This loss is proportional to the length of the wire.
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.
The proportional rent is from I% to 5:/.
So if a battle today were similarly costly, the proportional number of casualties would be 230,000.
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 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.
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.
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.
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.
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.
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.
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.
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.
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 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.
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.
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).
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.
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.
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 violence or completeness of combustion was proportional to the amount of phlogiston present.
7V k / R, and since Vk is proportional to the volume at absolute zero, the ratio T k /P k should exhibit additive relations.
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.
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.
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.;.
Two categories of rent, fixed and proportional, are payable to the state by mineowners.
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.
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.
(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.
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.
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.
He found that the amounts of the substances liberated in each cell were proportional to the chemical equivalent weights of those substances.
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.
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.
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.
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.
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.
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 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.
This causes a ballistic throw proportional to the induction through the bar at the moment when the two portions were separated.
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.
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.
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.
It is probable that the wind pressure is not strictly proportional to the extent of the surface exposed.
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?
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."