# How to use Ratio in a sentence

ratio
• The ratio of criminal proceedings to population is, as a rule, much higher in the south than in the north.

• This equation does not give us the value of the unknown factor but gives us a ratio between two unknowns.

• In the election of 1896 all the parties in the state declared in favour of the free and unlimited coinage of silver at the ratio of 16 to 1.

• The ratio "weight to volume" is the absolute density.

• In the latter he advocated the unlimited coinage of silver, irrespective of international agreement, at a ratio of 16 to 1, a policy with which his name was afterwards most prominently associated.

• The theoretical element is the ratio of the parallactic inequality to the solar parallax.

• The determination of this ratio is one of the most difficult problems in the lunar theory.

• If the magnet is not uni - form, the magnetization at any point is the ratio of the moment of an element of volume at that point to the volume itself, or I = m.ds/dv.

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

• The ratio I/H is called the susceptibility of the magnetized substance, and is denoted by «.

• The ratio of the residual magnetization to its previous maximum value measures the retentiveness, or retentivity, of the metal.'

• The ratio M/H is then found by one of the magnetometric methods which in their simplest forms are described below.

• It is often sufficient to find the ratio of the moment of one magnet to that of another.

• If the cardboard scale upon which the beam of light is reflected by the magnetometer mirror is a flat one, the deflections as indicated by the movement of the spot of light are related to the actual deflections of the needle in the ratio of tan 20 to 0.

• The specimen upon which an experiment is to be made generally consists of a wire having a " dimensional ratio " of at least 300 or goo; its length should be rather less than that of the magnetizing coil, in order that the field Ho, to which it is subjected, may be approximately uniform from end to end.

• 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.

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

• Archimedes' problem of dividing a sphere by a plane into two segments having a prescribed ratio,was first expressed as a cubic equation by Al Mahani, and the first solution was given by Abu Gafar al Hazin.

• Rabelais not only lectured on Galen and Hippocrates, but edited some works of the latter; and Michael Servetus (1511-1553), in a little tract Syruporum universa ratio, defended the practice of Galen as compared with that of the Arabians.

• Libitina was the goddess of funerals; her officers were the Libitinarii our undertakers; her temple in which all business connected with the last rites was transacted, in which the account of deaths - ratio Libitinae - was kept, served the purpose of a register office."

• To prevent excessive bending stresses the diameter of drum and sheave must bear a proper ratio to that of the rope.

• Thus, at every complete stroke of the piston, the air in the vessel or receiver was diminished by that fraction of itself which is expressed by the ratio of the volume of the available cylindrical space above the outward opening valve to the whole volume of receiver, nozzle and cylinder.

• He had discovered a contraction in the vein of fluid (vena contracta) which issued from the orifice, and found that, at the distance of about a diameter of the aperture, the section of the vein was contracted in the subduplicate ratio of two to one.

• It is used to determine the density of a body experimentally; for if W is the weight of a body weighed in a balance in air (strictly in vacuo), and if W' is the weight required to balance when the body is suspended in water, then the upward thrust of the liquid (I) (2) "F r an Minim ' 'i n or weight of liquid displaced is W-W, so that the specific gravity (S.G.), defined as the ratio of the weight of a body to the weight of an equal volume of water, is W/(W-W').

• The extension to the case where the liquid is bounded externally by a fixed ellipsoid X= X is made in a similar manner, by putting 4 = x y (x+ 11), (io) and the ratio of the effective angular inertia in (9) is changed to 2 (B0-A0) (B 1A1) +.a12 - a 2 +b 2 a b1c1 a -b -b12 abc (Bo-Ao)+(B1-A1) a 2 + b 2 a1 2 + b1 2 alblcl Make c= CO for confocal elliptic cylinders; and then _, 2 A? ?

• C - a 2 - 2 b2 +A, = and then as above in § 31, with a= c ch a, b=c sh a, a =-1 (a 2 +X) =c ch al, b1= c sh a (13) the ratio in (II) agrees with § 31 (6).

• I +W a W a), ' (k) 4 (I I) I+ w- R For a shot in air the ratio W'/W is so small that the square may be neglected, and formula (II) can be replaced for practical purpose in artillery by tan26= n2 = W i (0 - a) (k ð)7()4, (12) if then we can calculate /3, a, or (3-a for the external shape of the shot, this equation will give the value of 6 and n required for stability of flight in the air.

• The ratio of cases to population living in Dublin on loose porous gravel soil for the ten years1881-1891was I in 94, while that of those living on stiff clay soil was but 1 in 145.

• Although the double standard was in force, gold was practically demonetized by the monetary reform of 1872 because of the failure to fix a legal ratio between the two metals.

• If M 1, M2, and P 1, P 2 be the molecular weights and vapour pressures of the components A and B, then the ratio of A to B in the distillate is M 1 P 1 /M 2 P 2.

• P 1 greater than P2, if the molecular weight of A be much less than that of B, then it is obvious that the ratio M 1 P 1 /M 2 P 2 need not be very great, and hence the less volatile liquid B would come over in fair amount.

• These con-, ditions pertain in cases where distillation with steam is successfully practised, the relatively high volatility of water being counterbalanced by the relatively high molecular weight of the other component; for example, in the case of nitrobenzene and water the ratio is I to 5.

• It will be observed that the coast-line is very long in proportion to the area, the ratio being 1 m.

• Males exceed females in the ratio of 2% approximately.

• In the first place, the ratio of the heighi of his head to the length of his body is greater than it is in Euro peans.

• The Englishmans head is often one-eighth of the lengtl of his body or even less, and in continental Europeans, as a rule the ratio does not amount to one-seventh; but in the Japanese it exceeds the latter figure.

• In northern Europeans the leg is usually much more than onehalf of the bodys length, but in Japanese the ratio is one-half or even less; so that whereas the Japanese, when seated, looks almost as tall as a European, there may be a great difference between their statures when both are standing.

• The ratio of marriages is approximately 8.46 per thousand units of the population, and the ratio of divorces is 1.36 per thousand.

• Since of a the capacity C is the ratio of charge to potential, the sphere.

• In the absolute determination of capacity we have to measure the ratio of the charge of a condenser to its plate potential difference.

• If one condenser is charged, and then joined in parallel with another uncharged condenser, the charge is divided between them in the ratio of their capacities.

• He constructed two equal condensers, each consisting of a metal ball enclosed in a hollow metal sphere, and he provided also certain hemispherical shells of shellac, sulphur, glass, resin, &c., which he could so place in one condenser between the ball and enclosing sphere that it formed a condenser with solid dielectric. He then determined the ratio of the capacities of the two condensers, one with air and the other with the solid dielectric. This gave the dielectric constant K of the material.

• Blaine, on the other hand, contended that representation should be based on population instead of voters, as being fairer to the North, where the ratio of voters varied widely, and he insisted that it should be safeguarded by security for impartial suffrage.

• Then by relations (2) the heat, H, absorbed in the isothermal change BC, is to the work, W, done in the cycle ABCD in the ratio of o to (o' - o").

• 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 often impossible to observe the pressure-coefficient dp/de directly, but it may be deduced from the isothermal compressibility by means of the geometrically obvious relation, BE = (BEÃ†C) XEC. The ratio BEÃ†C of the diminution of pressure to the increase of volume at constant temperature, or - dp/dv, is readily observed.

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

• In thiscase the ratio of the specific heats is constant as well as the difference, and the adiabatic equation takes the simple form, pv v = constant, which is at once obtained by integrating the equation for the adiabatic elasticity, - v(dp/dv) =yp.

• They are continually changing partners, the ratio c/V representing approximately the ratio of the time during which any one molecule is paired to the time during which it is free.

• The atomic weight of gold was first determined with accuracy by Berzelius, who deduced the value 195.7 (H= i) from the amount of mercury necessary to precipitate it from the chloride, and 195.2 from the ratio between gold and potassium chloride in potassium aurichloride, KAuC1 4.

• The density gives very important information as to the molecular weight, since by the law of Avogadro it is seen that the relative density is the ratio of the molecular weights of the experimental and standard gases.

• This, the only coin minted by the government, should bear a fixed ratio of l000 cash to one tael of silver, but in practice there is no such fixed value.

• Syruporum universa ratio, &c. (Paris, 1537); four subsequent editions; latest, Venice, 1548 (six lectures on digestion; syrups treated in fifth lecture).

• Such a simple formula is only possible because the salts of sea-water are of such uniform composition throughout the whole ocean that the chlorine bears a constant ratio to the total salinity as newly defined whatever the degree of concentration.

• When, however, the air is present in much smaller ratio the combustion is incomplete, and carbon, carbon monoxide, carbon dioxide, hydrogen and water vapour are produced.

• The ratio p is given by e"` e, where e= 2.718; µ is the coefficient of friction and 0 the angle, measured in radians,, subtended by the arc of contact between the rope and the wheel.

• The ratio W/p increases very rapidly as 0 is increased,, and therefore, by making 0 sufficiently large, p may conveniently be made a small fraction of W, thereby rendering errors of observation of the spring balance negligible.

• The marriage rates in quinquennial periods up to 1905 were 19.6, 18.6, 21.0, 19.8, 15.6, 18.6, 18.6, 18.6, 17.4 and 17.4; the ratio of marriages to the marriageable population was for males (above 16 years) 61.5, for females (above 14) 46.0; the fecundity of marriages seemed to have increased, being about twice as high for foreigners as for natives.

• For cities of above 8000 inhabitants (for which alone comparative statistics are annually available), in 1902-1903 the ratio of average attendance to school enrolment, the average number of days' attendance of each pupil enrolled, and the value of school property per capita of pupils in average attendance were higher than in any other state; the average length of the school term was slightly exceeded in eight states; and the total cost of the schools per capita of pupils in average attendance (\$39.05) was exceeded in six other states.

• Thus, the gases are not present in simple multiples of their combining weights; atmospheric air results when oxygen and nitrogen are mixed in the prescribed ratio, the mixing being unattended by any manifestation of energy, such as is invariably associated with a chemical action; the gases may be mechanically separated by atmolysis, i.e.

• The ratio 47r would thus first appear as the ratio of the average breadth of a circle to the greatest breadth; the interpretation of 7 as the ratio of the circumference to the diameter being a secondary one.

• It is necessary, in applying formulae to specific cases, not only, on the one hand, to remember that the measurements are only approximate, but also, on the other hand, to give to any ratio such as 7r a value which is at least more accurate than the measurements.

• Denoting the constant ratio by fir, the area of a circle is ira 2, where a is the radius, and ir=3.14159 approximately.

• In the case of a wedge with parallel ends the ratio x2/h2 is replaced by x/h.

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

• The exact position of the core, and, therefore, of an index needle connected with it, is dependent on the ratio of the voltage applied to the terminals of the high resistance or insulator and the current passing through it, This, however, is a measure of the insulation-resistance.

• Hence the resistance of the insulator can be ascertained, since it is expressed in ohms by the ratio of the voltage of the battery in volts to the current through the C C galvanometer in amperes.

• Male factory hands greatly outnumbered female, standing in the ratio of four to one.

• Let E be the bulk modulus of elasticity, defined as increase of pressure = decrease of volume per unit volume where the pressure increase is so small that this ratio is constant, w the small increase of pressure, and - (dy/dx) the volume decrease, then E=e/(- dy/dx) or w Ã†= - dy/dx (I) This gives the relation between pressure excess and displacement.

• Experiments, which will be described most conveniently when we discuss methods of determining the frequencies of sources, prove conclusively that for a given note the frequency is the same whatever the source of that note, and that the ratio of the frequencies of two notes forming a given musical interval is the same in whatever part of the musical range the two notes are situated.

• 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.

• Or, if the same plate be moved in contact with two tuning-forks, we shall, by comparing the number of sinuosities in the one trace with that in the other, be enabled to assign the ratio of the corresponding numbers of vibrations per second.

• A mode of exhibiting the ratio of the frequencies of two forks was devised by Jules Antoine Lissajous (1822-1880).

• If two such flames are placed one under the other they may be excited by different sources, and the ratio of the frequencies may be approximately determined by counting the number of teeth in each in the same space.

• Kundt's dust-tube may also be employed for the determination of the ratio of the specific heats of a gas or vapour.

• If U is the velocity of sound in a gas at pressure P with density p, and if waves of length X and frequency N are propagated through it, then the distanc?e l between the dust-heaps is 2 = N - zN Vyp' where y is the ratio of the two specific heats.

• The rainfall is sufficient for good grazing, but except in the Flathead valley cultivation was long considered to be dependent on irrigation; and consequently farming was only incidental to stock raising and mining until after 1870, and as late as 1900 the ratio of improved farm land to the total land area was less than in any other state or territory except New Mexico, Wyoming, Arizona and Hawaii.

• But with the sole exception of proving that the volumes of spheres are in the triplicate ratio of their diameters, a theorem probably due to Eudoxus, no mention is made of its mensuration.

• It would be economical, therefore, to make the girder very deep. This, however, involves a much heavier web, and therefore for any type of girder there must be a ratio of depth to span which is most economical.

• The actual bridge must have the section of all members greater than those in the provisional design in the ratio k/(i -k).

• It was pointed out as early as 1869 (Unwin, Wrought Iron Bridges and Roofs) that a rational method of fixing the working stress, so far as knowledge went at that time, would be to make it depend on the ratio of live to dead load, and in such a way that the factor of safety for the live load stresses was double that for the dead load stresses.

• Let A be the dead load and B the live load, producing stress in a bar; p =B / A the ratio of live to dead load; f i the safe working limit of stress for a bar subjected to a dead load only and f the safe working stress in any other case.

• To prevent temperature from affecting the shunt ratio, Edison joined in series with the electrolytic cell a copper coil the resistance of which increased with a rise of temperature by the same amount that the electrolyte decreased.

• On the ground that the aim of every prosperous community should be to have a large proportion of hardy country yeomen, and that horticulture and agriculture demand such a high ratio of labour, as compared with feeding and breeding cattle, that the country population would be greatly increased by the substitution of a fruit and vegetable for an animal dietary.

• Lord Kelvin assumed as a superior limit of k, the ratio of amplitude to wave-length, the value io 2, which is a very safe limit.

• But it is found not to vary at all, even up to the second order of the ratio of the earth's velocity to that of light.

• This theory secures that the times of passage of the rays shall be independent of the motion of the system, only up to the first order of the ratio of its velocity to that of radiation.

• Aristotelian dialectics had always been taught in the schools; and reason as well as authority had been appealed to as the foundation of theology; but for the theologians of the 9th and 10th centuries, whose method had been merely that of restatement, ratio and auctoritas were in perfect accord.

• But the maximum pressure may exceed the mean in the ratio of 2 or 3 to I, as shown in fig.

• The other ratio of Revillout and Hultsch, 320 hons = cubit cubed, is certainly approximate.

• The log and kab are not found till the later writings; but the ratio of hin to issaron is practically fixed in early times by the proportions in Num.

• We may perhaps see the sense of this ratio through another system.

• Suppose that the ratio of 10, or any other particular number, to i is compounded of a very great number of equal ratios, as, for example, 1,000,000, then it can be shown that the ratio of 2 to i is very nearly equal to a ratio compounded of 301,030 of these small ratios, or ratiunculae, that the ratio of 3 to I is very nearly equal to a ratio compounded of 477,121 of them, and so on.

• The Ratio Studiorum took its shape during this time.

• If the refracting angleof the prism is small, then the ratio of the dispersion to the mean deviation of the two rays is the dispersive power of the material of the prism.

• The form of the limacon depends on the ratio of the two constants; if a be greater than b, the curve lies entirely outside the circle; if a equals b, it is known as a cardioid; if a is less than b, the curve has a node within the circle; the particular case when b= 2a is known as the trisectrix.

• This extraordinary production is memorable as having announced the discovery of the "third law" - that of the sesquiplicate ratio between the planetary periods and distances.

• An ingenious, though ineffective, proposal for the reform of the calendar was put forward in his Elenchus Calendarii Gregoriani (Frankfort, 1612); and he published a book on music, Melodiae condendae ratio (Erfurt, 1592), still worth reading.

• In the North there was little difference in 1900 in the ratios shown by city and country districts, but in the South the ratio in the latter was almost twice that reported for the former.

• In Alabama (70.8% in 1880), North and South Carolina, amid Arkansas the ratio exceeded 5o% in 1900.

• It may be readily shown that the external and internal centres are the points where the line joining the centres of the two circles is divided externally and internally in the ratio of their radii.

• It may be shown to be the locus of the vertex of the triangle which has for its base the distance between the centres of the circles and the ratio of the remaining sides equal to the ratio of the radii of the two circles.

• All exact relations pertaining to the mensuration of the circle involve the ratio of the circumference to the diameter.

• This ratio, invariably denoted by 7r, is constant for all circles, but it does not admit of exact arithmetical expression, being of the nature of an incommensurable number.

• Probably the earliest value for the ratio was 3.

• Accordingly, we find in Vieta a formula for the ratio of diameter to circumference, viz.

• His book, Van den Circkel (Delft, 1596), gave the ratio correct to 20 places, but he continued his calculations as long as he lived, and his best result was published on his tombstone in St Peter's church, Leiden.

• This gives the ratio correct to 35 places.

• In Germany the "Ludolphische Zahl " (Ludolph's number) is still a common name for the ratio.

• Grienberger, using Snell's method, calculated the ratio correct to 39 fractional places. ?

• About the same time John Machin calculated it correct to Ioo places, and, what was of more importance, gave for the ratio the rapidly converging expression 4 _ I I 5 I 3152+ 5 1 54 - 7 1 5b?.

• This achievement was anticipated or outdone by an unknown calculator, whose manuscript was seen in the Radcliffe library, Oxford, by Baron von Zach towards the end of the century, and contained the ratio correct to 152 places.

• From the city of Quebec westwards there is a constantly increasing ratio of southern forms, and when the mountain (so called) at Montreal is reached the representative Ontario flora begins.

• For the computation of the Christian date, the ratio of a mean year of the Hegira to a solar year is Year of Hegira 354s =0.970224.

• If V = N/A then N expresses the ratio of the volume of the instrument up to the zero of the scale to that of one of the scale-divisions.

• The total trade of the port increased from £3,853,593 in 1897 to £5, 6 75, 28 5 in 1905 and £7,009,758 in 1906 (the large increase being mainly due to a rise of over Li,000,000 in imports - mainly of coal, building materials and machinery), the average ratio of imports to exports being as three to two.

• Thus weighting, which was until recently thought to apply only to black silks, and from which coloured silks were comparatively free, is now cheapening and deteriorating the latter in pretty much the same ratio as the former.

• Bradley recognized the fact that the experimental determination of the aberration constant gave the ratio of the velocities of light and of the earth; hence, if the velocity of the earth be known, the velocity of light is determined.

• Curiously enough this is also approximately the ratio of the displacements found by Humphreys in the trunk series, the side branch and main branch in the order named, in cases where these displacements have been measured.

• The fact that in certain simple cases where a line when looked at equatorially splits into a triplet, the ratio of the charge to the mass is found by Lorentz's theory to be equal to that observed in the carrier of the kathode ray, shows that in these cases the electron moves as an independent body and is not linked in its motion to other electrons.

• Pappus gives several solutions of this problem, including a method of making successive approximations to the solution, the significance of which he apparently failed to appreciate; he adds his own solution of the more general problem of finding geometrically the side of a cube whose content is in any given ratio to that of a given one.

• The change in the character of the immigration of Japanese is shown by the fact that in the fiscal year 1906-1907 the ratio of female immigrants to males was as i to 8, in the fiscal year 1907-1908 it was as I to 2, and in the latter year, of 4593 births in the Territory, 2445 were Japanese.

• He generalized Weber's law in the form that sensation generally increases in intensity as the stimulus increases by a constant function of the previous stimulus; or increases in an arithmetical progression as the stimulus increases in a geometrical ratio; or increases by addition of the same amount as the stimulus increases by the same multiple; or increases as the logarithm of the stimulus.

• 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.

• This angle depends on the ratio of the magnetic moment of the needle b to the total force of the earth's field.

• Hence the above observation gives us a means of obtaining the ratio of the magnetic moment of the needle' b to the value of the earth's total force.

• But if the bodies are of different substances, say one of iron and the other of gold, the ratio of these magnitudes is found to depend upon something else besides bulk.

• When, as in the case of contact, a mutual relation is perceived between the motions of two particles, the changes of velocity are in opposite directions, and the ratio of their magnitudes determines the ratio of the masses of the particles; the motion being reckoned relative to any base which is unaffected by the change.

• It is found that this gives a consistent result; that is to say, if by an experiment with two particles A and B we get the ratio of their masses, and by an experiment with B and a third particle C we get the ratio of the masses of B and C, and thus the ratio of the masses of A and C, we should get the same ratio by a direct experiment with A and C. For the numerical measure of mass that of some standard body is chosen as a unit, and the masses of other bodies are obtained by comparison with this.

• The various expansions and developments have made it difficult to maintain the ratio between accommodation and requirements, and although overcrowding is troublesome only during some three or four hours a week, at "high 'Change" on market days, various complaints and suggestions provoked in 1906 an appeal from the chairman of directors to the Manchester corporation.

• The relative lowering of vapour pressure of the solution compared with that of the solvent is measured by the ratio of the extra mass absorbed from the solvent bulbs to the total mass absorbed from both series of bulbs.

• Substituting these values, we find that the relative lowering of vapour pressure in a very dilute solution is equal to the ratio of the numbers of solute and solvent molecules, or (p - p')/p = n/N.

• Now measurements of osmotic properties of these solutions show that their osmotic pressures are abnormally great and that, at extreme dilution, the ratio of their osmotic pressures to that of equivalent solutions of non-electrolytes is equal to the number of ions indicated by the electrolytic properties.

• Let us assume that the ratio p/p' of the vapour pressures of the solvent and solution is equal to the ratio of the number of free molecules of solvent to the whole number of molecules in the solution.

• If there are n molecules of solute to N of solvent originally, and each molecule of solute combines with a molecule of solvent, we get for the ratio of vapour pressures p/p'=(N - an)/(N - an+n), while the relative lowering of vapour pressure is (p - p')/p=n/(N - an).

• The most remarkable physical property of argon relates to the constant known as the ratio of specific heats.

• The ratio of specific heats of the principal gases is I.

• If, as for Boscovitch points, the whole energy is translatory, the ratio of specific heats must be I.

• These gases agree with argon in respect of the ratio of the specific heats and in being non-oxidizable under the electric spark.

• This operation is varied in detail according to the kind of plant to be propagated, but it is essential in all cases that the affinity between the two plants be near, that the union be neatly effected, and that the ratio as well as the season of growth of stock and scion be similar.

• In 1561, at the age of fourteen, he produced a work upon Latin spelling, called Orthographiae ratio.

• It can be easily seen that this ratio, according to Henry's law, must correspond to that of vapour-pressures, and so be independent of the solvent; in fact, in alcohol the figures are o 0066 and o o052.

• The first desideratum here mentioned - the want, namely, of an accurate statement of the relation between the increase of population and food - Malthus doubtless supposed to have been supplied by the celebrated proposition that "population increases in a geometrical, food in an arithmetical ratio."

• The thermal conductivity of the substance is the constant ratio of the rate of transmission to the temperature gradient.

• If Q is expressed in terms of this unit in equation (I), it is necessary to divide by c, or to replace k on the right-hand side by the ratio k/c. This ratio determines the rate of diffusion of temperature, and is called the thermometric conductivity or, more shortly, the diffusivity.

• The diffusivity can be deduced from observations at different depths x' and x", by observing the ratio of the amplitudes, which is (x '- x ") for a simple-harmonic wave.

• The increase of resistance with temperature was also very small, so that the ratio varied very little with temperature.

• Lorenz, assuming that the ratio k/k'=aG, had previously given 0 2 maz Bo g = E2/4a, (12) which is practically identical with the preceding for small differences of temperature.

• Surface.In respect of physical structure Germany is divided into two entirety distinct portions, which bear to one another a ratio of about 3 to 4.

• In case of injury, involving incapacity for more than, thirteen weeks (for the earlier period the Krankenkassen provide), the weekly sum payable during complete or permanent incapacity is fixed at the ratio of two-thirds of the earnings during the year preceding the accident, and in case of partial disablement, at such a proportion of the earnings as corresponds to the loss through disablement.

• While the proportion of like weights of fine gold and fine silver in 1866-1870 averaged J to 1555, it was I to 17-79 in 1876, I to 17.18 in 1877, and, in 1902, in consequence of the heavy fall in silver, the ratio became as much as I to 39.

• The total number of bullocks in the island is calculated to be less than 200,000; and although the ratio of consumption of meat is low in proportion to the population, some of the cattle for slaughter have to be imported.

• The male sex remains in excess until about the twentieth year, from which age the female sex preponderates in increasing ratio with advancing age.

• Through this space the fresh surface water finds its way, and dissolving the salt below rises in the inner tube as brine, but only to such a level that the two columns bear to one another the relation of ten to twelve, this being the inverse ratio of the respective weights of saturated brine and fresh water.

• We see therefore that while leaves, gathered in equal numbers from each of loo trees, are distributed about their mean with a standard deviation of 1.735 veins, the leaves gathered from a single tree are distributed about their mean with a standard deviation of 1.426 veins, the ratio between variability of the race and variability of the individual tree being 1 - (0-5699)1=0.822.

• The births registered in Singapore during 1898 numbered 3751, namely, 1960 males and 1791 females, being a ratio of 16.55 per mille.

• The deaths registered during the same period numbered 7602, namely, 5894 males and 1708 females, a ratio of 33.54 per mille.

• Realizing that the total weight of all the products of a chemical reaction must be exactly equal to the total weight of the reacting substances, he made the balance the ultima ratio of the laboratory, and he was able to draw correct inferences from his weighings because, unlike many of the phlogistonists, he looked upon heat as imponderable.

• The tendency is for property valuations to decline, the estimated valuation from 1873 to 1893 decreasing 27% in Cook county and 39% in the other counties, while the assessments from 1888 to 1898 were in inverse ratio to the increase of wealth.

• This ratio will become more equal for larger sizes on account of the additional thickness of larger object-glasses and the consequent additional absorption of light in transmission.

• The specific heat of a substance is sometimes defined as the thermal capacity of unit mass, but more often as the ratio of the thermal capacity of unit mass of the substance to that of unit mass of water at some standard temperature.

• The ratio of the times of cooling is equal to the ratio of the thermal capacities of the calorimeter and its contents in the two cases.

• If The Molecules Are Supposed To Be Like Smooth, Hard, Elastic Spheres, Incapable Of Receiving Any Other Kind Of Energy Except That Of Translation, The Specific Heat At Constant Volume Would Be The Increase Per Degree Of The Kinetic Energy Namely 3Pv/20=3R/2, That At Constant Pressure Would Be 5R/2, And The Ratio Of The Specific Heats Would Be 5/3 Or 1.666.

• In 1879 Maxwell Considered It One Of The Greatest Difficulties Which The Kinetic Theory Had Yet Encountered, That In Spite Of The Many Other Degrees Of Freedom Of Vibration Revealed By The Spectroscope, The Experimental Value Of The Ratio S/S Was 1.40 For So Many Gases, Instead Of Being Less Than 4/3.

• The Theoretical Value Of The Ratio S/S In This Case Would Be The Required 7/5.

• It Is Not At All Clear, However, That Energy Of Vibration Should Bear A Constant Ratio To That Of Translation, Although This Would Probably Be The Case For Rotation.

• For Such Gases, Assuming A Constant Ratio Of Rotation To Translation, The Specific Heat At Low Pressures Would Be Very Nearly Constant.

• This Would Account For An Increase Of S, And A Diminution Of The Ratio S/S, With Rise Of Temperature Which Apparently Occurs In Many Vapours.

• The Direct Methods Of Measuring The Ratio S/S, By The Velocity Of Sound And By Adiabatic Expansion, Are Sufficiently Described In Many Text Books.

• But notwithstanding the great variety of intrinsic brightness of the stars, the ratio of the number of stars of one magnitude to the number of the magnitude next lower (the " star-ratio ") is a guide to the uniformity of their distribution.

• Seeliger, who investigated this ratio for the stars of the Bonn Durchmusterung and Southern Durchmusterung, came to the conclusion (as summarized by Simon Newcomb) that for these stars the ratio ranges from 3.85 to 3.28, the former value being found for regions near the Milky Way and the latter for regions near the galactic poles.

• Thus the figure represents a section the (ideally simplified) uni verse cut perpendicular to C P' D the planes AB and CD between which the stars are contained, 1 This number is the 3/2th power of the ratio of the brightness of stars differing by a unit magnitude.

• In 1807 an account of the magnetic observations made during the tour with Humboldt was published in the first volume of the Memoires d'Arcueil, and the second volume, published in 1809, contained the important memoir on gaseous combination (read to the Societe Philomathique on the last day of 1808), in which he pointed out that gases combining with each other in volume do so in the simplest proportions-1 to 1, 1 to 2, 1 to 3 - and that the volume of the compound formed bears a simple ratio to that of the constituents.

• Comenius also wrote against the Socinians, and published three historical works - Ratio disciplinae ordinisque in unitate fratrum Bohemorum, which was republished with remarks by Buddaeus, Historia persecutionum ecclesiae Bohemicae (1648), and Martyrologium Bohemicum.

• In man, as the noblest of created things, the Trinity is seen most perfectly reflected; intellectus (vous), ratio (X6yos) and sensus (& ivota) make up the threefold thread of his being.

• In 1781 he favoured an amendment 'of the Articles of Confederation giving Congress power to enforce its requisitions, and in 1783, in spite of the open opposition of the Virginia legislature, which considered the Virginian delegates wholly subject to its instructions, he advocated that the states should grant to Congress for twenty-five years authority to levy an import duty, and suggested a scheme to provide for the interest on the debt not raised by the import duty - apportioning it among the states on the basis of population, counting three-fifths of the slaves, a ratio suggested by Madison himself.

• It had also the mathematical meaning of ratio; and in its use for definition it is sometimes transferred to essence as the object of definition, and has a mixed meaning, which may be expressed by " account."

• Babo, 1847, gave the law known by his name, that the " relative lowering" (p - po)lpo of the vapour-pressure of a solution, or the ratio of the diminution of vapour-pressure (p - po) to the vapour-pressure po of the pure solvent at the same temperature, was constant, or independent of the temperature, for any solution of constant strength.

• Raoult (Comptes Rendus, 1886-87) employed other solvents besides water, and showed that the relative lowering for different solvents and different dissolved substances was the same in many cases for solutions in which the ratio of the number of gramme-molecules n of the dissolved substance to the number of molecules N of the solvent was the same, or that it varied generally in proportion to the ratio n/N.

• In this case the ratio of the vapour-pressure of the solution p" to that of the solvent p' should be equal to the ratio of the number of free molecules of solvent N - an to the whole number of molecules N - an+n in the solution.

• Employing Joule's value of the mechanical equivalent of heat, then recently published, in connexion with the value of the ratio of the specific heats of air S/s=I.

• Adopting for steam the same value of the ratio of the specific heats, viz.

• In other words, the increase of pressure per degree (dp/d0) divided by p should be constant and equal to B; but observation shows that this ratio decreases, e.g.

• Their origin is the fact that where the bars appear nearly to coincide the apparent gaps bear the greatest ratio to the dark spaces; i.e.

• In 1906 the ratio of insane confined to institutions, to the total population, was to every 270.

• The National Democratic Convention declared for the immediate opening of the mints to the free and unlimited coinage of silver at the ratio with gold of 16 to 1; and it nominated for the presidency William Jennings Bryan of Nebraska, who also received the nomination of the People's party and of the National Silver party.

• The state of elementary education is comparatively good, rather more than two-thirds of the population being able to read and write, and the ratio of crime is proportionately low.

• The translation parallel to this axis is lox + mly + nhz (Xf + uv + vi) Ic. (8) The linear magnitude which measures the ratio of translation to rotation in a screw is called the pitch.

• Its type, as distinguished from its absolute magnitude, may be specified by a screw whose axis is the line of action of R, and whose pitch is the ratio G/R.

• In two turns this ratio is squared, and so on.

• The ratio of the axes of the ellipse is sec a, the longer axis being in the plane of 0.

• It is obvious that the ratio V (x,y,z) (22)

• The frequency of the gravest mode is to that of a uniform bar in the ratio .98 15.

• That this ratio should be less than unity agrees with the theory of constrained types already given.

• In other cases the safety of the joint against displacement by sliding depends on its power of exerting friction, and that power depends on the law, known by experiment, that the friction between two surfaces bears a constant ratio, depending on the nature 01 the surfaces, to the force by which they are pressed together.

• For the condition of equilibrium of forces not parallel is that they shall be represented in direction and magnitude by the sides and diagonals of certain parallelograms, and of parallel forces that they shall divide certain straight lines in certain ratios; and the parallel projection of a parallelogram is a parallelogram, and that of a straight line divided in a given ratio is a straight line divided in the same ratio.

• By its aid, for example, the whole of the properties a elliptical arches, whether square or skew, whether level or sloping in their span, are at once deduced by projection from those of symmetrical circular arches, and the properties of ellipsoidal and ellipticconoidal domes from those of hemispherical and circular-conoidal domes; and the figures of arches fitted to resist the thrust of earth, which is less horizontally than vertically in a certain given ratio, can be deduced by a projection from those of arches fitted to resist the thrust of a liquid, which is of equal intensity, horizontally and vertically.

• The ratio in which the utmost stress before breaking exceeds the safe working stress is called the factor of safety, and is determined empirically.

• It consists of two elements, the velocity ratio, which is the ratio of any two magnitudes bearing to each other the proportions of the respective velocities of the two points at a given instant, and the directional relation, which is the relation borne to each other by the respective directions of the motions of the two points at the same given instant.

• The comparative motion of two points at a given instant is capable of being completely expressed by one of Sir William Hamiltons Quaternions,the tensor expressing the velocity ratio, and the versor the directional relation.

• Velocity Ratio of Components of Motion.As the distance between any two points in a rigid body is invariable, the projections of their velocities upon the line joining them must be equal.

• Hence also the ratio of the com ponents of the velocities of two points A and B in the directions AP and BW respectively, both in the plane of rotation, is equal to the ratio of the perpendiculars Fni and Fn.

• The ratio of the two components of that velocity is = p/2lrr = tan 0.

• In the investigation, therefore, of the comparative motion, of the driver and follower, in an elementary combination, it is unnecessary to consider relations of angular direction, which are already fixed by the connection of each piece with the frame; so that the inquiry is confined to the determination of the velocity ratio, and of tbe directional relation, so far only as it expresses the connection between forward and backward movements of the driver and follower.

• Williss classification is founded, in the first place, on comparative motion, as expressed by velocity ratio and directional relation, and in the second place, on the mode of connection of the driver and follower.

• For otitside gearing that ratio is negative, Cs because the wheels turn contrary ways; for inside gearing it is positive, because they turn the same way.

• If the velocity ratio is to be -constant, as in, fYi Williss Class A, the wheels must be circular; and this is the most common form for wheels.

• If the velocity ratio is to be variable, as in s Williss Class B, the figures of the wheels are a pair of rolling curves, subject to the condition that the distance between their poles (which are the centres of rotation) shall be constant.

• When the velocity ratio is variable, the line of contact will shift its position in the plane C1OC2, and the wheels will be cones, with eccentric or irregular bases.

• In every case which occurs in practice, however, the velocity ratio is FIG.

• Hence also, in any pair of circular wheels which rotate continuously for one revolution or more, the ratio of the numbers of teeth and its reciprocal the angular velocity ratio must be expressible in whole numbers.

• They there fore study that the numbers of teeth in each pair of wheels whici work together shall either be prime to each other, or shall hav their greatest common divisor as small as is consistent with velocity ratio suited for the purposes of the machine.

• The angular velocity ratio due to the sliding contact of the teeth will be the same with that due to the rolling contact of the pitch-circles, if the line of connection of the teeth cuts the Ca line of centres at the pitchpoint.

• Consequently, one of the forms suitable for the teeth of wheels is the involute of a circle; and the obliquity of the action of such teeth is the angle whose cosine is the ratio of the radius of their base-circle to that of the pitch-circle of the wheel.

• Pulleys and drums for communi cating a constant velocity ratio are circular.

• The speed-cones are either continuous cones or conoids, as A, B, whose velocity ratio can be varied gradually while they are in motion by shifting the belt, or sets of pulleys whose radii vary by steps, as C, D, in which case the velocity ratio can be changed by shifting the belt from one pair of pulleys to another.

• The axes of rotation of a pair of turning pieces connected by a link are almost always parallel, and perpendicular to the line of connection n which case the angular velocity ratio at any instant is the recipocal of the ratio of the common perpendiculars let fall from the me of connection upon the respective axes of rotation.

• The velocity of the other connected point at such an instant is null, unless it also reaches a dead-point at the same instant, so that the line of connection is in the plane of the two axes of rotation, in which case the velocity ratio is indeterminate.

• It is often a question of importance to determine the number of teeth in a train of wheels best suited for giving a determinate velocity ratio to two axes.

• It was shown by Young that, to do this with the least total number of teeth, the velocity ratio of each elementary combination should approximate as nearly as possible to 3.59., This would in many cases give too many axes; and, as a useful practical rule, it may be laid down that from 3 to 6 ought to be the limit of the velocity ratio of an elementary combination in wheelwork.

• Let B/C be the velocity ratio required, reduced to its least terms, and let B be greater than C. If B/C is not greater than 6, and C lies between the prescribed minimum number of teeth (which may be called t) and its double 2t, then one pair of wheels will answer the purpose, and B and C will themselves be the numbers required.

• Then, if possible, B and, C themselves are to be resolved each into rnI factors (counting 1 as a factor), which factors, or multiples of them, shall be not less than t nor greater than 6t; or if B and C contain inconveniently large prime factors, an approximate velocity ratio, found by the method of continued fractions, is to be substituted for B/C as before.

• Double Hookes Coupling.It has been shown in 66 that the velocity ratio of a pair of shafts coupled by a universal joint fluctuates between the limits cos 0 and 1/cos 0.

• Then, from the principles of 60 it is evident that at each instant ai/ai = ai/aa, and consequently that ai; so that the fluctuations of angular velocity ratio caused by the first coupling are exactly neutralized by the second, and the first and last shafts have equal angular velocities at each instant.

• Then Ob is the velocity of the point b in magnitude and direction, and cb is the tangential velocity of B relatively to C. Moreover, whatever be the actual magnitudes of the velocities, the instantaneous velocity ratio of the points C and B is given by the ratio Oc/Ob.

• An important property of the diagram is that if points X and x are taken dividing the link CB and the whole acceleration of B about C, namely, cb in the same ratio, then Ax represents the acceleration of the point X in magnitude and direction; cb is called the acceleration image of the rod.

• Removing the summation signs in equation (52) in order to restrict its application to two points and dividing by the common time interval during which the respective small displacements ds and ds were made, it becomes Pdsfdt = Rds/dt, that is, Pv = Rv, which shows that the force ratio is the inverse of the velocity ratio.

• It follows at once that any method which may be available for the determination of the velocity ratio is equally available for the determination of the force ratio, it being clearly understood that the forces involved are the components of the actual forces resolved in the direction of motion of the points.

• The virtual centres 0,-,, O,i are at the respective axes of the wheels r and 1, and the centre O,-i divides the line through these two points externally in the ratio of the train of wheels.

• The principles of this reduction are that the ratio of the given to the equivalent force is the reciprocal of the ratio of the velocities of their points of application, and the ratio of the given to the equivalent couple is the reciprocal of the ratio of the angular velocities of the pieces to which they are applied.

• Let Ti be the tension of the free part of the band at that side towards which it tends to draw the pulley, or from which the pulley tends to draw it; 1, the tension of the free part at the other side; T the tension of the band at any intermediate point of its arc of contact with the pulley; 0 the ratio of the length of that arc to the radius of the pulley; do the ratio of an indefinitely small element of that arc to the radius; F=TiT2 the total friction between the band and the pulley; dF the elementary portion of that friction due to the elementary arc do; f the coefficient of friction between the materials of the band and pulley.

• The assumption that the pistons of an engine move with simple harmonic motion is increasingly erroneous as the ratio of the length of the crank r, to the length of the con oecting rod 1 increases.

• The ratio in France was low throughout the r 9th century, and during the last half fell only from 273 to 261, raising the proportion of the old above that resulting in northern Europe and Italy from emigration.

• The tendency of a community towards matrimony, or its "nuptiality," as it is sometimes termed, is usually indicated by the ratio to the total population of the persons married each year.

• The adherents of each of these churches outnumber their communicants in a ratio which is variously estimated.

• Maxwell suggested new methods for the determination of this ratio of the electrostatic to the electromagnetic units, and by experiments of great ingenuity was able to show that this ratio, which is also that of the velocity of the propagation of an electromagnetic impulse through space, is identical with that of light.

• For the hydrogen atom the ratio of charge to mass as deduced from electrolysis is about Io 1.

• Such pairs of colour may be regarded as infinite in number; but there are three pairs which stand out prominently, and admit of easy expression for the ratio in which each contributes to the total action.

• If the ratio a' la be sufficiently constant, as is often the case, the above relation reduces to the " condition of Airy," i.e.

• This combined condition is exactly fulfilled by holosymmetrical objectives reproducing with the scale 1, and by hemisymmetrical, if the scale of reproduction be equal to the ratio of the sizes of the two components.

• The rays with an angle of aperture smaller than u* would not have the same distance of intersection and the same sine ratio; these deviations are called "zones," and the constructor endeavours to reduce these to a minimum.

• 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.

• Fraunhofer, who defined the colours by means of the dark lines in the solar spectrum; and showed that the ratio of the dispersion of two glasses varied about 20% from the red to the violet (the variation for glass and water is about 50%).

• Thus a continued fraction equivalent to 7r (the ratio of the circumference to the diameter of a circle) is I I I I II 3+ 7+15+7+292+i-1-i+ ..

• For Example, In The Case Of Water Delivered From A Glass Tube, Which Is Cut Off Square And Held Vertically, A Will Be The External Radius; And It Will Be Necessary To Suppose That The Ratio Of The Internal Radius To A Is Constant, The Cases Of A Ratio Infinitely Small, Or Infinitely Near Unity, Being Included.

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

• Reasoning from some observations of Savart, Plateau finds in this way 4.38 as the ratio of the length of a division to the diameter of the jet.

• Viewed as a whole, `Ali Riza's forces, scattered as they inevitably were through the need of holding territory, were reasonably well distributed, in that, though the Turks were in the ensemble inferior in the ratio of I to 21, their handicap on the decisive battlefield reduced itself to the ratio of t to about II-.

• 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.

• In the particular case when the radii are in the ratio of I to 3 the epicycloid (curve a) will consist of three cusps external to the circle and placed at equal distances along its circumference.

• If the ratio of the radii be as I to 4, we obtain the four-cusped hypocycloid, which has the simple cartesian equation x 2'3+ y 213 = a 21 '.

• The " black body " is an ideal body with surface so constituted as to reflect no part of any radiations that fall upon it; in the case of such a body Kirchhoff and Balfour Stewart showed that unless energy were to be lost the rate of emission and absorption must be in fixed ratio for each specific wave-length.

• It is equally satisfactory to know that there is a nearly constant ratio on any given area (exceeding perhaps 1000 acres) between the true mean annual rainfall, the rainfall of the driest year, the two driest consecutive years and any other groups of driest consecutive years.

• It is instructive to note the ratio of increase of reservoir capacity and yield respectively for any given rainfall.

• After Rankine, a French engineer, Bouvier, gave the ratio of the maximum stress in a dam to the maximum vertical stress as 1 to the cosine squared of the angle between the vertical and the resultant which, in dams of the usual form, is about as 13 is to 9.

• The late Sir Benjamin Baker, F.R.S., suggested that the stresses might be measured by experiments with elastic models, and among others, experiments were carried out by Messrs Wilson and Gore a with indiarubber models of plane sections of dams (including the foundations) who applied forces to represent the gravity and water pressures in such a manner that the virtual density of the rubber was increased many times without interfering with the proper ratio between gravity and water pressure, and by this means the strains produced were of sufficient magnitude to be easily measured.

• A usual value of for hemp ropes on cast-iron pulleys is 0.3, and the exponential log ratio is therefore 0 3ur cosec 20 when 9 =7r.

• In order to obtain a greater ratio of R to E, without using a large number of sheaves, various arrangements are used, of which the' Weston differential pulley block is a typical example.

• But by observing the distance through which a body would fall in one second of time at the earth's surface, and by calculating from that on the supposition of the force diminishing in the ratio of the inverse square of the distance, he found that the earth's attraction at the distance of the moon would draw a body through 15 ft.

• The circuits in which the batterybattery P and and d being galvanometer called the ratio branches placed are called conjugate circuits, and the circuits P, Q, R, and S are called the arms of the bridge, the '44 S arms and S the measuring arm.

• The operation of determining the value of the resistance R therefore consists in altering the ratio of the three resistances P, Q,, and S, until the galvanometer indicates no current through it when the battery circuit is completed or closed by the key.

• In one form of Wheatstone's Bridge, known as the series pattern plug-resistance bridge, or Post Office pattern, the two ratio arms, P and Q, each consist of a series of coils of wire, viz.

• This arrangement forms the measuring arm of the bridge, the ratio arms being constructed on the series plug pattern just described.

• Thus while in1882-1883the ratio of illiterate recruits amounted to 9.75%, in 1901 less than one quarter per cent of the military drafts were without schooling.

• Coal gas, being a mixture of gases and vapours of liquids having very varying boiling points, must necessarily undergo physical changes when the temperature is lowered Vapours of liquids of high boiling point will be condensed more quickly than those having lower boiling points, but condensation of each vapour will take place in a definite ratio with the decrease of temperature, the rate being dependent upon the boiling point of the liquid from which it is formed.

• The fact that coal gas of an illuminating power of from 14 to 16 candles can be made from the ordinary gas coal at a fairly low rate, while every candle power added to the gas increases the cost in an enormous and rapidly growing ratio, has, from the earliest days of FIG.

• Cicero says, " Physiologia naturae ratio," and such was the meaning of the name Physiologus, given to a cyclopaedia of what was known and imagined about earth, sea, sky, birds, beasts and fishes, which for a thousand years was the authoritative source of information on these matters, and was translated into every European tongue.

• If we put the population of France at 40,000,000, the states in question could, at the same ratio, support a population of 140,000,000.

• The result of these conditions is that all the quantities required admit of development in series proceeding according to the powers of the eccentricities and inclinations of the orbits, and the ratio of the masses of the several planets to the mass of the sun.

• It will be seen that these numbers are nearly in the ratio of 2 to 5.

• It states that the squares of the periods of circulation round the sun of the several planets are in the same ratio as the cubes of their mean distances.

• Again, since the constant of aberration defines the ratio between the velocity of light and the earth's orbital speed, the span of the terrestrial circuit, in other words, the distance of the sun, is immediately deducible from known values of the first two quantities.

• This ratio is termed the eccentricity, and will be denoted by e.

• From this or otherwise it is readily deduced that the ordinates of an ellipse and of the circle described on the major axis are in the ratio of the minor to the major axis.

• For a given degree of opposition this burden will be shared between the conflicting presentations in the inverse ratio of their strength.

• Formulae for metallic reflection may be obtained from Fresnel's expressions by writing the ratio sin i / sin r equal to a complex quantity, and interpreting the imaginary coefficients in the manner explained above.

• A subsequent determination of the plane of polarization gives the ratio of the amplitudes of the vibrations in the component streams.

• Conceiving that the simplest principle is the most likely to be true, he assumed as a postulate that bodies falling freely towards the earth descend with a uniformly accelerated motion, and deduced thence that the velocities acquired are in the direct, and the spaces traversed in the duplicate ratio of the times, counted from the beginning of motion; finally, he proved, by observing the times of descent of bodies falling down inclined planes, that the postulated law was the true law.

• If we also assume the ratio of the current to the heat-flow to be the same in both postulates, we have a = TB, whence 0 2 = kr/T.

• One definition, which is of especial value in the geometrical treatment of the conic sections (ellipse, parabola and hyperbola) in piano, is that a conic is the locus of a point whose distances from a fixed point (termed the focus) and a fixed line (the directrix) are in constant ratio.

• This ratio, known as the eccentricity, determines the nature of the curve; if it be greater than unity, the conic is a hyperbola; if equal to unity, a parabola; and if less than unity, an ellipse.

• Archimedes contributed to the knowledge of these curves by determining the area of the parabola, giving both a geometrical and a mechanical solution, and also by evaluating the ratio of elliptic to circular spaces.

• The conics are distinguished by the ratio between the latus rectum (which was originally called the latus erectum, and now often referred to as the parameter) and the segment of the ordinate intercepted between the diameter and the line joining the second vertex with the extremity of the latus rectum.

• The magnification is also expressed as the ratio of the apparent size of the object observed through the microscope to the apparent size of the object seen with the naked eye.

• By the magnification of the objective is meant the ratio of the distance of distinct vision to the focal length of the objective.

• The ratio of half the length of the visible piece of the scale to its distance from the diaphragm on the stage gives the tangent of half the angular aperture.

• If the size of the image of a known interval of the objective micrometer is determined by an ordinary scale, and the distance of the image from the focal plane of the objective belonging to it is measured, then the focal length can be calculated from the ratio y/y'=fl', in which y is the size of the object, y' that of the image, and xi' the distance of the image from the focal plane belonging to it.

• In the case of the earth, this ratio is 1/0.0032813 or 305.

• All kinds of produce brought fabulous prices, and were exported to Victoria in such quantities that the exports rose from a value of £665,7 9 0 in 1851 to £1,509,883 in 1852, and £1,156,316 in 1853, while the population diminished in almost equal ratio.

• Alex could rest easy knowing that their family gender ratio would remain even.

• X-ray absorption column plotted against galaxy axial ratio from Malizia et al.

• However, the NO boosting power of this specific amino acid is heavily dependent upon the bonded ratio of L-Arginine to AKG.

• The actual margins used may be increased to preserve the aspect ratio of the DATA picture.

• If you press the Ctrl key while dragging a handle, the selection rectangle maintains the same aspect ratio it originally had.

• The reason is that tradition paper sizes were designed for film and have different aspect ratio than digital photos.

• The Tools menu contains some interesting options, such as deinterlacing and changing the aspect ratio.

• Letterbox format A technique for showing a wider aspect ratio format on narrower aspect ratio screen displayed in its original aspect ratio.

• This will expand the image so that it will once again have the correct aspect ratio.

• All of the games designed for a screen that has a standard aspect ratio seem to be ruined when played on a widescreen.

• When the picture aspect ratio is is set to " Auto ", it switches image size and shape all the time.

• The effects of the area ratio, the divergence angle and the cross-section aspect ratio are taken into account.

• The Swiss National bank is another central bank to have greatly reduced its dollar ratio in recent years.

• Cromoglycate / bronchodilator ratio = number of cromoglycate items prescribed / number of bronchodilator items prescribed in one year.

• Normally thought of as the ratio of a circle's circumference to its diameter, pi keeps turning up in odd places.

• For other citrus, try a ratio of two parts sweet citrus to one part sour.

• Since I raised the compression ratio not only can my P-type go faster but I am also inclined to drive it faster.

• Moreover, whatever the starting point the unemployment ratio will very quickly converge to the same stable level.

• A Dual Range transfer box allows a lower ratio to be selected for the torque convertor drive train.

• The Treasury will be issuing soon a consultation document on the statutory cash ratio deposit scheme.

• I would normally use either golden ratio or simplex optimization for functions where analytic derivatives are not available.

• Biodiesel can also be mixed, at any ratio, with conventional petroleum diesel can also be mixed, at any ratio, with conventional petroleum diesel.

• At the rear is a limited slip differential with a 3.46 to 1 ratio to reduce rear wheel slip under acceleration.

• The case fatality ratio for respiratory diphtheria is 5-10% .

• The UNEP Aridity Index (based on a ratio of annual precipitation to mean annual potential evapotranspiration) data added to the karst dataset.

• Gearbox; Longer second gearbox; Longer second gear, gear box ratio improves gear box spacing.

• If you need a lower gear ratio the hub allows you to fit a larger rear sprocket, and vise versa.

• If the 4th gear ratio is too low (high number) then it will limit the speed the scooter can achieve.

• The study has also produced a model to help glassmakers optimize furnace efficiency at any combination of production level and cullet ratio.

• The ratio K o = s ' he ratio K o = s ' h / s ' z is known as the coefficient of earth pressure at rest.

• Boiling heat transfer, burnout, critical heat flux ratio.

• For years, economic illiterates have been claiming that it would, supposedly by improving the ratio of working people to retirees.

• We conclude with methods of reducing the cost of inflation swaps through conditional indexation on the coverage ratio of a fund.

• The ratio of strontium isotopes changed rapidly in Early Jurassic oceans with the result that values are time diagnostic.

• There are also two new isotope ratio mass spectrometers for in vivo studies of energy and protein metabolism in patients.

• The stress ratio R (s min / s max) was equal to 0.1.

• A line join is trimmed when the ratio of miter length to stroke width is greater than the miter length to stroke width is greater than the miterlimit value.

• The ratio of loss and storage modulus, tan d, is also reported.

• Among their heritage can be included numerology (numbers and letter characters in a unified system) and the hypothetical Golden Ratio.

• Skimming the head also increases the compression ratio and to avoid detonation with low octane fuel a low compression piston is used.

• The geometric parameters taken into account are area ratio, diffuser length to annular gap ratio, and divergence angle.

• We have said that we intend to increase our dividend payout ratio to 40% .