Proportional Sentence Examples

This loss is proportional to the length of the wire.

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

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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

These are proportional to the capacities.

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.

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.

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.

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 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.

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.

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.

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 ECÆF.

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.

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.

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.

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 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.

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.

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.

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.

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.

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 ..

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.

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.

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.

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.'

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.

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."

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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 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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 %.

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.

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.

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.

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 [13] .

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

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.

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.

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.

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.

The loading time is inversely proportional to the part load.

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

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.

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.

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

The object is to compare the intensities of the incident and scattered light, for these will clearly be proportional.

It is equally evident that i varies as T, and therefore that it must be proportional to T/Xr, T being of three dimensions in space.

Any diameter is a mean proportional between the transverse axis and the focal chord parallel to the diameter.

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

By dividing a line into two halves the working speed will be dependent upon the KR of the longest half, and as both K and R are directly proportional to the length of the line, the KR product for the half of a circuit is but one quarter that of the whole length of the circuit, and the retardation is correspondingly small.

In the migration of birds we are still uncertain asto the exact nature and proportional value of the instinctive and intelligent factors.

Duties on profession (temettu) consist (a) of a fixed duty leviable at rates declared in a schedule forming part of the special law (Dec. 8, 1907) regulating the tax, and (b) of a proportional duty at the rate of 3% on the value of buildings occupied by companies or individuals in the prosecution of their business; of 3% on salaries (subject to certain deductions) of employes of such companies and individuals; and on government contractors and revenue farmers, at the rate of 3% of 10% of the value of contracts filled and of revenues farmed.

If we eliminate the reverse electromotive forces of polarization at the two electrodes, the conduction of electricity through electrolytes is found to conform to Ohm's law; that is, once the polarization is overcome, the current is proportional to the electromotive force applied to the bulk of the liquid.

This illustrates the first stage in the process of magnetization, when the moment is proportional to the field and there is no hysteresis or residual magnetism (see ante).

Now the effect upon P of each element of the plane is proportional to its area; but it depends also upon the distance from P, and possibly upon the inclination of the secondary ray to the direction of vibration and to the wave-front.

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

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

The assumption usually made is that the total kinetic energy of the molecules, including possible energy of rotation or vibration if the molecules consist of more than one atom, is proportional to the energy of translation in the case of an ideal gas.

The proof that the area of a circle is proportional to the square of its diameter would therefore precede the proof that the perimeter is proportional to the diameter; the former property is the easier to grasp, since the conception of the length of a curved line as the limit of the sum of a number of straight lengths presents special difficulties.

The core of the electromagnet is worked at a point far below magnetic saturation (see Magnetism); hence the field is nearly proportional to the square of the current, and the resistance offered to the rotating mercury by the friction against the sides of the cavity is nearly proportional to the square of the speed.

If an electro-dynamometer, made as above described, has its fixed circuit connected in series with the power-absorbing circuit and its movable coil (wound with fine wire) connected across the terminals of the power-absorbing circuit, then a current will flow through the fixed coil which is the same or nearly the same as that through the power-absorbing circuit, and a current will flow through the high resistance coil of the wattmeter proportional to the potential difference at the terminals of the power-absorbing circuit.

It is very evident that no mere hint with regard to the use of proportional numbers could have been of any service to him, but it is possible that the news brought by Craig of the difficulties placed in the progress of astronomy by the labour of the calculations may have stimulated him to persevere in his efforts.

In a diffraction spectrum the diffraction is proportional to the wavelength, and the spectrum is said to be "normal."

Rectification and quadrature of the circle have thus been, since the time of Archimedes at least, practically identical problems. Again, since the circumferences of circles are proportional to their diameters - a proposition assumed to be true from the dawn almost of practical geometry - the rectification of the circle is seen to be transformable into finding the ratio of the circumference to the diameter.

On this view, the function of the solvent is to give space for the solute to diffuse, and the pressure on a semi-permeable membrane is due to the excess of solvent molecules entering over those leaving in consequence of the smaller number which impinge on the membrane from the side of the solution; the defect in the number must be proportional, roughly at any rate, to the number of solute molecules, present, that is, to the strength of the solution.

Reinders (Ber., 1896, 29, p. 1369, 1899) have shown that the transformation is a monomolecular reaction, the velocity of transformation in moderately dilute solution being independent of the concentration, but proportional to the amount of the catalyst present (amine hydrochloride) and to the temperature.

If we imagine 0 to recede to infinity in any direction we learn that a system of parallel forces proportional to nh, mi,.

In order to obtain at all events a qualitative representation of these it is usual to introduce into thc equations frictional terms proportional to the velocities.

But there are cases in which the motions of both bodies are appreciable, and must be taken into accountsuch as the projection of projectiles, where the velocity of the recoil or backward motion of the gun bears an appreciable proportion to the forward motion of the projectile; and such as the propulsion of vessels, where the velocity of the water thrown backward by the paddle, screw or other propeller bears a very considerable proportion to the velocity of the water moved forwards and sideways by the ship. In cases of this kind the energy exerted by the effort is distributed between the two bodies between which the effort is exerted in shares proportional to the velocities of the two bodies during the action of the effort; and those velocities are to each other directly as the portions of the effort unbalanced by resistance on the respective bodies, and inversely as the weights of the bodies.

His invention of the proportional compass or sector - an implement still used in geometrical drawing - dates from 1597; and about the same time he constructed the first thermometer, consisting of a bulb and tube filled with air and water, and terminating in a vessel of water.

The range of Steele's observations was too small to show any certain deviation from the formula, but he notes capricious changes attributed to change of condition of the proved to be proportional to the square of the current, the Peltier effect is reversible with the current, and being directly proportional to the first power of the current, changes sign when the current is reversed.

Also the surface reactance X s is to a good approximation proportional to f.

Analyzes involved proportional hazards modeling and adjustment for confounding by known cardiovascular risk factors and for regression dilution bias.

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

However, in real terms the reduction of tied aid has not resulted in a proportional increase of untied aid.

Why is viscous drag said to be proportional to velocity?