# proportional proportional

# proportional Sentence Examples

• This loss is proportional to the length of the wire.

• The proportional rent is from I% to 5:/.

• Under the first head would be included proportional taxes dependent upon the value of the property taxed; under the second, taxes whose amount does not depend upon that value.

• The proportional rents are fixed by the Mines Administration according to the wealth, area and facility of working of the mine, and are inserted in the imperial firman governing the mine, and must be paid before the minerals are exported.

• As the source of monochromatic light a bright sodium burner is used, and the rotation, which is exactly proportional to H, is measured by an accurate polarimeter.

• Now, we know that the number of electrochemical equivalents electrolysed is proportional to the whole amount of electricity which passed through the circuit, and the product of this by the electromotive force of the battery is the work done by the latter, so that in this case also Joule showed that the heat generated was proportional to the work done.

• The Liber abaci, which fills 459 printed pages, contains the most perfect methods of calculating with whole numbers and with fractions, practice, extraction of the square and cube roots, proportion, chain rule, finding of proportional parts, averages, progressions, even compound interest, just as in the completest mercantile arithmetics of our days.

• The equation then becomes a 2 /V = k, or a = A / Vk, so that the molecular conductivity is proportional to the square root of the dilution.

• So if a battle today were similarly costly, the proportional number of casualties would be 230,000.

• Since the current passing through the balance when equilibrium is obtained with a given weight is proportional to the square root of the couple due to this weight, it follows that the current strength when equilibrium is obtained is proportional to the product of the square root of the weight used and the square root of the displacement distance of this weight from its zero position.

• If a mining concession is granted within lands which are private property or which are " real vakuf lands " (arazii-mevkufe-i-sahiha) only one-fifth of the proportional rent is payable to the state, the other four-fifths reverting to the land-owner or the vakufs, as the case may be.

• Two categories of rent, fixed and proportional, are payable to the state by mineowners.

• It is proportional, and is collected by deduction from salaries and pensions paid to servants of the state, where it is assessed on three-eighths of the income, and from interest on consolidated stock, where it is assessed on the whole amount; and by register in the cases of private individuals, who pay on three-fourths of their income, professional men, capitalists or manufacturers, who pay on one-half or nine-twentieths of their income.

• While furnishing - almost unconsciously, however - additional evidence for overthrowing that classification, there is, nevertheless, no attempt made to construct a better one; and the elaborate tables of dimensions, both absolute and proportional, suggestive as is the whole tendency of the author's observations, seem not to lead to any very practical result, though the systematist's need to look beneath the integument, even in parts that are so comparatively little hidden as birds' feet, is once more made beyond all question apparent.

• The violence or completeness of combustion was proportional to the amount of phlogiston present.

• When induction or magnetic flux takes place in a ferromagnetic metal, the metal becomes magnetized, but the magnetization at any point is proportional not to B, but to B - H.

• If, however, there is leakage, the current received on the galvanometer will be less than the current sent out, and the result will be a deflection of the needle proportional to the amount of leakage.

• By means of this " light-relay " the intensity of the light acting at any moment upon the sensitized paper is made proportional to the illumination of the selenium in the transmitter.

• We therefore have the fundamental theorem that the angular velocity of the body around the centre of attraction varies inversely as the square of its distance, and is therefore at every point proportional to the gravitation of the sun.

• (I) The bulk of the solution is unaltered, except that its temperature may be raised owing to the usual heating effect which is proportional to the square of the strength of the current.

• For crystalline bodies the value of or -) is nearly always small and constant, the magnetization being therefore independent of the form of the body and proportional to the force.

• The exhaust steam passing from the engine through the blastpipe and the chimney produces a diminution of pressure, or partial vacuum, in the smoke-box roughly proportional to the weight of steam discharged per unit of time.

• Quesnay and Mirabeau had advocated a proportional tax (impot de quotite), but Turgot a distributive tax (impot de repartition).

• If at least half of the harvest in any year is destroyed by accident, the lessee (a) in the case of a lease for several years, obtains, at the end of his lease, a refund of rent, by way of indemnity, unless he has been indemnified by preceding harvests; (b) in the case of a lease for a year only, may secure a proportional abatement of the current rent.

• The reason is that the heat produced in a given time in a wire is proportional to the square of the strength of the current passing through it, and hence the rate at which the heat is produced in the wire, and therefore its temperature, increases much faster than the current itself increases.

• 7V k / R, and since Vk is proportional to the volume at absolute zero, the ratio T k /P k should exhibit additive relations.

• If the covariant (f,4) 1 vanishes f and 4 are clearly proportional, and if the second transvectant of (f, 4 5) 1 upon itself vanishes, f and 4) possess a common linear factor; and the condition is both necessary and sufficient.

• To take a reading the torsion-head is turned until an aluminium pointer attached to the coil is brought to the zero position on a small scale; the strength of the field is then proportional to the angular torsion.

• The weight W is moved along the scale until the yoke just tilts over upon the stop S; the distance of W from its zero position is then, as can easily be shown, proportional to F, and therefore to B 2, and approximately to I 2.

• He found that the amounts of the substances liberated in each cell were proportional to the chemical equivalent weights of those substances.

• of a crowd of small compass needles (representative of magnetic molecules) is proportional to the 1.6th power of the aggregate maximum magnetic moment before or after completion of the cycle.

• The ordinates of the curve give the strain in cwts., and the abscissae the distance in miles measured from the Canso end; as the strain is proportional to the depth, 18 cwts.

• The strength of the field is proportional to the swing of the galvanometer-needle, and, when the galvanometer is calibrated, can be expressed in C.G.S.

• He also found that, for the same current, the amount of chemical action was independent of the size of the electrodes and proportional to the time that the current flowed.

• Thus the smallest rotation of either head communicates to the corresponding slide motion, which, if the screws are accurate, is proportional to the amount through which the head is turned.

• The close agreement between the results at least indicates that "the amount of heat produced by friction is proportional to the work done and independent of the nature of the rubbing surfaces."

• There were further handed over, under the Muharrem decree, to the public debt council, the tribute of Bulgaria, the amount of which has never even been fixed, but as compensation for which the tobacco tithe up to a yearly amount of £Tioo,000 was ceded to the council in the same conditions as the " six indirect contributions "; the proportional shares (generally known as the " contributive 1 For simplicity's sake, the lottery bonds having a special treatment different from that of the rest of the loans, these groups, when the new bonds of the reduced debt were exchanged against the old bonds of the original loans, became " series " thus: Series A, group i.; series B, group ii.;.

• For example, does the heat generated by friction vary as the friction and the time during which it acts, or is it proportional to the friction and the distance through which the rubbing bodies are displaced - that is, to the work done against friction - or does it involve any other conditions?

• of all these experiments may be summed up in the statement that the amount of chemical action is proportional to the quantity of electricity which passes through the cell.

• We may sum up the chief results of Faraday's work in the statements known as Faraday's laws: The mass of substance liberated from an electrolyte by the passage of a current is proportional (I) to the total quantity of electricity which passes through the electrolyte, and (2) to the chemical equivalent weight of the substance liberated.

• When there is no current the shutter covers the perforations and no light passes, but when a current traverses the wires they are depressed by electromagnetic action, carrying the shutter with them, and a quantity of light proportional to the current strength is admitted through the perforations.

• It may he shown theoretically that the absolute boiling-point is proportional to the molecular volume, and, since this property is additive, the boiling-point should also be additive.

• The experiment may be made in two different ways: (I) the magnetizing current is increased by a series of sudden steps, each of which produces a ballistic throw, the value of B after any one throw being proportional to the sum of that and all the previous throws; the magnetizing FIG.

• It is probable that the wind pressure is not strictly proportional to the extent of the surface exposed.

• The rate at which energy is lost being proportional to the frequency, it is obvious that the loss at frequency ioo may be deduced from that at any other frequency n by simply multiplying by too n.

• Let x be the number of molecules which dissociate per second when the number of undissociated molecules in unit volume is unity, then in a dilute solution where the molecules do not interfere with each other, xp is the number when the concentration is p. Recombination can only occur when two ions meet, and since the frequency with which this will happen is, in dilute solution, proportional to the square of the ionic concentration, we shall get for the number of molecules re-formed in one second ye where q is the number of dissociated molecules in one cubic centimetre.

• Van 't Hoff's formula is equivalent to taking the frequency of dissociation as proportional to the square of the concentration of the molecules, and the frequency of recombination as proportional to the cube of the concentration of the ions.

• An explanation of the failure of the usual dilution law in these cases may be given if we remember that, while the electric forces between bodies like undissociated molecules, each associated with equal and opposite charges, will vary inversely as the fourth power of the distance, the forces between dissociated ions, each carrying one charge only, will be inversely proportional to the square of the distance.

• To pass a steady current in the direction opposite to this electromotive force of polarization, the applied electromotive force E must exceed that of polarization E', and the excess E - E' is the effective electromotive force of the circuit, the current being, in accordance with Ohm's law, proportional to the applied electromotive force and represented by (E - E')/ R, where R is a constant called the resistance of the circuit.

• Other conditions remaining unchanged, the force between two poles is proportional to the product of their strengths; it is repulsive or attractive according as the signs of the poles are like or unlike.

• A thin sheet of magnetic matter magnetized normally to its surface in such a manner that the magnetization at any place is inversely proportional to the thickness h of the sheet at that place is called a magnetic shell; the constant product hI is the strength of the shell and is generally denoted by 4, or 4.

• - The so-called " ballistic " method of measuring induction is based upon the fact that a change of the induction through a closed linear conductor sets up in the conductor an electromotive force which is proportional to the rate of change.

• Under the influence of the transient current, the galvanometer needle undergoes a momentary deflection, or " throw," which is proportional to Q, and therefore to 8B, and thus, if we know the deflection produced by the discharge through the galvanometer of a given quantity of electricity, we have the means of determining the value of 8B.

• Kohlrausch has prepared water of which the conductivity compared with that of mercury was only o 4 oX 11 at 18° C. Even here some little impurity was present, and the conductivity of chemically pure water was estimated by thermodynamic reasoning as o 36X1011 at 18° C. As we shall see later, the conductivity of very dilute salt solutions is proportional to the concentration, so that it is probable that, in most cases, practically all the current is carried by the salt.

• Arrhenius has pointed out that the coefficient of affinity of an acid is proportional to its electrolytic ionization.

• It is found that the influence of different acids on this action is proportional to their specific coefficients of affinity.

• On the analogy between this case and that of the interface between two solutions, Nernst has arrived at similar logarithmic expressions for the difference of potential, which becomes proportional to log (P 1 /P 2) where P2 is taken to mean the osmotic pressure of the cations in the solution, and P i the osmotic pressure of the cations in the substance of the metal itself.

• This causes a ballistic throw proportional to the induction through the bar at the moment when the two portions were separated.

• - Another large class of ammeters depend for their action upon the fact that an electric current create; an electric field round its conductor, which varies in strength from point to point, but is otherwise proportional to the current.

• metres of the superficial area covering the mine, and a proportional duty varying from I% to 20% of the gross value of metal contained in the ore, according to the kind of metal and the method of extraction of the ore), £T45,141; and tax-papers (Tezkeres), £T58,434.

• Apart from this complication, it appeared that I was proportional to H when the value of H was less than 0 02.

• According to Joule's observations, the length of a bar of iron or soft steel was increased by magnetization, the elongation being proportional up to a certain point to the square of the intensity of magnetization; but when the " saturation point " was approached the elongation was less than this law would require, and a stage was finally reached at which further increase of the magnetizing force produced little or no effect upon the length.

• For soft iron, tungsten-steel and nickel little difference appeared to result from lowering the temperature down to - 186° C. (the temperature of liquid air); at sufficiently high temperatures, 600 to 1000° or more, it was remarked that the changes of length in iron, steel and cobalt tended in every case to become proportional to the magnetic force, the curves being nearly straight lines entirely above the axis.

• Various nickel-steels all expanded under magnetization, the increase being generally considerable and proportional to the field; in the case of an alloy containing 29% of nickel the change was nearly 40 times greater than in soft iron.

• They consider, however, that Kirchhoff's theory, which assumes change of magnetization to be simply proportional to strain, is still in its infancy, the present stage of its evolution being perhaps comparable with that reached by the theory of magnetization at the time when the ratio I/H was supposed to be constant.

• So far, the best results have been attained with aluminium, and the permeability was greatest when the percentages of manganese and aluminium were approximately proportional to the atomic weights of the two metals.

• The effect appeared to be closely connected with the intensity of magnetization, being approximately proportional to I.

• Soc., 1903, 71, 30), experimenting with wires of iron, steel and nickel, showed that in weak fields the change of resistance was proportional to a function a12-+b14-{-cl', where a, b and c are constants for each specimen.

• A large effect, proportional to the field, has been found by H.

• In the case of iron and nickel it was found that, when correction was made for mechanical stress due to magnetization, magnetic change of thermo-electric force was, within the limits of experimental error, proportional to magnetic change of length.

• to the magnetized cobalt was proportional to the square of the magnetic induction or of the magnetization.

• Curie has shown, for many paramagnetic bodies, that the specific susceptibility K is inversely proportional to the absolute temperature 0.

• This measure obliged all the great dignitaries, and the principal towns also, according to their means, to maintain a banderium of five hundred horsemen, or a proportional part thereof, and hold it ready, at the first summons, thus supplying the crown with a standing army 76,875 strong.

• Since the distance to be travelled by the secondary waves is still r, we see how the effect of the first zone, and therefore of the whole series is proportional to al(a+r).

• If on the other hand the number of zones be odd, the effects conspire; and the illumination (proportional to the square of the amplitude) is four times as great as if there were no obstruction at all.

• If when the aperture is given, the wave-length (proportional to k1) varies, the composition of the integrals is unaltered, provided E and n are taken universely proportional to X.

• A diminution of X thus leads to a simple proportional shrinkage of the diffraction pattern, attended by an augmentation of brilliancy in proportion to A-2.

• u 2 u It will be observed that, while the total intensity is proportional to ab, the intensity at the focal point is proportional to a 2 b 2.

• being thus inversely proportional to R.

• It may be instructive to contrast this with the case of an infinitely narrow annular aperture, where the brightness is proportional to Jo 2 (z).

• Foucault, who employed a scale of equal bright and dark alternate parts; it was found to be proportional to the aperture and independent of the focal length.

• In his experiments upon this subject Fraunhofer employed plates of glass dusted over with lycopodium, or studded with small metallic disks of uniform size; and he found that the diameters of the rings were proportional to the length of the waves and inversely as the diameter of the disks.

• In different gratings the lengths of the spectra and their distances from the axis were inversely proportional to the grating interval, while with a given grating the distances of the various spectra from the axis were as i, 2, 3, &c. To Fraunhofer we owe the first accurate measurements of wave-lengths, and the method of separating the overlapping spectra by a prism dispersing in the perpendicular direction.

• The formation of bands thus requires that the retarding plate be held upon the side already specified, so that zs be positive; and that the thickness of the plate (to which z is proportional) do not exceed a certain limit, which we may call 2T 0.

• For by (30) do = dv, and by (2) dv is proportional to ds.

• Under these circumstances the arc to be considered is bisected at 0, and its length is proportional to the width of the slit.

• In 1909 the proportional representation system was adopted for the election of town councillors.

• 656s, a way, and yp&4*t y, to write), a curve of which the radius vector is proportional to the velocity of a moving particle.

• In 1628 Castelli published a small work, Della misura dell' acque correnti, in which he satisfactorily explained several phenomena in the motion of fluids in rivers and canals; but he committed a great paralogism in supposing the velocity of the water proportional to the depth of the orifice below the surface of the vessel.

• He supposed that the filaments of water which graze along the sides of the pipe lose a portion of their velocity; that the contiguous filaments, having on this account a greater velocity, rub upon the former, and suffer a diminution of their celerity; and that the other filaments are affected with similar retardations proportional to their distance from the axis of the pipe.

• He supposed that the surface of the fluid, contained in a vessel which is emptying itself by an orifice, remains always horizontal; and, if the fluid mass is conceived to be divided into an infinite number of horizontal strata of the same bulk, that these strata remain contiguous to each other, and that all their points descend vertically, with velocities inversely proportional to their breadth, or to the horizontal sections of the reservoir.

• For a homogeneous liquid at rest under gravity, p is proportional to the depth below the surface, i.e.

• The proportional amount of these materials in a sandy soil on the Bagshot beds and a stiff Oxford clay is given below: - The pore-space within the soil, i.e.

• Great masses, as those of the great planets, would not be attracted with a force proportional to the mass because of the hindrance of the interposed portions.

• The taxation of the tsar's slyuzhnuie lyudi, or military tenants, was a first step towards the proportional taxation of the hitherto privileged classes.

• If now we wish to represent the variations in some property, such as fusibility, we determine the freezing-points of a number of alloys distributed fairly uniformly over the area of the triangle, and, at each point corresponding to an alloy, we erect an ordinate at right angles to the plane of the paper and proportional in length to the freezing temperature of that alloy.

• When a current is passed through a solid alloy, a series of Peltier effects, proportional to the current, are set up between the particles of the different metals, and these create an opposing electromotive force which is indistinguishable experimentally from a resistance.

• S netona President of the State, and composed the statute for the election of the Constituent Assembly by universal, equal, direct and secret franchise according to a proportional system based on d'Hondt's distributive principle which contains elaborate safeguards against the tyranny of the majority.

• Coulomb proved experimentally that the electric force just outside a conductor at any point is proportional to the electric density at that point.

• 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.

• The electric density on the sphere being uniform, the quantities of electricity on these areas are proportional to the areas, and if the electric force varies inversely as the square of the distance, the forces exerted by these two surface charges at the point in question are proportional to the solid angle of the little cone.

• Accordingly for a given ellipsoid the surface density of free distribution of electricity on it is everywhere proportional to the the tangent e plane e att that point.

• These are proportional to the capacities.

• 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.

• In 1909 the proportional representation system was adopted in the election of town councillors.

• done by a gas in isothermal expansion is assumed to be equivalent or proportional to the heat absorbed, H=R log e r/F'(t).

• He now proposed to define absolute temperature as proportional to the reciprocal of Carnot's function, so as to agree as closely as possible with the scale of the gas thermometer.

• 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 ECÃ†F.

• It is found by experiment that the change of pv with pressure at moderate pressures is nearly proportional to the change of p, in other words that the coefficient d(pv)/dp is to a first approximation a function of the temperature only.

• Trans., 1854, 1862) found that the cooling effect, do, was of the same order of magnitude as the deviations from Boyle's law in each case, and that it was proportional to the difference of pressure, dp, so that d0/dp was nearly constant for each gas over a range of pressure of five or six atmospheres.

• Reynolds, in his investigation, introducing no new form of law of distribution of velocities, uses a linear quantity, proportional to the mean free path of the gaseous molecules, which he takes to represent (somewhat roughly) the average distance from which molecules directly affect, by their convection, the state of the medium; the gas not being uniform on account of the gradient of temperature, the change going on at each point is calculated from the elements contributed by the parts at this particular distance in all directions.

• The heights of the columns above the surface of junction of the liquids are inversely proportional to the densities of the liquids.

• The heights to which the liquids rise, measured in each case by the distance between the surfaces in the reservoirs and in the tubes, are inversely proportional to the densities.

• According to Quincke, the surface tension of pure water in contact with air at 20° C. is 81 dynes per linear centimetre, while that of alcohol is only 25.5 dynes; and a small percentage of alcohol produces much more than a proportional decrease in the surface tension when added to pure water.

• The relation of the elevation of the boiling-point (t°) to the osmotic pressure (P) is very simply derived from the formula t=o 02407P 0, while the reduction of vapour pressure proportional to the concentration can be very easily obtained from the elevation of the boiling-point, or it may be obtained directly from tables of vapour tension.

• Ruppin's analysis of Baltic water, which has an alkalinity of 16 to 18 instead of the 5 or 6 which would be the amount proportional to the salinity, while the water of the Vistula and the Elbe with a salinity of o 1 per mille has an alkalinity of 28 or more.

• According to Kriimmel's calculation the proportional areas at a high temperature are as follows: Percentage of Ocean'Surface with Temperature.

• This deflecting force is directly proportional to the velocity and the mass of the particle and also to the sine of the latitude; hence it is zero at the equator and comes to a maximum at the poles.

• These are also called the Upper Limestone Shale, a similar group being found in places below the limestone, and called the Lower Limestone Shale, or, in the north of England, the Tuedian group. Going northward the beds of limestone diminish in thickness, with a proportional increase in the intercalated sandstones and shales, until in Scotland they are entirely subordinate to a mass of coal-bearing strata, which forms the most productive members of the Scotch coalfields.

• For many kinds of spring the change of form is practically proportional to the force, but the relation should always be determined experimentally.

• The radial distance x is at any instant proportional to the force acting through the spring.

• The angular displacement, 0, of the disk is made proportional to the displacement, s, of the point of application of the force by suitable driving gear.

• The angular velocity of the shaft is proportional to the rate of working.

• the relative angular displacement is proportional to the radius of the circle described by the end of a light lever operated by mechanism between the spring-connected parts.

• The change in the distance d is proportional to the change in the torque transmitted from the shaft to the pulley.

• The force Q, usually measured by a spring, required to maintain the beam in its central position is proportional to (P - p).

• Let us imagine that the systems had the initial values of their co-ordinates and momenta so arranged that the number of systems for which the co-ordinates and momenta were within a given range was proportional simply to the extension of the range.

• We have already seen that the#mean energy increases with the temperature: it will now be supposed that the mean energy is exactly proportional to the ture.

• Since the volume at constant pressure is exactly proportional to the absolute temperature, it follows that the coefficients of expansion of all gases ought, to within the limits of error introduced by the assumptions on which we are working, to have the same value 1/273.

• cAoyW -T6, burnt), which was present in all combustible bodies in an amount proportional to their degree of combustibility; for instance, coal was regarded as practically 1111 Sx sx sx or say Ex.

• Modern research has proved that such reactions are not occasioned by water acting as H 2 0, but really by its ions (hydrions and hydroxidions), for the velocity is proportional (in accordance with the law of chemical mass action) to the concentration of these ions.

• Now the height to which the tangent sight has been raised in order to direct the axis on G' is evidently proportional to the tangent of the angle OMS =AXS.

• by taking advantage of the different rates of diffusion of the two gases; the solubility of air in water corresponds with the "law of partial pressures," each gas being absorbed in amount proportional to its pressure and coefficient of absorption, and oxygen being much more soluble than nitrogen (in the ratio of 04114 to 02035 at o°); air expelled from water by boiling is always richer in oxygen.

• - The mensuration of the circle is founded on the property that the areas of different circles are proportional to the squares on their diameters.

• The lengths of arcs of the same circle being proportional to the angles subtended by them at the centre, we get the idea of circular measure.

• In the case, therefore, of any solid whose cross-section at distance x from one end is a quadratic function of x, the position of the crosssection through the centroid is to be found by determining the position of the centre of gravity of particles of masses proportional to So, S2, and 4S 1, placed at the extremities and the middle of a line drawn from one end of the solid to the other.

• On setting the dynamo in operation, a current passes through the shunt coil of the ohmmeter proportional to the voltage of the dynamo, and, if there is any sensible leakage through the insulator to earth, at the same time another current passes through the series coil proportional to the conductivity of the insulation of the wiring under the electromotive force used.

• Hence the deflection of the needle is proportional to the insulation resistance, and the scale can be graduated to show directly this resistance in megohms.

• His "theorie des debouches" amounts to this, that, products being, in last analysis, purchased only with products, the extent of the markets (or outlets) for home products is proportional to the quantity of foreign productions; when the sale of any commodity is dull, it is because there is not a sufficient number, or rather value, of other commodities produced with which it could be purchased.

• let a line be drawn perpendicular to AD and proportional to the displacement of the particle which was at the point before the disturbance began.

• We may say here that the energy or the intensity of the sound of given wave-length is proportional to the square of the amplitude.

• If V is the undisturbed volume of a small portion of the air at the undisturbed pressure P, and if it becomes V - v when the pressure increases to P+w, the average pressure during the change may be taken as PH-1-a), since the pressure excess for a small change is proportional to the change.

• 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.

• The whole series of fundamental and overtones gives the complete set of harmonics of frequencies proportional to 1, 2, 3, 4, ..., and wave-lengths proportional to 1, 2, 3, 4 ..

• Ann., 1870, 139, p. 104) which accorded with this result as far as R is concerned, but the diminution of velocity was found to be more nearly proportional to N om.

• Since the forces called into play by an extension or compression of the material are proportional to the cross-section, it follows that if we consider any case and then another case in which, with the same longitudinal disturbance, the cross-section is doubled, the force in the second case is doubled as well as the mass to be moved.

• Let us suppose that with constant excess of pressure, p, in the wind-chest, the amplitude produced is proportional to the pressure, so that the two tones issuing may be represented by pa sin 27-nit and pb sin 21rn 2 t.

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

• But inasmuch as the successive orders are proportional to A X 2 A 3, or µµ 2 µ 3, and X and µ are small, they are of rapidly decreasing importance, and it is not certain that any beyond those in equation (35) correspond to our actual sensations.

• It depends on the restoring force due to the displacement of the receiver not being accurately proportional to the displacement.

• It is easily shown that after a time we shall have to superpose on the original displacement a displacement proportional to the square of the particle velocity, and this will introduce just the same set of combination tones.

• In that case the loads on either side of C are proportional to m and l - m.

• In the triangle FDC, let FD be tangent to the curvelFC vertical, and Dqhorizontal; these three sides will necessarily be proportional respectively.to_the FIG.

• It follows that the number of the revolutions the mercury makes in a given time is proportional to the quantity of electricity which is passed through the meter.

• In these circumstances the number of rotations made by the armature in a given time is proportional to the product of the strength of the current flowing through the armature and that flowing through the field-coils, the former being the current to be measured.

• Its principle is as follows: Suppose there are two pendulum clocks, one having an ordinary pendulum and the other having a pendulum consisting of a fine coil of wire through which a current is passed proportional to the potential difference of the supply mains - in other words, a shunt current.

• They found that the absorbing powers of the metals, and therefore, by the principle of exchanges, their radiating powers also, are proportional to the square roots of their electric conductivities.

• The legislature or Grand Conseil (now composed of loo members) is elected (in the proportion of 1 member for every l000 inhabitants or fraction over 500) for 3 years by a direct popular vote, subject (since 1892) to the principles of proportional representation, while the executive or conseil d'etat (7 members) is elected (no proportional representation) by a popular vote for 3 years.

• In 1891 they introduced the "Initiative" into the cantonal constitution, and in 1892 the principle of proportional representation so far as regards the grand conseil, while Th.

• As a first result of experiment it was found that the resistance of similar shot was proportional, at the same velocity, to the surface or cross section, or square of the diameter.

• It is further assumed, as the result of experiment, that the resistance is proportional to the density of the air; so that if the standard density changes from unity to any other relative density denoted by then R= Td 2 p, and is called the coefficient of tenuity.

• To save the trouble of proportional parts the value of T(v) for unit increment of v is interpolated in a full-length extended ballistic table for T.

• In the same year a separate law was passed providing for primary elections for the choice of United States senators; but here also the method is not that of nomination by a plurality throughout the state, but by the vote of counties and legislative districts, so that this measure, like the other primary law, is not sufficiently direct to give Baltimore a vote proportional to its population.

• The torque required to hold the coils in their normal position is proportional to the mean value of the product of the currents flowing through two coils respectively, or to the mean value of the product of the current in the power-absorbing circuit and the potential difference at its ends, that is, to the power taken up by the circuit.

• If the quadrants of an electrometer are con - nected to the ends of a non-inductive circuit in series with the power-absorbing circuit, and if the needle is connected to the end of this last circuit opposite to that at which the inductionless re - sistance is connected, then the deflexion of the electrometer will be proportional to the power taken up in the circuit, since it is pro - portional to the mean value of (A - B) IC - 1 (A ±B)}, where A and B are the potentials of the quadrants and C is that of the needle.

• A relation which is of historical interest connects the logarithmic function with the quadrature of the hyperbola, for, by considering the equation of the hyperbola in the form xy=const., it is evident that the area included between the arc of a hyperbola, its nearest asymptote, and two ordinates drawn parallel to the other asymptote from points on the first asymptote distant a and b from their point of intersection, is proportional to log bla.

• There is a short " preface to the reader " by Briggs, and a description of a triangular diagram invented by Wright for finding the proportional parts.

• Neper being solicitous to know farther of him concerning this matter, he could give no other account of it than that it was by proportional numbers.

• In this table multiples of the differences, instead of proportional parts, are given.'

• On account of the great size of this table, and for other reasons, it never 2 The smallest number of entries which are necessary in a table of logarithms in order that the intermediate logarithms may be calculable by proportional parts has been investigated by J.

• Logistic or Proportional Logarithms. - The old name for what are now called ratios or fractions are logistic numbers, so that a table of log (a/x) where x is the argument and a a constant is called a table of logistic or proportional logarithms; and since log (a/x) =log a-log x it is clear that the tabular results differ from those given in an ordinary table of logarithms only by the subtraction of a constant and a change of sign.

• The usual practice in books seems to be to call logarithms logistic when a is 3600", and proportional when a has any other value.

• for numbers beginning with i followed by fifteen ciphers, and then by seventeen or a less number of significant figures) the logarithms were proportional to these significant figures.

• By studying the dispersion of colours in water, turpentine and crown glass Newton was led to suppose that dispersion is proportional to refraction.

• If the increase of the angle of refraction were proportional to the diminution of wave-length for a prism of any material, the resulting spectrum would also be normal.

• Hot wire voltmeters, like electrostatic voltmeters, are suitable for use with alternating currents of any frequency as well as with continuous currents, since their indications depend upon the heating power of the current, which is proportional to the square of the current and therefore to the square of the difference of potential between the terminals.

• Electromagnetic voltmeters consist of a coil of fine wire connected to the terminals of the instrument, and the current produced in that wire by a difference of potential between the terminals creates a magnetic field proportional at any point to the strength of the current.

• Since the capacity of a stream to carry matter in suspension is proportional to its velocity, it follows that any circumstance tending to retard the rate of flow will induce deposition.

• In the latter case, the densities of the fluids will be inversely proportional to the volumes thus displaced.

• The volume of the displaced liquid being then always the same, its density will be proportional to the whole weight supported, that is, to the weight of the instrument together with the weights required to be placed in the scale pan.

• In comparing the densities of different liquids, it is clear that this instrument is precisely equivalent to that of Fahrenheit, and must be employed in the same manner, weights being placed in the top scale only until the hydrometer sinks to the mark on the wire, when the specific gravity of the liquid will be proportional to the weight of the instrument together with the weights in the scale.

• Reinders (Ber., 1896, 29, p. 1369), who found that the reaction is monomolecular, and that the velocity constant of the reaction is proportional to the amount of the hydrochloride of the base present and also to the temperature, but is independent of the concentration of the diazoamine.

• Their share in bringing about the final settlement, which provided for equal representation in one house and proportional representation in the other, was so important that the settlement itself has come to be called the "Connecticut Compromise."

• de Maupertuis, is that a sportsman, when aiming at a bird on the wing, sights his gun some distance ahead of the bird, the distance being proportional to the velocity of the bird.

• Bradley had already perceived, in the case of the two stars previously scrutinized, that the apparent difference of declination from the maximum positions was nearly proportional to the sun's distance from the equinoctial points; and he realized the necessity for more observations before any generalization could be attempted.

• His conclusions may be thus summarized: (r) only stars near the solstitial colure had their maximum north and south positions when the sun was near the equinoxes, (2) each star was at its maximum positions when it passed the zenith at six o'clock morning and evening (this he afterwards showed to be inaccurate, and found the greatest change in declination to be proportional to the latitude of the star), (3) the apparent motions of all stars at about the same time was in the same direction.

• It is assumed further that the absorption is proportional to the incident radiation and (at any rate approximately) independent of the temperature, while the radiation is assumed to be a function of the temperature 6 Phil.

• Hence a part of what must be included in thermal energy is not simply proportional to temperature as is commonly assumed.

• According to Maxwell's law, however, the number of molecules having a velocity in the line of sight lying between v and vd-dv is proportional to e-1 3v2 dv, where (3 is equal to 312u 2; for v=u, we have therefore the ratio in the number of molecules having velocity u to those having no velocity in the line of sight e-0/1 2 =-- e-z = 22.

• Balmer, who showed that the four hydrogen lines in the visible part of the spectrum may be represented by the equation n = A(i - 4/s2), where n is the reciprocal of the wave-length and therefore proportional to the wave frequency, and s successively takes the values 3, 4, 5, 6.

• Roughly speaking the difference in frequency is proportional to the square of the atomic weight.

• The change of frequency (dn) for a series of lines which behave similarly is approximately proportional to the frequency (n) so that we can take the fraction do/n as a measure of the shift.

• What is known as the method of sines is used, for since the axes of the two magnets are always at right angles when the mirror magnet is in its zero position, the ratio M/H is proportional to the sine of the angle between the magnetic axis of the mirror magnet and the magnetic - = meridian.

• In this he gave equations resulting from the hypothesis that the magnetism of a ship is partly due to the permanent magnetism of hard iron and partly to the transient induced magnetism of soft iron; that the latter is proportional to the intensity of the inducing force, and that the length of the needle is infinitesimally small compared to the distance of the surrounding iron.

• If the bodies though of the same substance are of different sizes, the magnitudes of the additions of velocity are found to be inversely proportional to the volumes of the bodies.

• In fact, experiments upon the changes of velocity of bodies, due to a mutual influence between them, bring to light a property of bodies which may be specified by a quantity proportional to their volumes in the case of bodies which are perceived by other tests to be of one homogeneous substance, but otherwise involving also another factor.

• The Galileo-Newton theory of motion is that, relative to a suitably chosen base, and with suitable assignments of mass, all accelerations of particles are made up of mutual (so-called) actions between pairs of particles, whereby the two particles forming a pair have accelerations in opposite directions in the line joining them, of magnitudes inversely proportional to their masses.

• roughly proportional to the amount of salt dissolved.

• For gases such as oxygen and nitrogen dissolved in water the solubility as thus defined is independent of the pressure, or the mass of gas dissolved is proportional to the pressure.

• If a solid is immersed in a liquid a certain part of the energy of the system depends on, and is proportional to, the area of contact between solid and liquid.

• Similarly with two liquids like oil and water, which do not mix, we have surface energy proportional to the area of contact.

• the osmotic pressure is proportional to the absolute temperature.

• This result must hold good for any solution, but if the solution be dilute when saturated, that is, if the solubility be small, the equation shows that if there be no heat effect when solid dissolves to form a saturated solution, the solubility is independent of temperature, for, in accordance with the gas laws, the osmotic pressure of a dilute solution of constant concentration is proportional to the absolute temperature.

• In the case where l is negligible we have P/dP = T/dT, which on integration shows that the osmotic pressure, as in the special case of a dilute solution, is proportional to the absolute temperature.

• Graham showed that the diffusion was approximately proportional to the difference in concentration, and on these lines a theory of diffusion was founded on the lines of Fourier's treatment of the conduction of heat.

• The quantity of substance which diffuses through unit area in one second may be taken as proportional to the difference in concentration between the fluids at that area and at another parallel area indefinitely near it.

• proportional to the rate of variation - dc/dx of the concentration c with the distance x, so that the number of gramme-molecules of solute which, in a time dt, cross an area A of a long cylinder of constant cross section is dN = - DA(dc/dx)dt, where D is a constant known as the diffusion constant or the diffusivity.

• The average of the coagulative powers of salts of univalent, divalent and trivalent metals have been found by experiment to be proportional to the numbers 1: 35: 1023.

•  Thales discovered the theorem that the sides of equiangular triangles are proportional.

• A second rotation will, of course, produce a proportional augmentation of these increased quantities; and a continuance of turning will soon bring the intensities to their maximum, which is limited by an explosion between the plates" (Phil.

• It has also been shown that when different salts of the amine are used, their catalytic influence varies in amount and is almost proportional to their degree of ionization in aqueous solution.

• iroXb, many) was chosen for compounds like butylene, C 4 H 8, and ethylene, C 2 H 4, corresponding to the same composition in weight but differing in molecular formula, and having different densities in gas or vapour, a litre of butylene and isobutylene weighing, for instance, under ordinary temperature and pressure, about 2.5 gr., ethylene only one-half as much, since density is proportional to molecular weight.

• Since this has not been done we must adopt the approximate rule that the volume at absolute zero is proportional to that at the boiling-point.

• According to the above formula the critical temperature is given by 8aA/54b, and as the critical temperature is approximately proportional to the boiling-point, both being estimated on the absolute scale of temperature, we may conclude that the larger value of b corresponds to the lower boilingpoint, and indeed the isomer corresponding to the left-hand formula boils at 74°, the other at 114°.

• The final change in the system of parliamentary elections was made in 1899-1900, when proportional representation was introduced.

• Proportional representation aims at the protection of minorities, and its working out is a little intricate, or at all events difficult to describe.

• The following has been accepted as a clear definition of what proportional representation is:- " Each electoral district has the number of its members apportioned in accordance with the total strength of each party or political programme in that district.

• In 1902 there were 1,146,482 voters with 2,007,704 votes, the principles of multiple votes, with, however, a maximum of four votes and proportional representation, being in force for communal as for legislative elections.

• The election of 1894 had given the Liberals a much smaller number of seats than they ought to have had according to the number of votes they polled, and a cry arose for the establishment of proportional representation.

• The new cabinet at once (August 1899) introduced a bill giving complete proportional representation in parliamentary elections to all the arrondissements.

• Although it is seldom explicitly stated as an experimental law, it should really be regarded in this light, and may be briefly worded as follows: "The rate of transmission of heat by conduction is proportional to the temperature gradient."

• It is clear that the quantity transferred in any case must be jointly proportional to the area and the time.

• Taking Newton's law of cooling that the rate of loss of heat is simply proportional to the excess of temperature, the emissivity would be independent of the temperature.

• The magnitude of the stress per unit area parallel to the direction of flow is evidently proportional to the velocity gradient, or the rate of change of velocity per cm.

• Similarly if A is hotter than B, or if there is a gradient of temperature between adjacent layers, the diffusion of molecules from A to B tends to equalize the temperatures, or to conduct heat through the gas at a rate proportional to the temperature gradient, and depending also on the rate of interchange of molecules in the same way as the viscosity effect.

• The conductivity probably changes with temperature in the same way, being proportional to the product of the viscosity and the specific heat; but the experimental investigation presents difficulties on account of the necessity of eliminating the effects of radiation and convection, and the results of different observers often differ considerably from theory and from each other.

• The revenues of the joint budget consist of the revenues of the joint ministries, the net proceeds of the customs, and the quota, or the proportional contributions of the two states.

• In 1880 he was under-secretary of state for the home department, in 1881 for the colonies, and in 1882 secretary to the treasury; but he was always a stubborn fighter for principle, and upon finding that the government's Reform Bill in 1884 contained no recognition of the scheme for proportional representation, to which he was deeply committed, he resigned office.

• He worked hard also for Proportional Representation.

• The Leblanc process thus remained the sole purveyor of chlorine in its active forms, and in this way the fact is accounted for that, at least in Great Britain, the Leblanc process still furnishes nearly half of all the alkali made, though in other countries its proportional share is very much less.

• Since the curvature powers of the positive lenses are equal, the partial dispersions of the two glasses may be simply added together, and we then have: [0.543 +0.3741 The proportions given on the lower line may now be compared with the corresponding proportional dispersions for borosilicate flint glass 0.658, closely resembling the type 0.164 of Schott's list, viz.: [0.658 (A D = I.546) 50' 11 A slight increase in the relative power of the first lens of 0.543 would bring about a still closer correspondence in the rationality, but with the curves required to produce an object-glass of this type of 6 in.

• focal length a discrepancy of I unit in the 3rd decimal place in the above proportional figures would cause a linear error in the focus for that colour of only about .025 in., so that the largest deviation implied by the tables would be a focus for the extreme violet H ray about 037 longer than the normal.

• The wheel W is therefore mounted on a guided rod, which is forced upwards by suitable levers and weights, and this relief of pressure is precisely proportional to the pressure on the respective bearings.

• - T he modern equatorial should, for general purposes, be capable of carrying spectroscopes of considerable weight, so that the proportional strength of the axes and the rigidity of the instrument have to be considerably increased.

• The rise of temperature of a body, when heat is imparted to it, is found to be in general nearly proportional to the quantity of heat added.

• The thermal capacity of a body is measured by the quantity of heat required to raise its temperature one degree, and is necessarily proportional to the mass of the body for bodies of the same substance under similar conditions.

• This can be roughly estimated by observing the rate of change of temperature before and after the experiment, and assuming that the loss of heat is directly proportional to the duration of the experiment and to the average excess of temperature.

• There is, however, the advantage that the correction is rendered much less uncertain by this procedure, since the assumption that the loss of heat is proportional to the temperature-excess is only true for small differences of temperature.

• Specific Heat Of Mercury By Continuous Electric Method It Is Assumed As A First Approximation That The Heat Loss Is Proportional To The Rise Of Temperature Do, Provided That Do Is Nearly The Same In Both Cases, And That The Distribution Of Temperature In The Apparatus Is The Same For The Same Rise Of Temperature Whatever The Flow Of Liquid.

• According To The Elementary Kinetic Theory Of An Ideal Gas, The Molecules Of Which Are So Small And So Far Apart That Their Mutual Actions May Be Neglected, The Kinetic Energy Of Translation Of The Molecules Is Proportional To The Absolute Temperature, And Is Equal To 3/2 Of Pv, The Product Of The Pressure And The Volume, Per Unit Mass.

• A parallax of 0.01" denotes a distance a hundred times as great, and so on, the distance and parallax being inversely proportional.

• Regarded as a linear velocity, the parallactic motion is the same for all stars, being exactly equal and opposite to the solar motion; but its amount, as measured by the corresponding angular displacement of the star, is inversely proportional to the distance of the star from the earth, and foreshortening causes it to vary as the sine of the angular distance from the apex.

• 1858, 103, p. 529) found the lowering of the vapour-pressure to be nearly proportional to the strength of the solution for the same salt.

• His observations showed that the osmotic pressure was nearly proportional to the concentration and to the absolute temperature over a limited range.

• (is) The index n in the above formula, representing the rate of variation of c with temperature, is approximately the same as that expressing the rate of variation of the cooling effect Q, which is nearly proportional to c, and is given by the formula SQ= (n+i)c - b..

• Since the movements of the magnet are always small, the rotation of the magnet is proportional to the change in H, so long as M and the couple, 0, corresponding to unit twist of the suspension system remain constant.

• The gas does not obey Henry's law, that is, its solubility in water is not proportional to its pressure.

• In a third, " On some important points in the theory of heat " (1819), they stated that the specific heats of thirteen solid elements which they had investigated were nearly proportional to their atomic weights - a fact otherwise expressed in the " law of Dulong and Petit " that the atoms of simple substances have equal capacities for heat.

• The collapse of the gold-leaf is observed through an aperture in the case by a miscroscope, and the time taken by the goldleaf to fall over a certain distance is proportional to the ionizing current, that is, to the intensity of the radio-activity of the substance.

• Although Henry, Lee and Jefferson exercised great power, they were unable to secure a Constitution which embodied the demands of their party: universal suffrage, proportional representation and religious freedom.

• It is therefore adequately represented, for mathematical purposes, by a straight line AB drawn in the direction in question, of length proportional (on any convenient scale) to the magnitude of the force.

• The tensions in the successive portions of the string are therefore proportional to the respective lengths, and thelinesBH,CK.., are all equal.

• Hence these displacements are proportional to, JD, JC, and A therefore to DD, CC, where ~ CD is any line drawn FIG.

• to the sides of a triangle at the middle points will be in equilibrium provided they are proportional to the respective sides, and act all inwards or all outwards.

• For if we have an assemblage of particles whose mutual distances are small compared with the dimensions of the earth, the forces of gravity on them constitute a system of sensibly parallel forces, sensibly proportional to the respective masses.

• An infinitely small rotation about any axis is conveniently represented geometrically by a length AB measures along the axis and proportional to the angle of rotation, with the convention that the direction from A to B shall be related to the rotation as is the direction of translation to that of rotation in a righthanded screw.

• The length of the vector must be proportional to the moment of the couple, and its sense must be such that the sum of the moments of the two forces of the couple about it is positive.

• the line of intersection (B); the arms (AB,BC) will then be proportional to the respective moments.

• The two forces at B will cancel, and we are left with a couple of moment P.AC in the plane AC. If we draw three vectors to represent these three couples, they will be perpendicular and proportional to the respective sides of the triangle ABC; hence the third vector is the geometric sum of the other two.

• For this purpose the infinitesimal displacements of W the various joints are replaced by finite lengths proportional to them, and there- FIG.

• fore proportional to the velocities of the joints in some imagined motion of the deformable frame through its actual configuration; this is really (it may be remarked) a reversion to the original notion of virtual velocities.

• Pn have a resultant proportional to ~(m) which acts always through a point G fixed relatively to the given mass-system.

• - -, responding to any pole 0 is c n constructed for a system of - - ..---, forces acting parallel to p L - / through the positions of the N particles and proportional to -- / the respective masses; and its - successive sides are produced K, ~ to meet p in the points H, K,

• Since this is proportional to the mass, the relative masses to be attributed to various bodies can be determined practically by means of the balance.

• (28) For small velocities the resistance of the air is more nearly proportional to the first power of the velocity.

• A vector OU drawn parallel to PQ, of length proportional to PQ/~I on any convenient scale, will represent the mean velocity in the interval 1t, i.e.

• Another important example is that of a particle subject to an acceleration which is directed always towards a fixed point 0 and is proportional to the distance from 0.

• In elliptic harmonic motion the velocity of P is parallel and proportional to the semi-diameter CD which is conjugate to the radius CP; the hodograph is therefore an ellipse similar to the actual orbit.

• If q be any variable co-ordinate defining the position or (in the case of a system of bodies) the configuration, the velocity of each particle at any instant will be proportional to 4, and the total kinetic energy may be expressed in the form 1/8A42, where A is in general a function of q The special case where both cones are right circular and a is constant is important ~n astronomy and also in mechanism (theory of bevel wheels).

• The equation of the latter, referred to its principal axes, being as in II (41), the co-ordinates of the point J where it is met by the instantaneous axis are proportional to p, q, r, and the direction-cosines of the normal at J are therefore proportional to Ap, Bq, Cr, or X, u, v.

• (i6) The factors of ~, i~, ~, X, if, v on the right-hand side are proportional to the constituents of a possible infinitesimal displacement of the solid, and the whole expression is proportional (on, the same scale) to the work done by the given system of impulsive forces in such a displacement, As in 9 this must be equal to the total work done in such a displacement by the several forces, whatever they are, which make up the impulse.

• The motion of the body relative to 0 is therefore completely represented if we imagine the momental ellipsoid at 0 to roll without sliding on a plane fixed in space, with an angular velocity proportional at each instant to the radius-vector of the point of contact.

• If in (21) we imagine that x, y, I denote infinitesimal rotations of a solid free to turn about a fixed point in a given field of force, it appears that the three normal modes consist each of a rotation about one of the three diameters aforesaid, and that the values of in are proportional to the ratios of the lengths of corresponding diameters of the two quadrics.

• In the case of multiple freedom, the equations of small motion when modified by the introduction of terms proportional to the velocities are of the type daT -.

• The terms due to F in (33) are such as would arise from frictional resistances proportional to the absolute velocities of the particles, or to mutual forces of resistance proportional to the relative velocities; they are therefore classed as frictional or dissipative forces.

• Relations between Polygons of Loads and of Resistances.In a structure in which each piece is supported at two joints only, the well-known laws of statics show that the directions of the gross load on each piece and of the two resistances by which it is supported must lie in one plane, must either be parallel or meet in one point, and must bear to each other, if not parallel, the proportions of the sides of a triangle respectively parallel to their directions, and, if parallel, such proportions that each of the three forces shall be proportional to the distance between the other two,all the three distances being measured along one direction.

• According to a well-known principle of statics, because the loads or external pressures P1L~, &c., balance each other, they must be proportional to the sides of a closed polygon drawn respectively parallel to their directions.

• that is to say, their velocities are opposite as to inwardness and outwardness and inversely proportional to their areas.

• that is to say, the angular velocity about each axis is proportional to the sine of the angle between the other two.

• Through any point 0 in this common perpendicular draw 0A1 parallel to B~C~ and OAi parallel to B2C,; make those lines pro B1 C2 portional to the angular velocities D ~ about the axes to which they are P respectively paiallel; complete the ~ B2 parallelogram OA1 EA2, and draw the diagonal OE; divide BiBf in D into C, two parts, inversely proportional to the angular velocities about the axes which they respectively adjoin; A2 through D parallel to OE draw DT.

• The lengths ds, ds are proportional to the velocities of the points to whose paths they belong, and the proportions of those velocities to each other are deducible from the construction of the machine ~v the principles of pure mechanism explained in Chapter I.

• It appears that the rapidity with which a x rubbing surface wears away is proportional to Fio.

• 129) be the axis of a pivot, and let RPC be a portion of a curve such that at any point P the secant of the obliquity to the normal of the curve of a line parallel to the axis is inversely proportional to the ordinate PY, to which the velocity of P is proportional.

• In either case the tangential force, whether effort or resistance, exerted between the band and the pulley is their mutual friction, caused by and proportional to the normal pressure between them.

• It increases with the sectional area of the rope, and is inversely proportional to the radius of the curve into which it is bent.

• The elastic resistance evoked by this deflexion is proportional to the deflexion, so that if c is a constant depending upon the form,, material and, method of support of the shaft, the following equality must hold if the shaft is to rotate stably at the stated speed- -~ (y+e)ai=cy, from which y=Wafe/(gcWa2).

• being proportional to the increase in the square of the velocity, and independent of the time.

• A scheme of " proportional representation," the votes being counted in accordance with the system invented by G.

• Cavendish measured the capacity of disks and condensers of various forms, and proved that the capacity of a Leyden pane is proportional to the surface of the tinfoil and inversely as the thickness of the glass.

• One of the most important investigations he made in this way was to find out, as he expressed it, " what power of the velocity the resistance is proportional to."

• He found that the momentary dissipation was proportional to the degree of electrification at the time, and that, when the charge was moderate, its dissipation was not altered in bodies of different kinds or shapes.

• The temperature and pressure of the atmosphere did not produce any sensible change; but he concluded that the dissipation was nearly proportional to the cube of the quantity of moisture in the air.'

• These investigations led him to the announcement of the fundamental law of action between elements of current, or currents in infinitely short lengths of linear conductors, upon one another at a distance; summed up in compact expression this law states that the action is proportional to the product of the current strengths of the two elements, and the lengths of the two elements, and inversely proportional to the square of the distance between the two elements, and also directly proportional to a function of the angles which the line joining the elements makes with the directions of the two elements respectively.

• Ohm introduced the clear idea of current strength as an effect produced by electromotive force acting as a cause in a circuit having resistance as its quality, and showed that the current was directly proportional to the electromotive force and inversely as the resistance.

• between the quadrants was almost directly proportional to the potential of the needle.

• necessarily obey a law of deflection making the deflections proportional to the potential difference of the quadrants, but that an electrometer can be constructed which does fulfil the above law.

• The importance of this investigation resides in the fact that an electrometer of the above pattern can be used as a wattmeter, provided that the deflection of the needle is proportional to the potential difference of the quadrants.

• Assuming the electrometer to obey the above-mentioned theoretical law, the first reading is proportional to v 1 -v 2) and the second to v, - v 2 The difference of the readings is then proportional to (0, - v2) (v, - v3).

• But this last expression is proportional to the instantaneous power taken up in the inductive circuit, and hence the difference of the two readings of the electrometer is proportional to the mean power taken up in the circuit (Phil.

• Blondlot and P. Curie afterwards suggested that a single electrometer could be constructed with two pairs of quadrants and a duplicate needle on one stem, so as to make two readings simultaneously and produce a deflection proportional at once to the power being taken up in the inductive circuit.

• Throughout a wide range the deflections are proportional to the potential difference producing them.

• The latter chamber instead passed a bill for manhood suffrage at elections for the Second Chamber, on the condition that the elections for both chambers should take place on the basis of proportional representation.

• By this act proportional representation was established for both chambers, together with universal manhood suffrage at elections for the Second Chamber, a reduction of the qualifications for eligibility for the First Chamber and a reduction of the electoral term of this chamber from nine to six years, and finally payment of members of the First Chamber, who hitherto had not received any such emolument.

• For infinitely distant objects the radius of the chromatic disk of confusion is proportional to the linear aperture, and independent of the focal length (vide supra," Monochromatic Aberration of the Axis Point "); and since this disk becomes the less harmful with an increasing image of a given object, or with increasing focal length, it follows that the deterioration of the image is proportional to the ratio of the aperture to the focal length, i.e.

• This follows by considering equation (4) for the two pairs of colours ac and bc. Until recently no glasses were known with a proportional degree of absorption; but R.

• In using glasses not having proportional dispersion, the deviation of a third colour can be eliminated by two lenses, if an interval be allowed between them; or by three lenses in contact, which may not all consist of the old glasses.

• The twist or surface-shear being proportional to the torque, the horse-power can be calculated if the modulus of rigidity of the steel employed is known or if the amount of twist corresponding to a given power has previously been ascertained by direct experiment on the shaft before it has been put in place.

• The administrator is assisted by an executive committee of four persons elected from among its own members, or otherwise, by the provincial council on the proportional representation principle.

• Among the other decisions of the convention were: the choice of Pretoria as the seat of administration anti of Cape Town as the seat of the legislature, the renaming the Orange River Colony, Orange Free State Province; the provision of three membered constituencies and of proportional representation and the safe-guarding of the smaller communities by giving Natal and the Orange River colonies more members of parliament than they were entitled to on the voters basis.

• The draft act, with its " one vote one value " principle, its three-membered constituencies and its scheme for proportional representation, threatened Dutch supremacy in the rural districts, and aroused the opposition of Hofmeyr, who secured the passage of amendments through the Cape parliament which destroyed the principle of equal rights.

• Through the firmness of the Transvaal delegates, supported by the Progressives, the principle of equal rights was retained; the concession made to the Cape was the abandonment of proportional representation, while one-membered constituencies were substituted for three-membered constituencies.

• From this he showed that the rise of the liquid in tubes of the same substance is inversely proportional to their radii.

• He thus showed that at a curved part of the surface, a superficial particle would be urged towards the centre of curvature of the surface, and he gave reasons for concluding that this force is proportional to the sum of the curvatures of the surface in two normal planes at right angles to each other.

• If we suppose that the number of molecules within the range of the attraction of a given molecule is very large, the part of the pressure arising from attraction will be proportional to the square of the number of molecules in unit of volume, that is, to the square of the density.

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

• If the three fluids can remain in contact with one another, the sum of any two of the 3 quantities must exceed the third, and T 31 I by Neumann's rule the directions of the interfaces at the common edge must be parallel to the sides of a triangle, taken proportional to T12, T23, T31.

• (52) According to (52), the interfacial tension between any two bodies is proportional to the square of the difference of their densities.

• The problem is to make the sum of the interfacial tensions a minimum, each tension being proportional to the square of the difference of densities of the two contiguous liquids in question.

• p. 176, 1864), whose experiments led him to the conclusion that " other things being the same, the weight of a drop of liquid is proportional to the diameter of the tube in which it is formed."

• If This Condition Be Satisfied, The Mass (Or Weight) Of The Drop Is Proportional To T And To A.

• For All Fluids And For All Similar Tubes Similarly Wetted, The Weight Of A Drop Would Then Be Proportional Not Only To The Diameter Of The Tube, But Also To The Superficial Tension, And It Would Be Independent Of The Density.

• For a given fluid and a given orifice the length is approximately proportional to the square root of the head.

• When the head is given, Savart found the length to be proportional to the diameter of the orifice.

• The interval from one swelling to the next is the space described by the drop during one complete vibration,and is therefore (as Plateau shows) proportional ceteris paribus to the square root of the head.

• In so far as the vibrations may be regarded as isochronous, the distance between consecutive corresponding points of the recurrent figure, or, as it may be called, the wavelength of the figure, is directly proportional to the velocity of the jet, i.e.

• If K is the height of the flat surface of the drop, and k that of the point where its tangent plane is vertical, then T = 1(K - k) 2gp. Quincke finds that for several series of substances the surfacetension is nearly proportional to the density, so that if we call Surface-Tensions of Liquids at their Point of Solidification.

• If we place the base of the filament in each case on a base line in the order of the successive times of observation recorded, and at distances apart proportional to the intervals of time (8.30, 10.0, 10.30, 11.40, and so on) and erect the straightened-out filaments, the proportional length of each of which is here given for each period, a line joining the tips of the filaments gives the curve of growth.

• Since the circumference of a circle is proportional to its radius, it follows that if the ratio of the radii be commensurable, the curve will consist of a finite number of cusps, and ultimately return into itself.

• Those with the smallest proportional cultivated area are Westmorland, Middlesex, Northumberland, Surrey, Cumberland, the North and West Ridings of Yorkshire, Lancashire, Durham and Cornwall.

• The counties comprising the greatest proportional amount of woodland fall into two distinct groups - Hampshire, Surrey, Sussex and Kent, with Berkshire and Buckinghamshire; Monmouth, Herefordshire and Gloucestershire.

• Cambridgeshire, lying almost wholly within the area of the Fens, has the smallest proportional area of woodland of any English county.

• The largest proportional size of the facial bones, and the great projection of the jaws, confer on the gorilla's skull its small facial angle and brutal character,while its teeth differ from man's in relative size and number of fangs.

• In his household he spent "every fortnight 40 bushels of corn, 20 bushels of malt and an ox, besides a proportional quantity of other kinds of provisions."

• The equations of surfaces of equal angular motion would be of the form r =R (i --6 cos 2 0), where e is proportional to the square of the angular motion, supposed small, and R increases as e diminishes.

• The earth would intercept an amount of it proportional to the solid angle it subtends at the sun; that is to say, it would receive a deposit of meteoric matter about one-tenth of a millimetre, of density say 2, over its whole surface in the course of the year.

• As the loss by evaporation is a deduction lying between a constant figure and a direct proportional to the rainfall, we should err on the safe side in assuming the flow in the second driest year to be increased proportionally to the rainfall, or by the difference between 63 and 87 equal to 24% of the mean of 50 years.

• But in determining the capacity of reservoirs intended to yield a supply of water equal to the mean flow of two, three or more years, the error, though on the safe side, caused by assuming the evaporation to be proportional to the rainfall, is too great to be neglected.

• The rate of increase of velocity towards any isolated aperture through which water passes into the side of a well sunk in a deep bed of sand is, in the neighbourhood of that aperture, inversely proportional to the square of the distance therefrom.

• The vertical distance above the line ab of any point in the dotted line dc is proportional to the vertical component of the compressive stress on the line ale assumed to vary uniformly from face to face, and similarly the vertical distance of any point in the3-dot-and-dash line ae above the line ab is proportional to the vertical component of the stress determined experimentally.

• Among the measures adopted were: a'law (of doubtful constitutionality) requiring legislators to vote for the people's choice for a United States senator - this was adopted by a vote of 69,668 to 21,162; a corrupt practices act, regulating the expenditure of moneys in political campaigns and limiting a candidate's expenses to onefourth of one year's salary; an amendment permitting the establishment of state institutions elsewhere than at the capital; an amendment changing the time of state elections from June to November; an amendment permitting the legislature to pass a law providing for proportional representation, i.e.

• amounts proportional to the magnitude of each, and in addition to cause a loss M due to the weights of the parts themselves.

• As an example we may take the case where a brake is provided offering a resistance, c R, proportional to the load sustained, and where the values a and b are small compared with unity.

• Various other arrangements of friction brakes have been devised to give a resistance proportional to the load.

• a certain irrational function of 0, and the theorem is that the co-ordinates x, y, z of any point of the given curve can be expressed as proportional to rational and integral functions of 0, ¢, that is, of 0 and a certain irrational function of 0.

• In particular if D =o, that is, if the given curve be unicursal, the transformed curve is a line, 4 is a mere linear function of 0, and the theorem is that the co-ordinates x, y, z of a point of the unicursal curve can be expressed as proportional to rational and integral functions of 0; it is easy to see that for a given curve of the order m, these functions of 0 must be of the same order m.

• If D =t, then the transformed curve is a cubic; it can be shown that in a cubic, the axes of co-ordinates being properly chosen, 4) can be expressed as the square root of a quartic function of 0; and the theorem is that the co-ordinates x, y, z of a point of the bicursal curve can be expressed as proportional to rational and integral functions of 0, and of the square root of a quartic function of 0.

• And so if D =2, then the transformed curve is a nodal quartic; 4 can be expressed as the square root of a sextic function of 0 and the theorem is, that the co-ordinates x, y, z of a point of the tricursal curve can be expressed as proportional to rational and integral functions of 0, and of the square root of a sextic function of 0.

• It is a form of the theorem for the case D = r, that the coordinates x, y, z of a point of the bicursal curve, or in particular the co-ordinates of a point of the cubic, can be expressed as proportional to rational and integral functions of the elliptic functions snu, cnu, dnu; in fact, taking the radical to be r -0 2 .r - k 2 0 2, and writing 8 =snu, the radical becomes = cnu, dnu; and we have expressions of the form in question.

• In fact in a unicursal curve the co-ordinates of a point are given as proportional to rational and integral functions of a parameter, so that any point of the curve is determined uniquely by means of this parameter; that is, to each point of the curve corresponds one value of the parameter, and to each value of the parameter one point on the curve; and the (a, t3) correspondence between the two points is given by an equation of the form MO, I) u (4), 01 3 =0 between their parameters 0 and 4); at a united point 4)=0, and the value of 0 is given by an equation of the order a+ 0.

• 9), and covered with the purifying material B to a depth of about 6 in., the number of tiers and size of purifier boxes being proportional to the quantity of gas to be purified.

• The latter class of members as well as those for Stuttgart are elected on the principle of proportional representation.

• This is further borne out by the percentages given in the above table, from which it will be seen that the greatest proportional decrease of population has occurred in the two provinces of Munster and Connaught, which may be regarded as almost purely agricultural.

• F One more table may be given showing the proportional areas under the various kinds of crops, grass, woods and plantations, fallow, bog, waste, &c., over a series of years.

• As the result of emigration, which drains the Roman Catholic portion of the population more than any other, the Roman Catholics show a larger proportional decline in numbers than the Protestants; for example, between 1891 and 1901 the Roman Catholics decreased by over 6%, the Church of Ireland by a little over 3%, the Presbyterians by less than I %, while the Methodists actually increased by some I I %.

• that, all else being the same, the flux of heat is strictly proportional to the gradient of temperature.

• that, other things being alike, the strength of the current is at each point proportional to the gradient of potential.

• These figures are eight times in excess of the proportional result found for the whole of Persia.

• In intermediate cases the intensities of the two beams are proportional to the squares of the cosines of the angles that the principal plane of the second rhomb makes with the positions in which they have the greatest intensity.

• Further, if polarized light fall at the polarizing angle on a reflecting surface, the intensity of the reflected stream depends upon the azimuth of the plane of incidence, being proportional to the square of the cosine of the angle between this plane and the plane of the polarization.

• This result is not, however, conclusive; for an application of Huygens's principle shows that it is a consequence of the rotation of the plane of polarization by an amount proportional to the distance traversed, independently of the state of affairs within the active medium.

• From the leaning tower of Pisa he afforded to all the professors and students of the university ocular demonstration of the falsehood of the Peripatetic dictum that heavy bodies fall with velocities proportional to their weights, and with unanswerable logic demolished all the time-honoured maxims of the schools regarding the motion of projectiles, and elemental weight or levity.

• The effect is most easily shown by connecting a voltaic cell to a thermopile for a short interval, then quickly (by means of a suitable key, such as a Pohl commutator with the cross connectors removed) disconnecting the pile from the cell and connecting it to a galvanometer, which will indicate a current in the reverse direction through the pile, and approximately proportional to the original current in intensity, provided that the other conditions of the experiment are constant.

• of the couple should be directly proportional to the difference of temperature between the junctions.

• (2) If the Peltier effect was proportional to the thermoelectric power and changed sign with it, as all experiments appeared to indicate, there would A B be no absorption of heat C in the circuit due to the Peltier effect, and therefore no thermal source to account for the energy of the current, in the case in which the hot junction was at or above the neutral temperature.

• Edin., 1867-68), Tait was led to the conclusion that " the thermal and electric conductivities of metals varied inversely as the absolute temperature, and that the specific heat of electricity was directly proportional to the same."

• p. 201, 1867) made a number of relative measurements of the effect in different metals, which agreed qualitatively with observations of the thermoelectric power, and showed that the effect was proportional to the current for a given temperature gradient.

• The general results of the work appeared to support Tait's hypothesis that the effect was proportional to the absolute temperature, but direct thermoelectric tests do not appear to have been made on the specimens employed, which would have afforded a valuable confirmation by the comparison of the values of d 2 E/dT 2, as in Jahn's experiments.

• It is assumed that a flow of heat Q, due to conduction, tends to carry with it a proportional electric current C = aQ.

• Thus Canovas meant to keep up the appearance of a constitutional and parliamentary government with what most Spaniards considered a fair proportional representation of existing parties, except the Carlists and the most advanced Republicans, who only crept into the House of Deputies in some later parliaments.

• The latter possibility is also suggested by the curious fact that the visibility of the light does not seem to be proportional to the transparency of the atmosphere.

• These are: (1) that the friction is proportional to the normal pressure between the surfaces of contact, and therefore independent of the area of those surfaces, and (2) that it is independent of the velocity with which the surfaces slide one on the other.

• Both at very high and very low pressures the coefficient of friction is affected by the intensity of pressure, and, just as with velocity, it can only be regarded as independent of the intensity and proportional simply to the total load within more or less definite limits.

• The brightnesses of image points in a median section of the pencil are proportional to the aperture of the lens, supposing that the rays are completely reunited.

• Stokes, and which were published in the Proceedings of the Royal Society for 1855, that he discussed the mathematical theory of signalling through submarine cables, and enunciated the conclusion that in long cables the retardation due to capacity must render the speed of signalling inversely proportional to the square of the cable's length.

• The relation then between the work expended and the actual cooling work performed denotes the efficiency of the process, and this is expressed by Qt/(Q2-Q1); but as in a perfect refrigerating machine it is understood that the whole of the heat Q i is taken in at the absolute temperature T 11 and the whole of the heat Q2, is rejected at the absolute temperature T2, the heat quantities are proportional to the temperatures, and the expression T,/(T 2 -T,) gives the ideal coefficient of performance for any stated temperature range, whatever working substance is used.

• According to the Cartesians, this quantity was directly proportional to velocity; according to their opponents, it varied with the square of the velocity.

• The issue is whether the violence used in self-defense was proportional to the harm inflicted and to the reasonable apprehension of future harm.

• But the most important thing the centre-left coalition might achieve is proportional representation.

• collimated proportional counter filled with argon and carbon dioxide.

• The phosphorus in solution reacts with the molybdate ion to produce a blue coloration whose intensity is directly proportional to the concentration of phosphorus.

• The strategy is based on the latest research that suggests creatine's benefits are proportional to intracellular creatine concentrations  .

• The rate of formation of HbA 1c is proportional to the blood glucose concentration.

• constituencyes to the Assembly of the Republic are elected by proportional representation through a system of party lists in 11 multi-member constituencies.

• contend therefore that FESCO are acting in pursuit of the precautionary principle rather than on a proportional basis.

• Continental Congress of the peoples of Europe, elected by universal suffrage and proportional representation.

• For a single-chamber, executive and legislative, Continental Congress of the peoples of Europe, elected by universal suffrage and proportional representation.

• The properties are important in proportional counters, ionization chambers, drift chambers and in the prediction of the electrical breakdown of gases.

• drift velocity is proportional to E / N.

• exigencyfurthermore debatable whether the measures of internment are strictly proportional to the exigencies required by the situation.

• All the digits 0 to 9 have the same width in a proportional font.

• Hazard ratios were calculated using Cox proportional hazard ratios were calculated using Cox proportional hazards models that adjusted for potential confounders.

• inductor current is actually proportional to the derivative (or gradient) of the capacitor voltage.

• The position of the T2 servo is established by the liquid-filled bellows which positions the servo directly proportional to the compressor inlet temperature.

• Use the complex amplitude to calculate a quantity proportional to the measured irradiance.

• linearity of the transfer function is inversely proportional to the sensitivity.

• magnetic flux was inversely proportional to twice the charge on an electron.

• magnitude of the vector is proportional to the strength of the rotation.

• monopropellant required by the starter is proportional to the length of time the starter is operating.

• The first term, k P n reflects the reproduction tendency, which is proportional to the population.

• Member for North-East Hertfordshire experienced halfway through his speech, when he became peevish about proportional representation.

• The constant power throughout the entire speed range produces a torque curve inversely proportional to the speed.

• This method iterates over the entire collection, hence it requires time proportional to the size of the collection.

• This simple wall, or in some cases, flowmeter mounted instrument gives an analog output proportional to flow.

• Moving an iterator from one part of the sequence to another takes time proportional to the number of elements between the two.

• The default numerical method used by NEURON produces values which have an error proportional to dt.

• This definition also makes optical depth proportional to the amount of obscuring stuff along the line of sight.

• proportional to flow.

• proportional to distance.

• proportional representation nor the right to recall MPs.

• proportional counter is somewhat like a fluorescent light tube in reverse.

• proportional font.

• proportional spacing.

• proportional valves up to 4A ), including isolated supply to any sensor.

• proportional hazards regression to describe survival.

• An AR spectrum's peaks are not linearly proportional to power.

• The time required is roughly proportional to the number of elements in Z.

• The amount of travel will be directly proportional to the value of the sale.

• Timing Approximately proportional to the number of FITS keywords to be edited.

• The only way to guarantee that the council / assembly is broadly representative of the community is to have a broadly proportional electoral system.

• In other EU countries, including those using proportional representation, voters can specify candidates at European elections.

• One hundred and twenty-nine MSPs make up the Parliament, which is elected by proportional representation.

• Rabies The risk to travelers in endemic areas is proportional to their exposure to potentially rabid animals.

• reactance x s is to a good approximation proportional to f.

• Why our MSP wants to foist proportional representation on us I do not understand.

• The MECS (1-10 keV) is an imaging gas scintillation proportional counter similar to the LECS.

• Non proportional spacing Fonts in which letter spacing which does not vary for different width of character.

• The total numbers of condoms used by each couple were used to derive proportional failure rates with and without additional spermicide.

• tachometer generator -- device that supplies power at a frequency proportional to the driven speed which drives the synchronous motors in the indicator.

• New implementations of TCP rely on the theory that the loss rate is proportional to the TCP throughput.

• For very low E / N, the drift velocity is proportional to E / N.