6/L, and if there are n molecules in a unit of volume, their axes being distributed indifferently in all directions, the magnetization of the substance will be-3nHS 2 /L, and its susceptibility - 3S 2 /L (Maxwell, Electricity and Magnetism, § 838).

    0
    0
  • The mass of each is about 3 7 1 o T th part of that of a hydrogen atom, and with each is indissolubly associated a charge of negative electricity equal to about 3.1 Xio '° C.G.S.

    0
    0
  • In particular, he found that the calculated velocity with which it transmitted electromagnetic disturbances was equal to the observed velocity of light; hence he was led to believe, not only that his medium and the ether were one and the same, but, further, that light itself was an electromagnetic phenomenon.

    0
    0
  • He was lodged in `the Louvre, received the grant of an income equal to that he had hitherto enjoyed, and, with the title of "veteran pensioner" in lieu of that of "foreign associate" (conferred in 1772), the right of voting at the deliberations of the Academy.

    0
    0
  • It is equal to the actual diameter of the cylinder of rays admitted by a telescope.

    0
    0
  • The literary history of Siena, while recording no gifts to the world equal to those bequeathed by Florence, and without the power and originality by which the latter became the centre of Italian culture, can nevertheless boast of some illustrious names.

    0
    0
  • The subdeacons, no doubt, became a necessity when the deacons, whose number was limited to seven in memory of their original institution, were no longer equal to their duties in the " regions " of the imperial city, and left their lower work, such as preparation of the sacred vessels, to their subordinates.

    0
    0
  • Pre-Cape Rocks principally the yellow wood (Podocarpus)., sneezewood (Pteroxylon utile), stinkwood (Oreodaphne bullata), black ironwood (Olea laurifolia), white ironwood (Vepris lanceolata), and umtomboti (Exoecaria africana); all are very useful woods, and the yellow wood, sneezewood, stinkwood and ironwood when polished have grain and colour equal to maple, walnut and ebony.

    0
    0
  • Seven flous are regarded as equal to the French five-centime piece.

    0
    0
  • To say, for instance, that X is equal to A -B, is the same thing as to say that X is a quantity such that X and B, when added, make up A; and the above five statements of necessary connexion between two statements of equality are in fact nothing more than definitions of the symbols -, m of, =,, and loga.

    0
    0
  • We can, however, find a number whose square shall be as nearly equal to 5 as we please, and it is this number that we treat arithmetically as 1 15.

    0
    0
  • We find that the product a m X a m X a m is equal to a im; and, by definition, the product; /a X -la X Ala is equal to a, which is a'.

    0
    0
  • We take a fixed line OX, usually drawn horizontally; for each value of X we measure a length or abscissa ON equal to x.L, and draw an ordinate NP at right angles to OX and equal to the corresponding value of y .

    0
    0
  • (i.) To divide P by Q, we cut off from P successive portions each equal to Q, till we have a piece R left which is less than Q.

    0
    0
  • r= io, we get the ordinary expression of P/Q as an integer and a decimal; but, if P/Q were equal to 1/3, we could not express it as a decimal with a finite number of figures.

    0
    0
  • we cut off from Q successive portions each equal to R.

    0
    0
  • (iv.) If P and Q can be expressed in the forms pL and qL, where p and q are integers, R will be equal to (p-kq)L, which is both less than pL and less than qL.

    0
    0
  • (ii.) By means of the commutative law we can collect like terms of a monomial, numbers being regarded as like terms. Thus the above expression is equal to 6a 5 bc 2, which is, of course, equal to other expressions, such as 6ba 5 c 2.

    0
    0
  • Thus 2 x 2 - I - x +x-2 (x _ I) (x+2) is equal to x + 2 q, except when x=1.

    0
    0
  • Then (y), the coefficient - of A n - r a r in the expansion of (A+a)", is equal to (n-i)(0+ (r_l).

    0
    0
  • We know that (A+a)" is equal to a multinomial of n+I terms with unknown coefficients, and we require to find these coefficients.

    0
    0
  • In this table any number is equal to the sum of the numbers which lie horizontally above it in the preceding Column, And The Difference Of Any Two Numbers In A Column Is Equal To The Sum Of The Numbers Horizontally Between Them In The Preceding Column.

    0
    0
  • (ii.) In the same way, if we multiply the table by c, the sum of the first n numbers in any column is equal to the nth number in the next following column.

    0
    0
  • We want to express (23/13) 3 in the form a l b, where b is nearly equal to i.

    0
    0
  • We cannot, for instance, say that the fraction C _2 I is arithmetically equal to x+I when x= I, as well as for other values of x; but we can say that the limit of the ratio of x 2 - I to x - I when x becomes indefinitely nearly equal to I is the same as the limit of x+ On the other hand, if f(y) has a definite and finite value for y = x, it must not be supposed that this is necessarily the same as the limit which f (y) approaches when y approaches the value x, though this is the case with the functions with which we are usually concerned.

    0
    0
  • We know that log l oN(I+9) = log l oN+log 10 (I+0), and inspection of a table of logarithms shows that, when 0 is small, log 10 (I+B);s approximately equal to X0, where X is a certain constant, whose value is.

    0
    0
  • is approximately equal to -J(27rn).(nle) n; the approximation may be improved by Stirling's theorem log e 2 +log e 3 +...

    0
    0
  • We imagine a wave-front divided o x Q into elementary rings or zones - often named after Huygens, but better after Fresnelby spheres described round P (the point at which the aggregate effect is to be estimated), the first sphere, touching the plane at 0, with a radius equal to PO, and the succeeding spheres with radii increasing at each step by IX.

    0
    0
  • For the aggregate effect of the secondary waves is the half of that of the first Fresnel zone, and it is the central element only of that zone for which the distance to be travelled is equal to r.

    0
    0
  • The middle element alone contributes without deduction; the effect of every other must be found by introduction of a resolving factor, equal to cos 0, if 0 represent the difference of phase between this element and the resultant.

    0
    0
  • In the applications with which we are concerned, t, n are very small quantities; and we may take P = x yn - At the same time dS may be identified with dxdy, and in the de nominator p may be treated as constant and equal to f.

    0
    0
  • By the principle of energy the illumination over the entire focal plane must be equal to that over the diffracting area; and thus, in accordance with the suppositions by which (3) was obtained, its value when integrated from E= co to = -1-x, and from n = - oo to n = -1-oo should be equal to ab.

    0
    0
  • We conclude that a double line cannot be fairly resolved unless its components subtend an angle exceeding that subtended by the wave-length of light at a distance equal to the horizontal aperture.

    0
    0
  • If the angle subtended by the components of a double line be twice that subtended by the wave-length at a distance equal to the horizontal aperture, the central bands are just clear of one another, and there is a line of absolute blackness in the middle of the combined images.

    0
    0
  • It has already been suggested that the principle of energy requires that the general expression for I 2 in (2) when integrated over the whole of the plane, n should be equal to A, where A is the area of the aperture.

    0
    0
  • Analytically expressed ff+ co x I 2 d dn=ff dxdy= A (9) We have seen that Io (the intensity at the focal point) was equal to A 2 /X 2 f2.

    0
    0
  • 12 -7r2R4 x2 f 2 The roots of Jo(z) after the first may be found from We may compare this with the corresponding result for a rectangular aperture of width a, tlf = X/a; and it appears that in consequence of the preponderance of the central parts, the compensation in the case of the circle does not set in at so small an obliquity as when the circle is replaced by a rectangular aperture, whose side is equal to the diameter of the circle.

    0
    0
  • If the angular interval between the components of a double star were equal to twice that expressed in equation (15) above, the central disks of the diffraction patterns would be just in contact.

    0
    0
  • Verdet has compared Foucault's results with theory, and has drawn the conclusion that the radius of the visible part of the image of a luminous point was equal to half the radius of the first dark ring.

    0
    0
  • Observed through this the structure of some wire gauze just disappeared at a distance from the eye equal to 17 in., the gauze containing 46 meshes to the inch.

    0
    0
  • In the case of a single lens of glass with the most favourable curvatures, Sf is about equal to a 2 f, so that a 4 must not exceed off.

    0
    0
  • For the alteration of wave-length entails, at the two limits of a diffracted wave-front, a relative retardation equal to mndX.

    0
    0
  • Then, if Q be any radiant point and Q' its image (primary focus) in the spherical mirror AP, we have 1 1 2cos4) v l + u 'a ' ' where v 1 = AQ', u =AQ, a =OA, =angle of incidence QAO, equal to the angle of reflection Q'AO.

    0
    0
  • In the present application 4' is not necessarily equal to; but if P correspond to a line upon the grating, the difference of retardations for consecutive positions of P, so far as expressed by the term of the first order, will be equal to mX (m integral), and therefore without influence, provided v (sin 0-sin0') = nzX (11), where a denotes the constant interval between the planes containing the lines.

    0
    0
  • 17 APQ is the arc of the circle representative of the wavefront of resolution, the centre being at 0, and the radius OA being equal to a.

    0
    0
  • When the secondary disturbance thus obtained is integrated with respect to dS over the entire plane of the lamina, the result is necessarily the same as would have been obtained had the primary wave been supposed to pass on without resolution, for this is precisely the motion generated when every element of the lamina vibrates with a common motion, equal to that attributed to dS.

    0
    0
  • Retaining only the real part of (16), we find, as the result of a local application of force equal to DTZ cos nt (17), the disturbance expressed by TZ sin 4, cos(nt - kr) ?

    0
    0
  • The force operative upon the positive half is parallel to OZ, and of amount per unit of area equal to - b 2 D = b 2 kD cos nt; and to this force acting over the whole of the plane the actual motion on the positive side may be conceived to be due.

    0
    0
  • According to (18), the effect of the force acting at dS parallel to OZ, and of amount equal to 2b2kD dS cos nt, will be a disturbance - dS sin cos (nt - kr) (20), regard being had to (12).

    0
    0
  • It may be readily deduced that the directions of minimum deviation for a pencil of parallel rays lie on the surface of cones, the semi-vertical angles of which are equal to the values given in the above table.

    0
    0
  • It is apparent, therefore, that all drops transmitting intense light after one internal reflection to the eye will lie on the surfaces of cones having the eye for their common vertex, the line joining the eye to the sun for their axis, and their semi-vertical angles equal to about 41° for the violet rays and 43° for the red rays.

    0
    0
  • The upper edge was folded over for a distance equal to the space from neck to waist - this folded portion was called Ior67rTV^y ua or &71-XotS, - and the whole garment was then doubled and wrapped round the body below the armpits, the left side being closed and the right open.

    0
    0
  • to the east and thus made himself numerically equal to his enemy, but elsewhere left barely 45,000 men to oppose 150,000.

    0
    0
  • To do so a general enlargement takes place until it may reach the size and weight equal to the original pair.

    0
    0
  • Welch produced oedema of the lungs experimentally by increasing the pressure in the pulmonary vessels by ligature of the aorta and its branches, but this raised the blood pressure only about one-tenth of an atmosphere, while in some of Loeb's experiments the osmotic pressure, due to retained metabolic products, was equal to over thirty atmospheres.

    0
    0
  • Some other observers, however, have not got such good results with a chloride-free diet, and Marishler, Scheel, Limbecx, Dreser and others, dispute Widal's hypothesis of a retention of chlorides as being the cause of oedema, in the case of renal dropsy at all events; they assert that the chlorides are held back in order to keep the osmotic pressure of the fluid, which they assume to have been effused, equal to that of the blood and tissues.

    0
    0
  • If a point be in motion in any orbit and with any velocity, and if, at each instant, a line be drawn from a fixed point parallel and equal to the velocity of the moving point at that instant, the extremities of these lines will lie on a curve called the hodograph.

    0
    0
  • This became all the more apparent as his own health failed during 1907; for, though he was obliged to leave much of the leadership in the Commons to Mr Asquith, his possible resignation of the premiership was strongly deprecated; and even after November, when it became clear that his health was not equal to active work, four or five months elapsed before the necessary change became a fait accompli.

    0
    0
  • Io,680 Local Government Board-Common Poor Fund 756 £24,703,087 The total expenditure was equal to a rate in the pound of s.

    0
    0
  • Grades are made, whenever possible, in favour of the load, and of such degree that the power required to haul out the loaded cars shall be approximately equal to that for hauling back the empties, viz.

    0
    0
  • This resistance is equal to the square of the velocity of the current in feet per minute, Air.

    0
    0
  • The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.

    0
    0
  • The blower then heats the end of the cylinder again and rapidly spins the pipe about its axis; the centrifugal effect is sufficient to spread the soft glass at the end to a radius equal to that of the rest of the cylinder.

    0
    0
  • of Spain for permission to make glasses, vases and cups of fine crystal, equal to those of Venice, but to be sold at one-third less than Venetian glasses.

    0
    0
  • Marineus Siculus, writing early in the 16th century, says that the best glass was made at Barcelona; and Gaspar Baneiros, in his Chronographia, published in 1562, states that the glass made at Barcelona was almost equal to that of Venice and that large quantities were exported.

    0
    0
  • When the results of this theory were compared with the quantity of water actually discharged, Newton concluded that the velocity with which the water issued from the orifice was equal to that which a falling body would receive by descending through half the height of water in the reservoir.

    0
    0
  • - A body immersed in a fluid is buoyed up by a force equal to the weight of the liquid displaced, acting vertically upward through the centre of gravity of the displaced liquid.

    0
    0
  • For if the body is removed, and replaced by the fluid as at first, this fluid is in equilibrium under its own weight and the thrust of the surrounding fluid, which must be equal and opposite, and the surrounding fluid acts in the same manner when the body replaces the displaced fluid again; so that the resultant thrust of the fluid acts vertically upward through the centre of gravity of the fluid displaced, and is equal to the weight.

    0
    0
  • When the body is floating freely like a ship, the equilibrium of this liquid thrust with the weight of the ship requires that the weight of water displaced is equal to the weight of the ship and the two centres of gravity are in the same vertical line.

    0
    0
  • (ii.) the weight of liquid which the body displaces in the position of equilibrium is equal to the weight W of the body; and (iii.) the C.G., B, of the liquid displaced and G of the body, must lie in the same vertical line GB.

    0
    0
  • of the fluid, equal to the weight vertically upward through the movement of a weight P through a distance c will cause the ship to heel through an angle 0 about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a 2 -hV/A, b 2 - hV/A, (I) h denoting the vertical height BG between C.G.

    0
    0
  • (16) Along the path of a liquid particle 4)' is constant, and putting it equal to 2Uc2, (r 2 - a 3 /r) sin 2 0 = c 2, sin 2 0 = c2r/(r3 - a3), (17) the polar equation; or y 2 = c2r3/(r3 - a 3), r3 = a3y2 /(y2._ c2), (18) a curve of the 10th degree (C10).

    0
    0
  • ,In a fluid, the circulation round an elementary area dxdy is equal to dv du udx + (v+dx) dy- (u+dy) dx-vdy= () dxdy, so that the component spin is dv du (5) 2 dx - dy) in the previous notation of § 24; so also for the other two components and n.

    0
    0
  • The stream lines xBAJ, xA'J' are given by = 0, m; so that if c denotes the ultimate breadth JJ' of the jet, where the velocity may be supposed uniform and equal to the skin velocity Q, m=Qc, c=m/Q.

    0
    0
  • The continuity is secured if the liquid between two ellipsoids X and X 11 moving with the velocity U and 15 1 of equation (II), is squeezed out or sucked in across the plane x=o at a rate equal to the integral flow of the velocity I across the annular area a l.

    0
    0
  • The canes in each case are assumed to contain 88% of juice and 12% of fibre, and the extraction by milling to be 75% of the weight of canes - the evaporative power of the factory being equal to 622 tons per 24 hours.

    0
    0
  • Whatever pressure be brought to bear upon it, the vegetable or woody fibre of crushed sugar-canes will hold and retain for the from moment a quantity of moisture equal to its own weight, Yield .

    0
    0
  • The megass coming from the first mill was saturated with steam and water, in weight equal to between 20% and 30% and up to 40% of the original weight of the uncrushed canes.

    0
    0
  • But the great achievement of recent manufacture is the production, without the use of animal charcoal, of a cheaper, but good and wholesome article, in appearance equal to refined sugar for all intents and purposes, except for making preserves of fruits in the old-fashioned way.

    0
    0
  • The firstmentioned process consists of charging and feeding the vacuum pan with the richest syrup, and then as the crystals form and this syrup becomes thereby less rich the'pan is fed with syrup of lower richness, but still of a richness equal to that of the mother-liquor to which it is added, and so on until but little mother-liquor is left, and that of the poorest quality.

    0
    0
  • It would appear that the purchasing power of the inhabitants of India has increased of late years, and there is a growing demand for refined sugar, fostered by the circumstance that modern processes of manufacture can make a quality of sugar, broadly speaking, equal to sugar refined by animal charcoal, without using charcoal, and so the religious objections to the refined sugars of old days have been overcome.

    0
    0
  • For warmth, for dryness, for absence of fog, and for facility of walking after rain, just when the air is at its purest and its best, there is nothing equal to gravel; but when gravel has been rendered foul by infiltration with organic matters it may easily become a very hotbed of disease.

    0
    0
  • It forms colourless, transparent rhombohedra, like those of Iceland spar; the angles are nearly equal to right angles, being 73° 30', so that the crystals look like cubes: hence the name of "cubic saltpetre."

    0
    0
  • In other machines a roll of narrow paper, in width equal to the circumference of the cigarette, is converted into a long tube, filled with tobacco, and automatically cut off into proper lengths.

    0
    0
  • A further condition was enacted that an indemnity of 10,000,000 soles was to be paid by the country finally remaining in possession - a sum equal to about L1,000,000 to-day.

    0
    0
  • But the Army of the Tennessee had been on the verge of annihilation on the evening of the first day, and Grant's leadership throughout was by no means equal to the emergency, though he displayed his usual personal bravery and resolution.

    0
    0
  • Grant possessed or acquired both to such a degree that he proved fully equal to the emergency.

    0
    0
  • She seemed to consider Swedish affairs as far too petty to occupy her full attention; while her unworthy treatment of the great chancellor was mainly due to her jealousy of his extraordinary reputation and to the uneasy conviction that, so long as he was alive, his influence must at least be equal to her own.

    0
    0
  • In the critical situation after the battle of Pavia (1525) she proved herself equal to the emergency, maintained order in the kingdom, and manoeuvred very skilfully to detach Henry VIII.

    0
    0
  • In its speculative parts the book is quite equal to those that had gone before, but in its literary and historical parts there are indications of a mind in which a longpractised logic had become a rooted habit.

    0
    0
  • The skill developed in modern times is at inia in least equal to anything which the past can show, and ~ the results produced are much more imposing.

    0
    0
  • Joun has produced, and is thorou~hly capable of producing, bronzes at least equal to the best of Seimin s masterpieces, yet he has often been induced to put Seimins name on objects for the sake of attracting buyers who attach more value to cachet than to quality.

    0
    0
  • The Hirado expert has not yet attained technical skill equal to that of the Chinese.

    0
    0
  • The actual purchase price of the 17 lines was calculated at 43 millions sterling (about double their cost price), on the following basis: (a) An amount equal to 20 times the sum obtained by multiplying the cost of construction at the date of purchase by the average ratio of the profit to the cost of construction during the six business terms of the company from the second half-year of 1902 to the first half-year of 1905.

    0
    0
  • In addition, taking advantage of the accuracy with which the bolometer can determine the position of a source of heat by which it is affected, he mapped out in this infra-red spectrum over 700 dark lines or bands resembling the Fraunhofer lines of the visible spectrum, with a probable accuracy equal to that of refined astronomical observations.

    0
    0
  • It is probable that Defoe, with his extensive acquaintance with English history, and his astonishing power of working up details, was fully equal to the task of inventing it.

    0
    0
  • But a great part of the book, especially the latter portion, is dull; and in fact it may be generally remarked of Defoe that the conclusions of his tales are not equal to the beginning, perhaps from the restless indefatigability with which he undertook one work almost before finishing another.

    0
    0
  • over so-called allies who were strangers to the old pan-Ionian assembly and to the policy of the league, and was practically equal to Sparta on land.

    0
    0
  • The unit of mechanical force in the " centimetre, gramme, second " (C.G.S.) system of units is the dyne, which is approximately equal to 1/981 part of the weight of one gramme.

    0
    0
  • If the two small conducting spheres are placed with centres at a distance d centimetres, and immersed in an insulator of dielectric constant K, and carry charges of Q and Q' electrostatic units respectively, measured as above described, then the mechanical force between them is equal to QQ'/Kd 2 dynes.

    0
    0
  • If a small conducting body is charged with Q electrostatic units of electricity, and placed in any electric field at a point where the electric force has a value E, it will be subject to a mechanical force equal to QE dynes, tending to move it in the direction of the resultant electric force.

    0
    0
  • In the same manner, if an electrified body carries a positive charge Q electrostatic units and is placed in an electric field at a place where the electric force or electromotive intensity has a value E units, it is urged in the direction of the electric force with a mechanical force equal to QE dynes.

    0
    0
  • Accordingly the number of electric cells into which the space round is cut up is equal to twice the energy stored up, or each cell contains half a unit of energy.

    0
    0
  • The solid angles subtended by all normal sections of a cone at the vertex are therefore equal, and since the attractions of these sections on a particle at the vertex are proportional to their distances from the vertex, they are numerically equal to one another and to the solid angle of the cone.

    0
    0
  • Another corollary of the fact that there is no electric force in the interior of a charged conductor is that the potential in the interior is constant and equal to that at the surface.

    0
    0
  • Hence when the ball is touched against the inside of the canister before withdrawing it a second time, the fact that the system is found subsequently to be completely discharged proves that the charge - Q induced on the inside of the canister must be exactly equal to the charge +Q on the ball, and also that the inducing action of the charge -{-Q on the ball created equal quantities of electricity of opposite sign, one drawn to the inside and the other repelled to the outside of the canister.

    0
    0
  • Since the potential of a small charge of electricity dQ at a distance r is equal to dQ/r, and since the potential of all parts of a conductor is the same in those cases in which the distribution of surface density of electrification is uniform or symmetrical with respect to some point or axis in the conductor, we can calculate the potential by simply summing up terms like rdS/r, where dS is an element of surface, o- the surface density of electricity on it, and r the distance from the symmetrical centre.

    0
    0
  • Then consider a thin annulus thin of the wire of width dx; the charge on it is equal to thin rod.

    0
    0
  • This mass is equal to 47rabcp,u; therefore Q = A47rabcp s and b =pp, where p is the length of the perpendicular let fall from the centre of the ellipsoid on the tangent plane.

    0
    0
  • We have then a very important theorem as follows: - If any closed surface be described in an electric field which wholly encloses or wholly excludes electrified bodies, then the total flux through this surface is equal to 47r - times the total quantity of electricity within it.'

    0
    0
  • The normal section of the cone at that point is equal to dS cosO, and the solid angle dw is equal to dS cos0/x 2.

    0
    0
  • Then if we have any number of sources enclosed by any surface, the total flow per second through this surface is equal to the total strengths of all the sources.

    0
    0
  • Hence the total flux is - (+ d2V d 2 V d2V dye + dz2) dy dz, dx2 and by the previous theorem this must be equal to 4'rrp dxdydz.

    0
    0
  • Hence the total flux through the surface considered is - {(dV i /dn l)-}-(dV 2 /dn 2)}dS, and this by a previous theorem must be equal to 47radS, or the total included electric quantity.

    0
    0
  • Hence if dS and dS' are the areas of the ends, and +E and - E' the oppositely directed electric forces at the ends of the tube, the surface integral of normal force on the flux over the tube is EdS - E'dS' (20), and this by the theorem already given is equal to zero, since the tube includes no electricity.

    0
    0
  • The above is a statement of Coulomb's law, that the electric fores at the surface of a conductor is proportional to the surface density of the charge at that point and equal to 41r times the density.3 See Maxwell, Electricity and Magnetism, vol.

    0
    0
  • Every tube of electric force must therefore begin and end on electrified surfaces of opposite sign, and the quantities of positive and negative electricity on its two ends are equal, since the force E just outside an electrified surface is normal to it and equal to a/41r, where a is the surface density; and since we have just proved that for the ends of a tube of force EdS = E 1 dS', it follows that adS = a'dS', or Q = Q', where Q and Q' are the quantities of electricity on the ends of the tube of force.

    0
    0
  • Since the potential rises proportionately to the quantity in the conductor, the ends of these ordinates will lie on a straight line and define a triangle whose base line is a length equal to the total quantity Q and V height a length equal to the final potential V.

    0
    0
  • This can be done by placing at B an equal negative point-charge -q in the place which would be occupied by the optical image of A if PO were a mirror, that is, let -q be placed at B, so that the distance BO is equal to the distance AO, whilst AOB is at right angles to PO.

    0
    0
  • Then the potential at any point P in this ideal plane PO is equal to q/AP-q/BP=0, whilst the resultant force at P due to the two point charges is 2gAO/AP 3, and is parallel to AB or normal to PO.

    0
    0
  • As the temperature 0" is lowered, the area of the cycle increases, but since W can never exceed H', there must be a zero limit of temperature at which the pressure would vanish and the area of the cycle become equal to the whole heat absorbed at the higher temperature.

    0
    0
  • Combining this with the first law, for a Carnot cycle of finite range, if H is the heat taken in at 0', and H" is the heat rejected at 0", the work W done in the cycle is equal to the difference H' - H", and we have the simple relations, W/(0' - o") =H'/o' =H" o".

    0
    0
  • of temperature (o' - o") is small, the figure ABCD may be regarded as a parallelogram, and its area W as equal to the rectangle BE XEC. This is accurately true in the limit when (0' - 0") is infinitesimal, but in practice it is necessary to measure specific heats, &c., over finite ranges of temperature, and the error involved is generally negligible if the range does not exceed a few degrees.

    0
    0
  • (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.

    0
    0
  • (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.

    0
    0
  • Finally, the substance is reconverted into the first state at the temperature 0", completing the cycle by the abstraction of a quantity of heat By the application of the first law, the difference of the quantities of heat absorbed and evolved in the cycle must be equal to the work represented by the area of the cycle, which is equal to (p' - p") (v" - v') in the limit when the difference of pressure is small.

    0
    0
  • By the application of the second law, relations (2), the same work area is equal to (o' - o")L'lo'.

    0
    0
  • The whole quantity of heat required to raise the temperature from 0" to 0' at constant pressure along the path EC is H+h, which is equal to S(0' - o"), where S is the specific heat at constant pressure.

    0
    0
  • Since the amounts of heat supplied at constant pressure from E to F and from E to C are in the limit proportional to the expansions EF and EC which they produce, the ratio S/s is equal to the ratio ECÆF.

    0
    0
  • (I I) This expression shows that the rate of variation of the total heat with temperature at constant pressure is equal to the specific heat at constant pressure.

    0
    0
  • To find the total heat of a substance in any given state defined by the values of p and 0, starting from any convenient zero of temperature, it is sufficient to measure the total heat required to raise the substance to the final temperature under a constant pressure equal to p. For instance, in the boiler of a steam engine the feed water is pumped into the boiler against the final pressure of the steam, and is heated under this constant pressure up to the temperature of the steam.

    0
    0
  • Observing that F is a function of the co-ordinates expressing the state of the substance, we obtain for the variation of S with pressure at constant temperature, dS/dp (0 const) '=' 2 F/dedp =-0d 2 v/d0 2 (p const) (12) If the heat supplied to a substance which is expanding reversibly and doing external work, pdv, is equal to the external work done, the intrinsic energy, E, remains constant.

    0
    0
  • (13) If, on the other hand, the heat supplied is equal to - vdp, we see from (I I) that F remains constant.

    0
    0
  • The coefficient of expansion at constant pressure is equal to the coefficient of increase of pressure at constant volume.

    0
    0
  • The difference of the specific heats by equation (6) is constant and equal to R.

    0
    0
  • The isothermal elasticity - v(dp/dv) is equal to the pressure p. The adiabatic elasticity is equal to y p, where -y is the ratio S/s of the specific heats.

    0
    0
  • The heat absorbed in isothermal expansion from vo to v at a temperature 0 is equal to the work done by equation (8) (since d0 =o, and 0(dp/d0)dv =pdv), and both are given by the expression RO log e (v/vo).

    0
    0
  • Under this condition the increase of intrinsic energy would be equal to the heat absorbed, and would be indicated by fall of temperature of the calorimeter.

    0
    0
  • (18) Experiments at two temperatures suffice to determine both c and n if we assume that b is equal to the volume of the liquid.

    0
    0
  • The energy is less than that of an ideal gas by the term npc. If we imagine that the defect of volume c is due to the formation of molecular aggregates consisting of two or more single molecules, and if the kinetic energy of translation of any one of these aggregates is equal to that of one of the single molecules, it is clear that some energy must be lost in co-aggregating, but that the proportion lost will be different for different types of molecules and also for different types of co-aggregation.

    0
    0
  • In any small reversible change in which the substance absorbs heat, dH, from external sources, the increase of entropy, d0, must be equal to dH/9.

    0
    0
  • If the change is not reversible, but the final state is the same, the change of entropy, do, is the same, but it is no longer equal to dII/B.

    0
    0
  • The increment of 00 is always greater than that of the total heat F=E+pv, except in the special case of an equilibrium change at constant temperature and pressure, in which case both are equal to the heat absorbed in the change, and the function G remains constant.

    0
    0
  • If 0', E', v'; and 4)", E", v", refer to unit mass of the substance in the first and second states respectively in equilibrium at a temperature 0 and pressure p, the heat absorbed, L, per unit mass in a change from the first to the second state is, by definition of the entropy, equal to 0(4)"-4)'), and this by the first law is equal to the change of intrinsic energy, E" - E', plus the external work done, p(v" - v'), i.e.

    0
    0
  • His tact was equal to his learning.

    0
    0
  • Brazil has had a large immigration (in 1895 equal to 169,524, but in 1904 only 12,447).

    0
    0
  • It had been suggested, and Bohr had adopted this view, that the nuclear charge was equal to the atomic number, i.e.

    0
    0
  • When the event in question happened between the 1st of January and the 1st of the following July, the sum of the Olympic year and of the year before Christ is always equal to 776.

    0
    0
  • When the event took place between the summer solstice and the 1st of January following, the sum of the Olympic year and of theyear before Christ is equal to 777.

    0
    0
  • Initiated from childhood in all the arts of diplomacy at what was then the focus of civilization, and as much a warrior by nature as his imperial kinsman Manuel, Bela showed himself from the first fully equal to all the difficulties of his peculiar position.

    0
    0
  • The brain-cavity was extremely small, and insignificant in comparison to the bodily bulk, which was equal to that of the largest rhinoceroses.

    0
    0
  • The advance continued to Colmar, where the elector, who was now in command of the Germans, stood on the defensive with forces equal to Turenne's own.

    0
    0
  • The difference in the weights corresponds to the volume of gas at a pressure equal to the difference of the recorded pressures.

    0
    0
  • Hydro- statical principles can be applied to density determinations in four typical ways: (I) depending upon the fact that the heights of liquid columns supported by the same pressure vary inversely as the densities of the liquids; (2) depending upon the fact that a body which sinks in a liquid loses a weight equal to the weight of liquid which it displaces; (3) depending on the fact that a body remains suspended, neither floating nor sinking, in a liquid of exactly the same density; (4) depending on the fact that a floating body is immersed to such an extent that the weight of the fluid displaced equals the weight of the body.

    0
    0
  • the weight of a volume of water equal to that of the solid.

    0
    0
  • For this purpose the position angle of the eye-piece micrometer is set to that of the head, and the eye-piece is displaced from the axis of the tube (in the direction of the movable segment) by an amount equal to half the angle under measurement.

    0
    0
  • The eye-piece is fixed in the axis, and the segments are symmetrically displaced from the axis each by an amount equal to half the angle measured.

    0
    0
  • On the other hand it is not necessary to reset the telescope after each reversal of the segments.4 When Bessel ordered the Konigsberg heliometer, he was anxious to have the segments made to move in cylindrical slides, of which the radius should be equal to the focal length of the object-glass.

    0
    0
  • " the introduction of a diaphragm having two circular apertures touching each other in a point coinciding with the line of collimation of the telescope, and the diameter of each aperture exactly equal to the semidiameter of the cone of rays at the distance of the diaphragm from the focal point of the object-glass."

    0
    0
  • If this estimate is correct there exists dissolved in the ocean a quantity of silver equal to T3,300 million metric tons, that is to say 46,700 times as much silver as has been produced from all the mines in the world from the discovery of America down to 1902.

    0
    0
  • In the oldest form of this class of working, where the size of the pillar is equal to the width of the stall or excavation, about 4 of the whole seam will be removed, the remainder being left in the pillars.

    0
    0
  • The carrying frame, while the work is going on, is fixed in position by jackscrews bearing against the roof of the seam, which, when the cut is completed, are withdrawn, and the machine shifted laterally through a distance equal to the breadth of the cut and fixed in position again.

    0
    0
  • Water-pressure engines, driven by a column of water equal to the depth of the pit, have also been employed for hauling.

    0
    0
  • reduced up to the point of final discharge into the atmosphere, whereby a greater useful effect is realized than is the case when the air streams freely from the circumference with a velocity equal to that of the rotating fan.

    0
    0
  • For flat ropes the drum or bobbin consists of a solid disk, of the width of the rope fixed upon the shaft, with numerous parallel pairs of arms or horns, arranged radially on both sides, the space between being just sufficient to allow the rope to enter and coil regularly upon the preceding lap. This method has the advantage of equalizing the work of the engine throughout the journey, for when the load is greatest, with the full cage at the bottom and the whole length of rope out, the duty required in the first revolution of the engine is measured by the length of the smallest circumference; while the assistance derived from gravitating action of the descending cage in the same period is equal to the weight of the falling mass through a height corresponding to the length of the largest lap, and so on, the speed being increased as the weight diminishes, and vice versa.

    0
    0
  • In some cases, therefore, a combined form is adopted, the body of the drum being cylindrical, and a width equal to three or four laps conical on either side.

    0
    0
  • He had much bf the Arab nature, was singularly temperate, and equal to any amount of fatigue.

    0
    0
  • The general theory of this kind of brake is as follows: - Let F be the whole frictional resistance, r the common radius of the rubbing surfaces, W the force which holds the brake from turning and whose line of action is at a perpendicular distance R from the axis of the shaft, N the revolutions of the shaft per minute, co its angular velocity in radians per second; then, assuming that the adjustments are made so that the engine runs steadily at a uniform speed, and that the brake is held still, clear of the stops and without oscillation, by W, the torque T exerted by the engine is equal to the frictional torque Fr acting at the brake surfaces, and this is measured by the statical moment of the weight W about the axis of revolution; that is T =Fr=WR...

    0
    0
  • Under the laws of Iowa a wife enjoys property rights equal to those of her husband.

    0
    0
  • When a stage is reached such that the number of molecules lost to the liquid by evaporation is exactly equal to that regained by condensation, we have a liquid in equilibrium with its own vapour.

    0
    0
  • dpndgn, and therefore equal to the initial extension.

    0
    0
  • Let the whole energy E of the system be supposed equal to Ei+E2, where E2 is of the form E2 = ?

    0
    0
  • If each of the fractions (3) is put equal to i/4h, it is readily found, from the first property of the normal state, that, of the s molecules of the first kind, a number sal (h3m3 /13)e hm (u2+v2+w2)dudvdw (4) Velocities.

    0
    0
  • Each of the molecules enumerated in expression (9) will move parallel to the edge of this cylinder, and each will describe a length equal to its edge in time dt.

    0
    0
  • Each impinging molecule exerts an impulsive pressure equal to mu on the boundary before the component of velocity of its centre of gravity normal to the boundary is reduced to zero.

    0
    0
  • There are many thousands of lines in the mercury spectrum, so that from this evidence it would appear that for mercury vapour n ought to be very great, and y almost equal to unity.

    0
    0
  • From Dulong and Petit's law that Cm is the same for all elements, it follows that n+3 must be the same for all atoms. Moreover, the value of Cm shows that n+3 must be equal to six.

    0
    0
  • His answer was always found equal to the questioner.

    0
    0
  • At times he showed qualities as a guerillero quite equal to those of the Carlists, like Zumalacarregui and Cabrera, by his daring marches and surprises.

    0
    0
  • In the lower margin of the page he inserted a selection of various readings, the relative importance of which he denoted by the first five letters of the Greek alphabet in the following manner: - a was employed to denote the reading which in his judgment was the true one, although he did not venture to place it in the text; 1 3, a reading better than that in the text; y, one equal to the textual reading; S and e, readings inferior to those in the text.

    0
    0
  • The fact that the interior angles of all triangles are equal to two right angles is not part of the definition, but is universally true.

    0
    0
  • In the intervening period the assessed valuation of realty in Boston increased more than 100%, while that of personalty slightly diminished (the corresponding figures for the entire United States from 1860 to 1890 being 172% and 12%), yet the most competent business and expert opinions regarded the true value of personalty as at least equal to and most likely twice as great as that of realty.

    0
    0
  • i it will be seen that in order to strike T the axis must be directed to G' at a height above T equal to TG, while the line of sight or line joining the notch of the tangent sight and apex of the dispart or foresight must be (/ ?` directed on T.

    0
    0
  • The drum is divided into loo graduations, each equal to 5.4'.

    0
    0
  • In purity of race the Aragonese are probably equal to the Castilians, to whom, rather than to the Catalans or Valencians, they are also allied in character.

    0
    0
  • His admiral Margarito, a naval genius equal to George of Antioch, with 600 vessels kept the eastern Mediterranean open for the Franks, and forced the all-victorious Saladin to retire from before Tripoli in the spring of 1188.

    0
    0
  • The sepals and petals are free or more or less united, the stamens as many or twice as many as the petals; the carpels, usually free, are equal to the petals in number, and form in the fruit follicles with two or more seeds.

    0
    0
  • On the other hand, it is worth noticing that the words " quadrature " and " cubature " are originally due to geometrical rather than numerical considerations; the former implying the construction of a square whose area shall be equal to that of a given surface, and the latter the construction of a cube whose volume shall be equal to that of a given solid.

    0
    0
  • That the area of a parallelogram is equal to the area of a rectangle on the same base and between the same parallels, or that the volume of a cone is one-third that of a cylinder on the same base and of the same height, may be established by a proof which is admitted to be rigorous, or be accepted in good faith without proof, and yet fail to be a matter of conviction, even though there may be a clear conception of the relative lengths of the diagonal and the side of a square or of the relative contents of two vessels of different shapes.

    0
    0
  • Then MA'B'N is a right trapezium, whose area is equal to that of Cabd; and it is related to the latter in such a way that, if any two lines parallel to AC and BD meet AB, CD, MN, A'B', in E, G, P, E', and F, H, Q, F', respectively, the area of the piece PE'F'Q of the right trapezium 'B.

    0
    0
  • is equal to the area of the piece Gefh of the original,; trapezium.

    0
    0
  • Then, if we take ordinates Kb, Lg, Mc, Nd, Pf, equal to B'B, GG', C'C, D'D, FF', the figure abgcdfe will be the equivalent trapezoid, and any ordinate drawn from the base to the a LM N P e X top of this trapezoid will be equal to the portion of this ordinate (produced) which falls within the original figure.

    0
    0
  • The volume is therefore equal to S.

    0
    0
  • These two theorems may be stated as follows: (i) If any plane figure revolves about an external axis in its plane, the volume of the solid generated by the revolution is equal to the product of the area of the figure and the distance travelled by the centroid of the figure.

    0
    0
  • (ii) If any line in a plane revolves about an external axis in the plane, the area of the curved surface generated by the revolution is equal to the product of the length of the line and the distance travelled by the centroid of the line.

    0
    0
  • On any line OX take a length ON equal to xG, and from N draw NP at right angles to OX and equal to uH; G and H being convenient units of length.

    0
    0
  • Then we may, ignoring the units G and H, speak of ON and NP as being equal to x and u respectively.

    0
    0
  • The " mean ordinate " or average ordinate is an ordinate of length 1 such that Hl is equal to the area of the trapezette.

    0
    0
  • It therefore appears as a calculated length rather than as a definite line in the figure; except that, if there is only one ordinate of this length, a line drawn through its extremity is so placed that the area of the trapezette lying above it is equal to a corresponding area below it and outside the trapezette.

    0
    0
  • from a line drawn through 0 parallel to the ordinates) is equal to the mean distance (§ 32) of the trapezette from this axis; moments with regard to the central ordinate are therefore sometimes described in statistics as " moments about the mean."

    0
    0
  • In the notation of the integral calculus, this area is equal to f x o udx; but the notation is inconvenient, since it implies a division into infinitesimal elements, which is not essential to the idea of an area.

    0
    0
  • - Since all points on any ordinate are at an equal distance from the axis of u, it is easily shown that the first moment (with regard to this axis) of a trapezette whose ordinate is u is equal to the area of a trapezette whose ordinate is xu; and this area can be found by the methods of the preceding sections in cases where u is an algebraical function of x.

    0
    0
  • u m _, we know uo and um; and u I - uo and u m - u m _ i are taken to be equal to zhu'o and Zhu'„, respectively.

    0
    0
  • The tangent of the angle of deflection 0 of this needle measured from its position, when the shunt coil is disconnected, is equal to the ratio of the voltage of the dynamo to the current through the insulator.

    0
    0
  • This act appropriated £ 20,000 annually for five years for the establishment and maintenance of elementary schools, required each city and town to raise by taxation a sum for the same purpose equal to onehalf of its share from the proceeds of the state fund, and provided for the election of school commissioners in each town and of trustees of each school.

    0
    0
  • Generally, if any condition in the wave is carried forward unchanged with velocity U, the change of 4 at a given point in time dt is equal to the change of as we go back along the curve a distance dx = Udt at the beginning of dt.

    0
    0
  • This is generally equal to the number of waves issuing from the source per second, and therefore equal to its frequency of vibration.

    0
    0
  • Therefore the momentum entering through a square centimetre at B per second is equal to the momentum leaving through a square centimetre at A.

    0
    0
  • 9) is equal to that entering at B, an assumption no longer tenable when the form changes.

    0
    0
  • We shall show that if we sum these up for a whole wave the potential energy is equal to the kinetic energy.

    0
    0
  • The pressure on CD is equal to the A C momentum which it receives per second.

    0
    0
  • As with light the ratio involved in the second law is always equal to the ratio of the velocity of the wave in the first medium to the velocity in the second; in other words, the sines of the angles in question are directly proportional to the velocities.

    0
    0
  • At the instant that the original wave reaches F the wave from E has travelled to a circle of radius very nearly equal to EF-not quite, as S is not quite in the plane of the rails.

    0
    0
  • The wave from D has travelled to a circle of radius nearly equal to DF, that from C to a circle of radius nearly CF, and so on.

    0
    0
  • As these " secondary waves " return to S their distance apart is nearly equal to twice the distance between the rails, and the observer then hears a note of wave-length nearly 2EF.

    0
    0
  • For this purpose the axis is furnished at its upper part with a screw working into a toothed wheel, and driving it round, during each revolution of the plate, through a space equal to the interval between two teeth.

    0
    0
  • His remarkable result that two waves give some sense of pitch, in fact a tone with wavelength equal to the interval between the waves, has been confirmed by other observers.

    0
    0
  • But the harmonics are most readily heard if we fortify the ear by an air cavity with a natural period equal to that of the harmonic to be sought.

    0
    0
  • For this it is necessary that the total force on an element due to the sum of the displacements should be equal to the sum of the forces due to the two displacements considered separately.

    0
    0
  • C is a constant, equal to the coefficient of viscosity in Helmholtz's theory, but less simple in Kirchhoff's theory.

    0
    0
  • Since the conditions in the region PQ remain always the same, the momentum perpendicular to AB entering the region at Q is equal to the momentum perpendicular to AB leaving the region at P. But, since the motion at Q is along AB, there is no momentum there perpendicular to AB.

    0
    0
  • We must show then that the force called out by the sum of the disturbances is equal to the sum of the forces called out by each train separately.

    0
    0
  • Hence the amount carried out at A is equal to that carried in at B.

    0
    0
  • But if y is the displacement at A, dy/dx is the extension at A, and the force acting is a pull across A equal to Y&uodyldx, where Y is Young's modulus of elasticity.

    0
    0
  • Intermittent illumination, however, with frequency equal to that of the fork shows at once that the jet is really broken up into drops, one for each vibration, and that these move over in a steady procession.

    0
    0
  • Hence the stream of air does work during half the vibration and this is not abstracted during the other half, and so it goes on increasing the motion until the supply of energy in blowing is equal to the loss by friction and sound.

    0
    0
  • By similar reasoning it may be shown that the number of beats per second is always equal to the difference between the numbers of vibrations in the same time corresponding to the two interfering notes.

    0
    0
  • 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.

    0
    0
  • It is equal to the difference between local time on the standard meridian, and at the place defined, one hour of time corresponding to 15° difference of longitude.

    0
    0
  • Among veld plants the elandsboontje provides tanning material equal to oak bark.

    0
    0
  • Till quite recent times this Gospel, though nominally equal to the others in authority, has unquestionably not aroused the same interest or feelings of attachment as they have, partly from its not bearing the name of an apostle for its author, as the first and fourth do, partly, also, owing to the fact that the first and third, while they include most of what is found in it, contain much additional matter, which is of the highest value.

    0
    0
  • Some light grey sandstone found in Rocky Canon, Gallatin county, looks much like the Berea (Ohio) sandstone; and a sandstone quarried at Columbus, Yellowstone county, was manufactured into grindstones equal to those made from the Berea stone.

    0
    0
  • Broadly, the least costly arrangement is that in which the cost of the superstructure of a span is equal to that of a pier and foundation.

    0
    0
  • For a plate girder bridge of less height than the train, the wind is to be taken to act on a surface equal to the projected area of one girder and the exposed part of a train covering the bridge.

    0
    0
  • If the web is a braced web, then the vertical component of the stress in the web bars cut by the section must be equal to S.

    0
    0
  • Lay off kf, hg, horizontal and equal to 1.

    0
    0
  • Obviously no is horizontal and equal to 1.

    0
    0
  • Differentiating and equating to zero, the cost is least when dC _ LP +La =o, dl = l2 P=ale=G; that is, when the cost of one pier is equal to the cost erected of the main girders of one span.

    0
    0
  • The sum of the two upward vertical reactions must clearly be equal to the sum of the loads.

    0
    0
  • Remembering that in this case the centre bending moment Ewl will be equal to wL 2 /8, we see that the horizontal tension H at the vertex for a span L (the points of support being at equal heights) is given by the expression 1..

    0
    0
  • The value of H is equal to the maximum tension on the bottom flange, or compression on the top flange, of a girder of equal span, equally and similarly loaded, and having a depth equal to the dip of the suspension bridge.

    0
    0
  • in length would be drawn equal to to in.; then if the true radius at the centre were to,000 ft., this radius, if the curve were undistorted, 1, FIG.

    0
    0
  • - In order that a girder may become straight under its working load it should be constructed with a camber or upward convexity equal to the calculated deflection.

    0
    0
  • All these measures could not alter the fact that the national economy became less and less equal to the tasks imposed upon it by the war.

    0
    0
  • This silly libel so enraged the performers at the Opera that they hanged and burned with him, the Dijon academy, which had founded his fame, announced the subject of "The Origin of Inequality," on which he wrote a discourse which was unsuccessful, but at least equal to the former in merit.

    0
    0
  • For the weighing of gold, gems, opium, &c., the fuang, equal to s tical, and the salung, equal to 4 tical, are used.

    0
    0
  • The unit of land measure is the rai, which is equal to 400 square wah, and is subdivided into four equal ngan.

    0
    0
  • Let E be the effective elasticity of the aether; then E = pc t, where p is its density, and c the velocity of light which is 3 X 10 10 cm./sec. If = A cos" (t - x/c) is the linear vibration, the stress is E dE/dx; and the total energy, which is twice the kinetic energy Zp(d/dt) 2 dx, is 2pn2A2 per cm., which is thus equal to 1.8 ergs as above.

    0
    0
  • In the simplest case, that of uniform translation, these components of the gradient will each be constant throughout the region; at a distant place in free aether where there is no motion, they must thus be equal to -u,-v,-w, as they refer to axes moving with the matter.

    0
    0
  • A very few articles (spirits, beer, wine, tobacco, tea, coffee, cocoa) yield practically all of the customs revenue, and, so far as these articles are produced within the country, they are subject to an excise duty, an internal tax precisely equal to the import duty.

    0
    0
  • His work Eratosthenes Batavus, published in 1617, describes the method and gives as the result of his operations between Alkmaar and Bergen-opZoom a degree of the meridian equal to 55,100 toises =117,449 yds.

    0
    0
  • In North America the Carolina parakeet, Conurus carolinensis, at the beginning of the i 9th century used to range in summer as high as the shores of lakes Erie and Ontario - a latitude equal to the south of France; and even much later it reached, according to trustworthy information, the junction of the Ohio and the Mississippi, though now its limits have been so much curtailed that its occurrence in any but the Gulf States is doubtful.

    0
    0
  • 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.

    0
    0
  • observing that any factor 1/I-x l is=l+x l +x 2l +..., we see that in the term Nx the coefficient is equal to the number of partitions of n, with the parts I, 2,, ..,withh repetitions.

    0
    0
  • +Nxnzk+.., we see that in the term Nx n z k of the development the coefficient N is equal to the number of partitions of n into k parts, with the parts I, 2, 3, 4,, without repetitions.

    0
    0
  • The formula shows that except for numbers of the form (3n 2 n) the number of partitions without repetitions into an odd number of parts is equal to the number of partitions without repetitions into an even number of parts, whereas for the excepted numbers these numbers differ by unity.

    0
    0
  • we see that in the term Nx z of the development the coefficient Nis equal to the number of partitions of n into k parts, with the parts I, 2, 3, 4, ..., with repetitions.

    0
    0
  • 1), and the potentiometer wire itself has a resistance equal to one of these coils.

    0
    0
  • The eye is single, and in addition to the eye there is often an " eye-spot, "Monospilus being unique in having the eye-spot alone and no eye, while Leydigiopsis (Sars, Igo') has an eye with an eye-spot equal to it or larger.

    0
    0
  • She proved equal to the occasion, partly because she was in all probability innocent of anything worse than a qualified acquiescence in Seymour's improprieties and a girlish admiration for his handsome face.

    0
    0
  • Then, in 1540, the name was restricted to an area approximately equal to that of modern Costa Rica.

    0
    0
  • Good whisky is made in Maryland and in parts of Pennsylvania from rye, but all efforts in other states to produce from Indian corn a whisky equal to the Bourbon have failed, and it is probable that the quality of the Bourbon is largely due to the character of the Kentucky lime water and the Kentucky yeast germs. The average annual product of the state from 1880 to 1900 was about 20,000,000 gallons; in 1900 the product was valued at $9,786,527; in 1905 at $11,204,649.

    0
    0