# Zero sentence example

zero

- Dean pushed each of the four buzzers, with zero response.
- Zero is a cardinal number.
- When the cost of recording all the data is zero, the cost of processing it is zero, and the cost of accessing it zero, then the many sciences, especially human health, will be democratized.
- The locks will open at zero four twenty-five.
- Therefore every form of degree 2, except of course that one whose weight is zero, is a perpetuant.Advertisement
- Going from zero to one puppy might increase your utility a great amount.
- Both Deans agreed the letters were polite but of zero historical interest and strangely unloving.
- "It was zero this morning," he reminded her.
- Now, evidently, the third transvectant of f, expressed in this form, with the cubic pxgxrx is zero, and hence from a property of the covariant j we must have j = pxgxrx; showing that the linear forms involved are the linear factors of j.
- It was an infuriating conversation, resulting in a big, fat zero.Advertisement
- The survival rate on wounds like that are zero.
- This can be verified by equating to zero the five coefficients of the Hessian (ab) 2 axb2.
- One of the most important questions in investigating a linear algebra is to decide the necessary relations between a and b in order that this product may be zero.
- Hence in any infinitesimal part of the fluid the circulation is zero round every small plane curve passing through the vortex line; and consequently the circulation round any curve drawn on the surface of a vortex filament is zero.
- The potential of a conductor has already been defined as the mechanical work which must be done to bring up a very small body charged with a unit of positive electricity from the earth's surface or other boundary taken as the place of zero potential to the surface of this conductor in question.Advertisement
- It must be such a potential distribution that the potential in the interior will be to constant, since the electric force must be zero.
- In general the dielectric constant is reduced with decrease of temperature towards a certain limiting value it would attain at the absolute zero.
- Salmon built a seemingly unassailable lead only to see it cut to zero on the last run.
- I think no matter what, energy costs will fall dramatically in the future, probably to near zero, because the economic incentives to unlock that technical puzzle are so overwhelming.
- In general any pencil of lines, connected with the line a x by descriptive or metrical properties, has for its equation a rational integral function of the four forms equated to zero.Advertisement
- The linear invariant a s is such that, when equated to zero, it determines the lines ax as harmonically conjugate to the lines xx; or, in other words, it is the condition that may denote lines at right angles.
- The angle which the magnetic axis makes with the plane of the horizon is called the inclination or Along an irregular line encircling the earth in the neighbourhood of the geographical equator the needle takes up a horizontal position, and the dip is zero.
- The opposite and parallel forces acting on the poles are always equal, a fact which is sometimes expressed by the statement that the total magnetism of a magnet is zero.
- The equipotential surfaces are two series of ovoids surrounding the two poles respectively, and separated by a plane at zero potential passing perpendicularly through the middle of the axis.
- For a given strength, therefore, the potential depends solely upon the boundary of the shell, and the potential outside a closed shell is everywhere zero.Advertisement
- If a bar of hard steel is placed in a strong magnetic field, a certain intensity of magnetization is induced in the bar; but when the strength of the field is afterwards reduced to zero, the magnetization does not entirely disappear.
- The downward course of the curve is, owing to hysteresis, strikingly different from its upward course, and when the magnetizing force has been reduced to zero, there is still remaining an induction of 7500 units.
- 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.
- Several pieces of apparatus have been invented for comparing the magnetic quality of a sample with that of a standard iron rod by a zero method, such as is employed in the comparison of electrical resistances by the Wheatstone bridge.
- Inside the torsion-head is a commutator for automatically reversing the current, so that readings may be taken on each side of zero, and the arrangement is such that when the torsion-head is exactly at zero the current is interrupted.Advertisement
- 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.
- When the magnetizing current is broken, the magnetization at once undergoes considerable diminution, then gradually falls to zero, and a similar sudden change followed by a slow one is observed when a feeble current is reversed.
- Honda subjected tubes of iron, steel and nickel to the simultaneous action of circular and longitudinal fields, and observed the changes of length when one of the fields was varied while the other remained constant at different successive values from zero upwards.
- When no current is passing through the coil and the magnetic field is of zero strength, the needles arrange themselves in positions of stable equilibrium under their mutual forces, pointing in.
- When the strong magnetizing field is gradually diminished to zero and then reversed, the needles pass from one stable position of rest to another through a condition of instability; and if the field is once more reversed, so that the cycle is completed, the needles again pass through a condition of instability before a position of stable equilibrium is regained.Advertisement
- Supposing Ewing's hypothesis to be correct, it is clear that if the magnetization of a piece of iron were reversed by a strong rotating field instead of by a field alternating through zero, the loss of energy by hysteresis should be little or nothing, for the molecules would rotate with the field and no unstable movements would be possible.'
- If the structure of the molecule is so perfectly symmetrical that, in the absence of any external field, the resultant magnetic moment of the circulating electrons is zero, then the application of a field, by accelerating the right-handed (negative) revolutions, and retarding those which are left-handed, will induce in the substance a resultant magnetization opposite in direction to the field itself; a body composed of such symmetrical molecules is therefore diamagnetic. If however the structure of the molecule is such that the electrons revolving around its atoms do not exactly cancel one another's effects, the molecule constitutes a little magnet, which under the influence of an external field will tend to set itself with its axis parallel to the field.
- This is sometimes treated as a debt of 5s.; an alternative method is to recognize that our zero is really arbitrary, and that in fact we shift it with every operation of addition or subtraction.
- In the first class come equations in a single unknown; here the function which is equated to zero is the Y whose values for different values of X are traced, and the solution of the equation is the determination of the points where the ordinates of the graph are zero.
- (v.) An alternative method of obtaining the rule of transposition is to change the zero from which we measure.Advertisement
- If r+s>n, a product such as E r E 3, worked out by the previous rules, comes out to be zero.
- The component vibrations at P due to the successive zones are thus nearly equal in amplitude and opposite in phase (the phase of each corresponding to that of the infinitesimal circle midway between the boundaries), and the series which we have to sum is one in which the terms are alternately opposite in sign and, while at first nearly constant in numerical magnitude, gradually diminish to zero.
- If, on the other hand, the point be well immersed in the geometrical shadow, the earlier zones are altogether missing, and, instead of a series of terms beginning with finite numerical magnitude and gradually diminishing to zero, we have now to deal with one of which the terms diminish to zero at both ends.
- The sum of such a series is very approximately zero, each term being neutralized by the halves of its immediate neighbours, which are of the opposite sign.
- It vanishes when u =mlr, m being any whole number other than zero.Advertisement
- In the first quadrant there is no root after zero, since tan u> u, and in the second quadrant there is none because the signs of u and tan u are opposite.
- The first root after zero is thus in the third quadrant, corresponding to m =1.
- Let us now consider the distribution of brightness in the image of a double line whose components are of equal strength, and at such an angular interval that the central line in the image of one coincides with the first zero of brightness in the image of the other.
- For a certain distance outwards this remains sensibly unimpaired and then gradually diminishes to zero, as the secondary waves become discrepant in phase.
- Since at these points the resultant due to the whole aperture is zero, any two portions into which the whole may be divided must give equal and opposite resultants.Advertisement
- The vibrations corresponding to the two parts are precisely antagonistic, since if both were operative the resultant would be zero.
- As this increases from zero, the two processions which correspond to the two halves of the aperture begin to overlap, and the overlapping gradually increases until there is almost complete superposition.
- At the point 0 the intensity is one-quarter of that of the entire wave, and after this point is passed, that is, when we have entered the geometrical shadow, the intensity falls off gradually to zero, without fluctuations.
- If, instead of supposing the motion at dS to be that of the primary wave, and to be zero elsewhere, we suppose the force operative over the element dS of the lamina to be that corresponding to the primary wave, and to vanish elsewhere, we obtain a secondary wave following quite a different law.
- When the liquid is bounded by a cylindrical surface, the motion of a vortex inside may be determined as due to a series of vorteximages, so arranged as to make the flow zero across the boundary.
- The circulation being always zero round a small plane curve passing through the axis of spin in vortical motion, it follows conversely that a vortex filament is composed always of the same fluid particles; and since the circulation round a cross-section of a vortex filament is constant, not changing with the time, it follows from the previous kinematical theorem that aw is constant for all time, and the same for every cross-section of the vortex filament.
- Hence the total electric flux due to a charge Q through an enclosing surface is 41rQ, and therefore is zero through one enclosing no electricity.
- But the force perpendicular to the curved surface of this cylinder is everywhere zero.
- Then since the generating lines of the tube are lines of force, the component of the electric force perpendicular to the curved surface of the tube is everywhere zero.
- Hence if dS and dS' are the areas of the ends, and +E and - E' the oppositely directed electric forces at the ends of the tube, the surface integral of normal force on the flux over the tube is EdS - E'dS' (20), and this by the theorem already given is equal to zero, since the tube includes no electricity.
- The electric force outward from that point is - dV/dn, where do is a distance measured along the outwardly drawn normal, and the force within the surface is zero.
- Let us then suppose that a conductor originally at zero potential has its potential raised by administering to it small successive doses of electricity dq.
- Then the charge at A together with the induced surface charge on the plate makes a certain field of electric force on the left of the plate PO, which is a zero equipotential surface.
- If then we put a negative point-charge -qr/d at B, it follows that the spherical surface will be a zero potential surface, for q rq 1 (24).
- It is then a zero potential surface, and every point outside is at zero potential as far as concerns the electric charge on the conductors inside.
- As the temperature 0" is lowered, the area of the cycle increases, but since W can never exceed H', there must be a zero limit of temperature at which the pressure would vanish and the area of the cycle become equal to the whole heat absorbed at the higher temperature.
- Taking this ideal limit as a theoretical or absolute zero, the value of H may be represented on the diagram by the whole area included between the two adiabatics BAZ, CDZ' down to the points where they intersect the isothermal of absolute zero, or the zero isopiestic OV asymptotically at infinity.
- If the substance in any state such as B were allowed to expand adiabatically (dH = o) down to the absolute zero, at which point it contains no heat and exerts no pressure, the whole of its available heat energy might theoretically be recovered in the form of external work, represented on the diagram by the whole area BAZcb under the adiabatic through the state-point B, bounded by the isometric Bb and the zero isopiestic bV.
- In order to restore the substance to its original temperature 0' at constant pressure, it would be necessary to supply a further quantity of heat, H, represented by the area between the two adiabatics from FC down to the absolute zero.
- To find the total heat of a substance in any given state defined by the values of p and 0, starting from any convenient zero of temperature, it is sufficient to measure the total heat required to raise the substance to the final temperature under a constant pressure equal to p. For instance, in the boiler of a steam engine the feed water is pumped into the boiler against the final pressure of the steam, and is heated under this constant pressure up to the temperature of the steam.
- We may therefore reasonably assume that the limiting values of the specific heats at zero pressure do not vary with the temperature, provided that the molecule is stable and there is no dissociation.
- In the special case of a substance isolated from external heat supply, dH=o, the change of entropy is zero in a reversible process, but must be positive if the process is not reversible.
- Zero hour was to be 5:20 A.M.
- Zero hour was at 5:20 A.M.
- Zero hour was at 6:5 A.M.
- The weighing is conducted in the usual way by vibrations, except when the weight be small; it is then advisable to bring the pointer to zero, an operation rendered necessary by the damping due to the adhesion of water to the fibre.
- The apparatus is so designed that when the plummet is suspended in air, the index of the beam is at the zero of the scale; if this be not so, then it is adjusted by a levelling screw.
- The maximum separation is consequently at 45° from zero.
- The measures can be made on both sides of zero for eliminating index error.
- For this purpose the zero or pure blue is represented by a solution of i part of copper sulphate and 9 parts of ammonia in 190 parts of water.
- 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.
- Each impinging molecule exerts an impulsive pressure equal to mu on the boundary before the component of velocity of its centre of gravity normal to the boundary is reduced to zero.
- To examine what is meant by a zero value of n we refer to formula (15).
- When the target is completely concealed it is necessary to lay the gun on an aiming point more or less out of the line of fire, or to lay on a " director " with a large amount of deflection, and to align aiming posts with the sights at zero to give the direction of the target, and afterwards perhaps to transfer the line of sight to some other distant object, all of which require a far greater scope of deflection than is afforded by the deflection leaf.
- In the case of the triangle, for instance, b is zero, so that the area is lha.
- Either or both of the bounding ordinates may be zero; the top, in that case, meets the base at that extremity.
- C. Vogel's spectroscopic measures in 1889.2 Previously to each obscuration, the star was found to be moving rapidly away from the earth; its velocity then diminished to zero pari passu with the loss of light, and reversed its direction during the process of recovery.
- In the Puget Sound Basin an occasional cold east wind during a dry period in winter causes the temperature to fall below zero.
- If, however, we put on external forces of the required type X it is obvious that any wave can be propagated with any velocity, and our investigation shows that when U has the value in (6) then and only then X is zero everywhere, and the wave will be propagated with that velocity when once set going.
- If the difference of phase be varied gradually from zero to - X, the resulting sound will 2 gradually decrease from a maximum to a minimum.
- Differentiating and equating to zero, the cost is least when dC _ LP +La =o, dl = l2 P=ale=G; that is, when the cost of one pier is equal to the cost erected of the main girders of one span.
- Although Bessel was the first to systematically treat of these functions, it is to be noted that in 1732 Daniel Bernoulli obtained the function of zero order as a solution to the problem of the oscillations of a chain suspended at one end.
- In 1764 Leonhard Euler employed the functions of both zero and integral orders in an analysis into the vibrations of a stretched membrane; an investigation which has been considerably developed by Lord Rayleigh, who has also shown (1878) that Bessel's functions are particular cases of Laplace's functions.
- Mehler, who proved that a simple relation existed between the function of zero order and the zonal harmonic of order n.
- Like the corresponding ammeters, they have the great advantage that the scales are equidivisional and that there is no dead part in the scale, whereas both the electrostatic and electrothermal voltmeters, above described, labour under the disadvantage that the scale divisions are not equal but increase with rise of voltages, hence there is generally a portion of the scale near the zero point where the divisions are so close as to be useless for reading purposes and are therefore omitted.
- Andrews's conception of the critical temperature of gases by defining the absolute boiling-point of a substance as the temperature at which cohesion and heat of vaporization become equal to zero and the liquid changes to vapour, irrespective of the pressure and volume.
- Conversely, the isotherms of January are convex southward, with a monthly mean below 32 in the northern third of the interior, and of zero on the mid-northern boundary.
- The "magnetic equator" is an imaginary line encircling the earth, along which the vertical component of the earth's magnetic force is zero; it nearly coincides with the terrestrial equator.
- Since the equation to a circle of zero radius is x 2 +y 2 =o, i.e.
- But freights had come down by 1900 to half the rates predicated by Caird; indeed, during a portion of the interval they ruled very close to zero, as far as steamer freights from America were concerned.
- At extremely rare intervals the thermometer has fallen below zero, as was the case in the remarkable cold wave of the lath-13th of February 1899, when an absolute minimum of 17° was registered at Valley Head.
- 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.
- If we suppose the lower part of the instrument replaced by a uniform bar of the same sectional area as the stem and of volume V, the indications of the instrument will be in no respect altered, and the bottom of the bar will be at a distance of N scale-divisions below the zero of the scale.
- This formed the zero of the scale.
- If the mercury in the thermometer stand above this zero the spirit must be reckoned weaker than the hydrometer indicates by the number on the thermometer scale level with the top of the mercury, while C f if the thermometer indicate a temperature a? ?!
- The scale engraved upon one face of the stem contains fifty-five divisions, the top and bottom being marked o or zero and the alternate intermediate divisions (of which there are twenty-six) being marked with the letters of the alphabet in order.
- In Beck's hydrometer the zero of the scale corresponds to density 1 000 and the division 30 to density.
- In the centesimal hydrometer of Francceur the volume of the stem between successive divisions of the scale is always, oath of the whole volume immersed when the instrument floats in water at 4° C. In order to graduate the stem the instrument is first weighed, then immersed in distilled water at 4° C., and the line of flotation 7.1 F marked zero.
- The length of 100 divisions of the scale, or the length of the uniform stem the volume of which would be equal to that of the hydrometer up to the zero graduation, Francceur called the "modulus" of the hydrometer.
- He experimented with an air-thermometer, in which the temperature was defined by measurement of the length of a column of mercury; and he pointed out that the extreme cold of such a thermometer would be that which reduced the "spring" of the air to nothing, thus being the first to recognize that the use of air as a thermometric substance led to the inference of the existence of a zero of temperature.
- If we compare Balmer's formula with the general equation of Ritz, we find that the two can be made to agree if the ordinary hydrogen spectrum is that of the side branch series and the constants a', b, c and d are all put equal to zero.'
- A band might in that case fade away towards zero frequencies, and as s increases, return again from infinity with diminishing distances, the head and the tail pointing in the same direction; or with a different value of constants a band might fade away towards infinite frequencies, then return through the whole range of the spectrum to zero frequencies, and once more return with its tail near its head.
- It arises from the ellipticity of the orbit, is zero at pericentre and apocentre, and reaches its greatest amount nearly midway between these points.
- 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 order to eliminate any error due to the zero of the scale D not being exactly below the mirror magnet, the support L is then removed to the west side of the instrument, and the settings are repeated.
- A carefully made ship's compass is usually employed, though in some cases the compass card, with its attached magnets, is made reversible, so that the inclination to the zero of the card of the magnetic axis of the system of magnets attached to the card can be eliminated by reversal.
- His name is most widely known in connexion with his work on the liquefaction of the so-called permanent gases and his researches at temperatures approaching the zero of absolute temperature.
- If the ship be inclined to starboard or to port additional deviation will be observed, reaching a maximum on north and south points, decreasing to zero on the east and west points.
- At the limit of dilution, when the concentration of a solution approaches zero, we have seen that thermodynamical theory, verified by experiment, shows that the osmotic pressure has the same value as the gas pressure of the same number of molecules in the same space.
- If L is zero or negligible, X = - P(v - v) and we have dP/dT = - P/T or dP/P = - dT/T, which on integration gives log P =log T+C, or P= kT, i.e.
- The great altitude accounts for very severe winter cold, occasionally ro to 25° below zero F., accompanied by blizzards (tipi) sometimes fatal to travellers overtaken by them.
- In fact, one quarter of the whole kingdom, consisting of the provinces of North and South Holland, the western portion of Utrecht as far as the Vaart Rhine, Zeeland, except the southern part of ZeelandFlanders, and the north-west part of North Brabant, lies below the Amsterdam zero; and altogether 38% of the country, or all that part lying west of a line drawn through Groningen, Utrecht and Antwerp, lies within one metre above the Amsterdam zero and would be submerged if the sea broke down the barrier of dunes and dikes.
- This will become zero if V 1 is 2V 2, that is, if the linear velocity of the cupcentres is one-half that of the jet of water impinging upon them.
- An example may prove this, but before quoting it, the question of determining b must be decided; this results immediately from the above quotation, b being the volume Vat the absolute zero (T =0); so the volume of isomers ought to be compared at the absolute zero.
- 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.
- (a) In the practice of the resistance method, both ends of a short bar are kept at a steady temperature by means of solid copper blocks provided with a water circulation, and the whole is surrounded by a jacket at the same temperature, which is taken as the zero of reference.
- If h also is zero, it becomes the equation of variable flow in the soil.
- In summer the temperature varies from 70° to 90° F., and in winter from 50° above to 10° below zero.
- Sleep is not exhaustion of the neuron in the sense that prolonged activity has reduced its excitability to zero.
- Waves of intense cold occur, lasting for several days, and one may have to endure a cold of 12° below zero, rising to a maximum of 17° below freezing-point.
- At Ghazni the snow has been known to lie long beyond the vernal equinox; the thermometer sinks to io° and 15° below zero (Fahr.); and tradition relates the entire destruction of the population of Ghazni by snowstorms more than once.
- This Is The Value Of The Minimum Of Atomic Heat Calculated By Perry From Diatomic Hydrogen, But The Observations Themselves Might Be Equally Well Represented By Taking The Imaginary Limit 3, Since The Quantity Actually Observed Is The Mean Specific Heat Between O° And 182 5° C. Subsequent Experiments On Other Metals At Low Temperatures Did Not Indicate A Similar Diminution Of Specific Heat, So That It May Be Doubted Whether The Atomic Heats Really Approach The Ideal Value At The Absolute Zero.
- In the next two days it reached zero magnitude, thus becoming the brightest star in the northern heavens, but after that it rapidly decreased.
- This product is interpreted as another directed line, forming the fourth term of a proportion, of which the first 1 Strictly speaking, this illustration of Tait's is in error by unity because in our calendar there is no year denominated zero.
- In octonions the analogue of Hamilton's vector is localized to the extent of being confined to an indefinitely long axis parallel to itself, and is called a rotor; if p is a rotor then wp is parallel and equal to p, and, like Hamilton's vector, wp is not localized; wp is therefore called a vector, though it differs from Hamilton's vector in that the product of any two such vectors wp and coo- is zero because w 2 =o.
- The total heat of the saturated vapour at any temperature is usually defined as the quantity of heat required to raise unit mass of the liquid from any convenient zero up to the temperature considered, and then to evaporate it at that temperature under the constant pressure of saturation.
- The total heat of steam, for instance, is generally reckoned from the state of water at the freezing-point, o° C. If h denote the heat required to raise the temperature of the liquid from the selected zero to the temperature t° C., and if H denote the total heat and L the latent heat of the vapour, also at t° C., we have evidently the simple relation H =L+h..
- To find the total heat H of a vapour, we have H =E+p(v - b), where the intrinsic energy E is measured from the selected zero 9 0 of total heat.
- The assumption n=s/R simplifies the adiabatic equation, but the value n=3.5 gives So =0.497 at zero pressure, which was the value found by Callendar experimentally at 108° C. and 1 atmosphere pressure.
- That of Biot is far more complicated and troublesome, but admits greater accuracy of adaptation, as it contains five constants (or six, if 0 is measured from an arbitrary zero).
- So =0.478 calories per degree at zero pressure, L=540 2 calories at loo° C. (JolyCallendar), n= 3'33, cioo = 26.30 c.c., b=t c.c., h=o 9970t+wL (v -w).
- In spite of these admonitions all but a few instrument makers have continued to make the vicious type of instrument consisting of a pair of gold-leaves suspended within a glass shade or bottle, no means being provided for keeping the walls of the vessel continually at zero potential.
- (3) For equilibrium we must have R=o, which requires Xo, Y=o; in words, the sum of, the components of the system must be zero for each of two perpendicular directions in the plane.
- If we equate these to zero we get the co-ordinates of the instantaneous centre.
- Again it is necessary and sufficient for equilibrium that the sum of the projections of the forces on each of two perpendicular directions should vanish, and (moreover) that the sum of the moments about some one point should be zero.
- - the sum of the moments of the forces about each of the three points which are not collinear must be zero.
- If they are not all parallel they must be concurrent, and their vectorsum must be zero.
- If the plane in question be chosen perpendicular to the direction of the vector-sum of the given forces, the vector-sum of the components Q is zero, and these components are therefore equivalent to a couple (~ 4).
- In the analogous theory of infinitely small displacements of a solid, a null-line is a line such that the lengthwise displacement of any point on it is zero.
- If the extraneous forces are n equilibrium the total work which they would perform in any such displacement would be zero, since they reduce to a zero force and a zero couple.
- Conversely, we can show that if the, virtual work of the extraneous forces be zero for every infinitesimal displacement of the body as rigid, these forces must be in equilibrium.
- For by giving the body (in imagination) a displacement of translation we learn that the sum of the resolved parts of the forces in any assigned direction is zero, and by giving it a displacement of pure rotation we learn that the sum of the moments about any assigned axis is zero.
- 49, on the body in its displaced position have zero moment about J; this is evidently the case, for instance, in the problem of rocking Stones.
- This may be described as a simple harmonic oscillation whose amplitude diminishes asymptotically to zero according to the law ehlr.
- Since the impulse of the force in any element of time & has zero moment about 0, the same will be true of the additional momentum generated.
- If A or B vanish we have an equiangular spiral, and the velocity at infinity is zero.
- Now the moment of this localized vector with respect to any axis through G is zero, to the first order of &, since the perpendicular distance of G from the tangent line at G is of the order (ot)2.
- If there are no extraneous forces, or if the extraneous forces have zero moment about any axis through G, the vector which represents the resultant angular momentum relative to G is constant in every respect.
- If the extraneous forces have zero moment about G the angular velocity 0 is constant.
- This is the same as the motion about a fixed point under the action of extraneous forces which have zero moment about that point.
- It frequently happens that the extraneous forces have zero moment about the axis of symmetry, as e.g.
- To apply this to liquids p must be made zero, and then StE = I, as is well known.
- Now from the laws of statics it is known that, in order that a system of forces applied to a system of connected points may be in equilibrium, it is necessary that the sum formed by putting together the products of the forces by the respective distances through which their points of application are capable of moving simultaneously, each along the direction of the force applied to it, shall be zero, products being considered positive or negative according as, the direction of the forces and the possible motions of their points of application are the same or opposite.
- Even when the thermometer fell 6° below zero, all appeared in good spirits and vigorous health.
- The images of the Gauss theory being of the third order, the next problem is to obtain an image of 5th order, or to make the coefficients of the powers of 3rd degree zero.
- For a single lens of very small thickness and given power, the aberration depends upon the ratio of the radii r: r', and is a minimum (but never zero) for a certain value of this ratio; it varies inversely with the refractive index (the power of the lens remaining constant).
- The total aberration of two or more very thin lenses in contact, being the sum of the individual aberrations, can be zero.
- The angle of contact of the first fluid is 180 and that of the second is zero.
- For water in a clean glass tube the angle of contact is zero, and h= 2T/pgr.
- F(ka), (2) where, as before, T is the superficial tension, p the density, and F is given by the following table: - The greatest value of F thus corresponds, not to a zero value of k 2 a 2, but approximately to k 2 a 2 = 4858, or to A = 4.508 X 2a.
- - When the internal pressure is equal to the external, the film forms a surface of which the mean curvature at every point is zero.
- Hence a catenoid whose directrix coincides with the axis of revolution has at every point its principal radii of curvature equal and opposite, so that the mean curvature of the surface is zero.
- Now if the pressure is equal on both sides of a liquid film, and if its mean curvature is zero, it will be in equilibrium.
- In front of the body the relative velocity of the fluid and the body varies from V where the fluid is at rest, to zero at the cutwater on the front surface of the body.
- Winter temperatures as low as 36° below zero are known for the higher altitudes; in the south, summer temperatures of 110° and higher have been recorded.
- The theory refers to radiation homogeneous at all points within a single closed boundary maintained at uniform temperature; in the actual case we have a double boundary, one the sun's surface, and the other infinitely remote, or say, non-existent, and at zero temperature; and it is assumed that the density of radiation in the free space varies inversely as the squares of the distance from the sun.
- The line a" a" drawn from zero parallel to the first line, produced to the boundaries of the diagram, will cut the vertical at the end of the first year at the percentage of the driest year's flow which may be safely drawn continuously from the reservoir throughout the two years.
- The shearing stresses are zero along the lines of principal stress and reach a maximum on lines at 45° thereto.
- The lower beam carries on a saddle a scale which is raised nearly to the top of the glass case in which the machine is enclosed, and as the beams sway this scale plays past a scratch on the glass, which is so placed that when the zero point on the scale coincides with the scratch the beams are horizontal.
- While these endeavors had produced zero income, the activities endeared him to the local ladies of the historical society who fluttered around the dapper gentleman like chicks at feed time.
- Therefore, zero or minimum tillage and direct seeding are important elements of conservation agriculture.
- We now use matrix perturbation theory to compute the covariance of based on this zero approximation.
- Or is the ' moment ' a purely mathematical abstraction, that is, a zero of time?
- Therefore, coefficient alpha will be equal to zero.
- By redefining the zero of time the voltage amplitude can always be made real.
- All results should ideally be zero, as the subjects should not be showing any atrophy.
- When the pressure gage reaches zero wait one or two minutes before opening the autoclave.
- If the input baud rate is set to zero, the input baud rate is specified by the value of the output baud rate.
- I continued my search with it set on zero, knowing the Iron would give a double bleep.
- To build a date or time string with field separators, a leading zero function should be used, to avoid code bloat.
- With all the stalls and people milling around driver did a good job, and achieved a zero body count.
- Thus, to refer again to the acoustical analogue in which plane waves are incident upon a perforated rigid screen, the circumstances of the case are best represented by the first method of resolution, leading to symmetrical secondary waves, in which the normal motion is supposed to be zero over the unperforated parts.
- If the fluid is a liquid, it can have a free surface without diffusing itself, as a gas would; and this free surface, being a surface of zero pressure, or more generally of uniform atmospheric pressure, will also be a surface of equal pressure, and therefore a horizontal plane.
- In the winter the temperature descends below zero during exceptionally cold spells.
- If the linear velocity of the cups in feet a second is V 1, and the linear velocity of the jet is V2, then the velocity of the jet relative to the cup is V2 - V1 feet a second, and if the whole energy of the water is to be given up to the cups, the water must leave the cup with zero absolute velocity.
- The limiting condition may be found by putting it equal to zero.
- The box, I, has a hinged bottom with a projecting click finger which, as the box de - scends, plays idly over the staves of a ladder arc. When the weight is removed from the platform, the counterbalance, E, causes the finger, G, to run back to its zero position, carrying with it the finger M, and causing the click finger of the box, I, to trip open the bottom of the box and let the penny fall out.
- The lever, J, regains its zero position, and all is ready for another weighing.
- The steelyard is exactly in balance when there is no weight on the platform and Q is at the zero end of its run, at 0.
- By this means the zero of the scale on the drum can be adjusted to the fixed index on the casing when there are no goods on the platform.
- This lever is so counterbalanced that when there is no weight in the pan the pendulum is vertical, and the index arm should then stand at zero.
- The zero adjust - ment is effected by means of levelling screws in the base of the frame.
- By the second part of the drop the motion of the poise is reversed and the poise is run back to the zero From the Notice issued by the Standards Department of the Board of Trade, by permission of the Controller of H.M.
- When the poise is at the zero end, and there is no load on the platform, the end of the steelyard is down, and has locked the ratchet wheel by means of the pawl; the shaft being thus locked, the sprocket wheels are stopped, the drum-shaft runs free by the friction clutch, and the two pulleys which are connected by the crossed band are running idle.
- Consequently the motion of the mitre wheels is reversed and the poise is run back to zero.
- When the poise arrives at zero it frees the clutch which connects the pulley and the sprocket wheel, and the machine is then ready for the next load.
- The essential features which distinguish this from other systems are (I) the limitation of the number of different symbols, only ten being used, however large the number to be represented may be; (2) the use of the zero to indicate the absence of number; and (3) the principle of local value, by which a symbol in effect represents different numbers, according to its position.
- To prevent confusion the zero or " nought " is introduced, so that the successive figures, beginning from the right, may represent ones, tens, hundreds,.
- The zero, called " nought," is of course a different thing from the letter 0 of the alphabet, but there may be a historical connexion between them (§ 79).
- 5, the zero o falling into its natural place immediately before the commencement of the first unit.
- It is convenient to introduce the zero; thus 0 I 2345 6789 o I 2345 indicates that after getting to 4 we make a fresh start from 4 as our zero.
- Then, if this difference is zero or is divisible by 7, II or 13, the original number is also so divisible; and conversely.
- Since represented 60, and o was the next letter, the latter appears to have been used to denote absence of one of the fractions; but it is not clear that our present sign for zero was actually derived from this.
- In calculating an average it should be observed that the addition of any numerical quantity (positive or negative) to each of the measurements produces the addition of the same quantity to the average, so that the calculation may often be simplified by taking some particular measurement as a new zero from which to measure.
- In mathematics, the term " infinite " denotes the result of increasing a variable without limit; similarly, the term " infinitesimal," meaning indefinitely small, denotes the result of diminishing the value of a variable without limit, with the reservation that it never becomes actually zero.
- In summer the temperature may rise as high as 106° F., while in winter it often sinks to 13° or even 20° below zero.
- The sheltered bays near Fiume enjoy an equable climate; but in all other districts the temperature in mid-winter falls regularly below zero, and the summer heats are excessive.
- At normal incidence the intensity of the reflected light, measured by the square of the amplitude, is { (µ -1) /(µ+ I) } 2 in both cases; but whereas in the former the intensity increases uniformly with i to the value unity for i =90°, in the latter the intensity at first decreases as i increases, until it attains the value zero when i -Fr = 90°, or tan i =,u - the polarizing angle of Brewster - and then increases until it becomes unity at grazing incidence.
- Thus A is zero at grazing incidence and at the critical angle, and attains its maximum value 7r-4 tan1 (I/p) at an angle of incidence given by sin e i=2/(p.2+I).
- The signs of the Peltier and Thomson effects will be the same as the signs of the coefficients given in Table I., if we suppose the metal s to be lead, and assume that the value of s may be taken as zero at all temperatures.
- 4, which is given as an illustration, the cold junctions are supposed to be at o° C. and the hot junctions at 100° C. Noll's values (Table I.) are taken for the E.M.F., and it is supposed that the coefficient of the Thomson effect is zero in lead, i.e.
- The line of lead is taken to be horizontal in the diagram, because the thermoelectric power, p, may be reckoned from any convenient zero.
- Temperatures below zero are rare for any locality; and the same may be said of temperatures above 95° in summer.
- In the case of the circle, the centre is the focus, and the line at infinity the directrix; we therefore see that a circle is a conic of zero eccentricity.
- If, however, we fix the points lying towards the margin of the field of view, the diaphragm gradually cuts off more and more of the rays which were necessary to fill the pupil, and in consequence the brightness gradually falls off to zero.
- In this case also the illumination must fall to zero by the vignetting of the pencils coming from objects at the margin of the field of view.
- Losses due to absorption are almost zero when the lenses are very thin, as with lenses of small diameter.
- These diffracting details become especially distinct if the direct lighting cone of rays, the spectrum of zero:order or the chief maximum, is not allowed to enter the objective and instead only two or more diffraction maxima are taken up; the details then appear bright on a dark background.
- The micrometer stands at zero if the zero mark of the cylinder coincides with the index and the fixed mark is at a known division.
- The calculation is most convenient if the micrometer is left in the position of zero and the object is moved till one of its edges corresponds to the zero mark of the eyepiece scale.
- The freezing-points of those oils which are fluid at the ordinary temperature range from a few degrees above zero down to - 28° C. (linseed oil).
- The temperature attainable depends on the strength and condition of the sulphuric acid; ordinarily it can be reduced to zero F., and temperatures 20° lower have frequently been obtained.
- Under these conditions, the actual evaporating temperature T 1, in a wellconstructed ammonia compression machine, after allowing for the differences necessary for the exchange of heat, would be about 5° below zero, and the discharge temperature T would be about 75°.
- An ideal machine, working between 5° below zero and 75° above, has a coefficient of about 5.7, or nearly six times that of an ideal compressed-air machine of usual construction performing the same useful cooling work.
- Assuming, as in the previous example, that T 2 is 75° F., and that T 3 is 5° below zero, the results for various refrigerating agents are as follows: TABLE II.
- This needle or coil must be so damped that when the current is cut off it returns to zero at once without overshooting the mark.
- My understanding was limited to knowing zero degrees latitude began at the equator and increased to ninety degrees at the poles.
- He was dressed in all black again from turtleneck to heavy boots despite the heat of early afternoon, the color emphasizing the zero body fat of his lean body.
- Particles with zero or integer spin are called bosons after Satyendra Bose, who together with Einstein described their kind of statistical mechanics.
- Zero (0) is returned to indi- cate a zero value, rather than the null string.
- Nancy is the Ground Zero of idle chit chat; which is odd considering what could be spread about her.
- We recommend that gene sequences be numbered so that the first base of the first codon is numbered zero.
- As for coke zero, it's coke zero, it's coke light under a different guise.
- Residues with alternate conformations (using shelx occupancies) were getting marked as zero occupancy atoms.
- The allocated colors in a shared colormap do not generally start at zero and they are not necessarily contiguous.
- Use of truncation toward zero in implicit conversion has not always been guaranteed in C either, by the way.
- All vehicles replaced by hydrogen fuel cell vehicles with zero CO 2 emissions, powered by renewable, short-rotation coppice produced fuel.
- The researchers can cool a beam of hydrogen atoms using a helium cryostat to just 10 degrees above absolute zero.
- If the server's global debug level is greater than zero, then debugging mode will be active.
- I'd never felt decadent enough to burn film that fast, but with digital there's zero marginal cost.
- The payoff of mutual defection, DD, provides the baseline outcome that yields a payoff of zero to both participants.
- Then for a given value of the optimum gain can be found by setting the partial derivative of with respect to to zero.
- In addition, a technology park would be built alongside a ' Ground Zero Museum ' containing detritus and mementos from the Cold War.
- A zero value occurring on the leading diagonal does not mean the matrix is singular.
- The spectral leakage increases since zero padding introduces a discontinuity in the data stream.
- The locations on the board at which zero vibration displacement occurs are called nodes, and the maximum displacement amplitudes occur at the antinodes.
- The system also allows for driving shorter distances with just electrical power and therefore zero emissions.
- In a topologically trivial spacetime, one could make the electro static potential zero, by a gage transformation.
- A perfect black body radiator has an emissivity of unity, so all other surfaces have emissivity between zero and one.
- A zero reference button is the only external control on the Encoder.
- They played quite a few tracks from the latest album including my current fave Zero Friction.
- Either zero or its contract with billion or more grabbed the checkered flag.
- What would be the perfect foil for the Zero?
- Its three and four wheeled electric forklifts offer reduced noise and zero emissions, making them ideal garden centers and greenhouses.
- In the UK, board manufacturers are advertising low formaldehyde or zero formaldehyde emission boards made to the stringent German " E1 " standard.
- Pixels where the two images were equal are zero, and appear as gray.
- Options are also available for fire retardant formulas including low smoke zero halogen.
- They take numbers as decimal unless starting with 0x (or 0X ), meaning hexadecimal; a leading zero does not mean octal.
- Diagnosis of secondary hypothyroidism can be done by measuring cTSH at zero and 30 minutes post TRH stimulation.
- The Cuban youth illiteracy rate is zero, unmatched by any other Latin American country, where the average is 7% .
- Fifteen years ago, its net foreign indebtedness was zero.
- A zero length mark will make a hanging indent instead.
- The rate of Dutch house-price inflation then slowed from 20% in 2000 to nearly zero by 2003.
- The key is for them to reduce their alcohol intake to zero, or near zero.
- Parameter $ 0 is set from argument zero at shell invocation.
- Whoever has the highest karma at the end of the week gets made moderator, then their karma gets reset to zero.
- On the contrary 3 of the 4 zero anisotropy events identified are seen at heliographic latitudes greater than 42 degrees south.
- The benefit is a dramatic reduction in spectral leakage, enabling any measure of zero padding to be used.
- For this is where the Earth's prime meridian, the line of zero degrees longitude, originates.
- A negative or reverse magnetic force applied for reducing magnetic induction to zero.
- The pri- Mary components are a stream head, a driver, and zero or more modules between the stream head and driver.
- In quantum mechanics, a system can never have an energy of exactly zero.
- For each reading, first set the instrument to read zero absorbance with a tube containing acidified methanol alone (the blank ).
- In the calculation median seeing conditions are assumed, the zenith angle is zero, and the deformable mirror is conjugate to 6.5 km.
- This " optical molasses " can slow millions of atoms to temperatures just millionths of a degree above absolute zero.
- Rule 3: Zero in the numerator of a fraction A numerator of a fraction A numerator is allowed to take on the value of zero in a fraction.
- He hopes to compose the first oratorio to be performed in zero gravity.
- The use of these blocks in mango orchards was shown to reduce losses from 20% to zero.
- Using the equation l p = h. If the momentum of the electrons is zero, then the wavelength they have is infinite.
- As a result, the collective payoff deteriorates, reaching the zero level around generation 120.
- The peaks arise because the denominator will approach zero at sinusoidal frequencies, resulting in exceedingly sharp spectral peaks.
- But Cambridgeshire CID wanted her to take zero tolerance a step further by giving them the names of the alleged dope peddlers.
- The combination of ground temperatures only slightly below zero, high ice contents and steep slopes, makes mountain permafrost particularly vulnerable to changes.
- If pgid is zero, the process ID of the process specified by PID is used.
- Catching everyone by surprise, the temperature suddenly plummeted to zero.
- These zero percentage polarization values then result in zero polarized intensity values.
- From their point of view zero popularity is a time wasting.
- In basement reservoirs matrix porosity is effectively close to zero and most of the storage capacity and permeability is due to fractures.
- Instead, upon notifying the affected product vendor, 3Com provides its customers with zero day protection through its intrusion prevention technology.
- For this is where the earth's prime meridian, the line of zero degrees longitude, originates.
- In a formal argument we claim the transition probability of OK to ERROR is zero.
- If the code is 4, and the second number is not zero, compute the quotient (first divided by second ).
- The output of the expert system is a trust quotient, in the range from zero to one.
- The output radix must be at least 2. The precision must be zero or greater.
- Zero Representation Another of the Home Secretary's Good Ideas is to limit the right of accused rapists to represent themselves in court.
- Reactions may commonly be zero order, first order or second order with respect to a particular reactant.
- Higher order bits in pixel representations are assumed to be zero.
- Brachial systolic and diastolic pressure and ankle systolic pressures were measured using a Hawksley random zero sphygmomanometer and Doppler probe.
- To get them for the starting model for the least squares do zero cycles.
- The output shows however that the associated standard deviation is equal to zero.
- The resulting vector, stored in the variable bad, contains the subscripts of the elements of data that are less than zero.
- A blade that is radially symmetrical is said to have zero skew.
- Returns: the session timeout limit in seconds; zero means there is no limit.
- Values through car churchill insurance wheels zero tolerance ' ago mainly relying.
- If all the light is absorbed, then percent transmittance is zero, and absorption is infinite.
- The superposed epoch studies were carried out using the time of the southward turning as time zero.
- It may be set to any integer value greater than or equal to zero.
- You could eventually get back to the element vanadium which would have an oxidation state of zero.
- Away from Ground Zero the magnetic field lines are not vertical.
- The Excess is £ 500 which can be reduced to zero by paying the collision damage waiver of £ 4 per day.
- A minimum width of zero makes field completion optional.
- If a zero fare is charged, consumers will demand bus journeys up to the point where the demand curve cuts the x-axis.
- A correction factor for C P in cases where yaw angle is not zero is given by where is the yaw angle is not zero is given by where is the yaw angle.
- Trusts scoring zero are shown at the left margin; trusts with no value are shown at the right margin.
- You must not let your ammo reach zero or the cheat won't work.
- If you need to force a scalar to a number, add a zero to it.
- Callers should then dial " 44 " for the UK, then your telephone number, dropping the initial zero.
- At a few hundred degrees above absolute zero, objects radiate strongly in the shorter wave infrared.
- For numbers smaller than 10, a leading zero is present.
- Closure of the reactors by 2009 would allow Sellafield to reprocess all remaining Magnox fuel before the 2020 " near zero " deadline.
- Despite the Chancellor's much stated policy aim to raise UK productivity, 2005 looks like ground zero.
- Prices Price including postage and packing to UK only (vat zero rated) - £ 70.
- The main part of the screen contains the paper on which you write and the cursor blinks away at line zero, column zero.
- The consequences of supposing AN to be zero have already been traced.
- The discordance in zero, when known to exist, is really of no consequence, because the observations can be so arranged as to eliminate it.
- Repsolds in more recent micrometers under construction give a second motion to the eyepiece at right angles to the axis of the micrometer screw; this enables the observer to determine the zero of position-angle for his movable webs with the same accuracy as he formerly could only do for the so-called position-angle webs.
- The purpose of his paper was to show that if the axis, by which the observer imparts motion to the slide on which the travelling web is mounted, is provided with two disks at its extremities, so that the observer can use the thumb and finger of both hands in rotating it, there is no difficulty, after a little practice, in keeping the web constantly bisecting the star in transit, and that with a little practice the mean of the absolute errors in following the star becomes nearly zero.
- Both type-wheels are then set to zero by the lever provided for that purpose, and released by the current from the letter-blank key; then all subsequent signals will be recorded similarly at the sending and receiving ends..
- The special form of curb sender mentioned, termed the " Interpolator," has been devised so as to secure the correct re-transmission of any given number of consecutive elements of a letter which are of the same sign, for when signals are received at the end of a long cable the relay arm will not return to its zero position between consecutive elements of the same sign, but will remain on the respective contact surface during the whole time occupied by such consecutive elements.
- It was seen that the effect of the impact of the incident electric waves upon the vertical receiving wire was to create in it electrical oscillations, or in other words, high frequency alternating electric currents, such that whilst the potential variations were a maximum at the top or insulated end of the antenna the current at that point was zero and at the base the potential variation was zero and the current amplitude a maximum.
- All such plants agree in reducing transpiration to zero during the unfavourable season, although few or no xerophytic characters may be demonstrable during the period favorable to growth.
- Experimentally (by extrapolation from the" law of the rectilinear diameter ") the critical volume is four times the volume at absolute zero (see Condensation Of Gases).
- The relative abundance of nitrates and nitrites at the bottom of deep oceans as compared with the surface can be explained in the same way, for at the bottom the temperature is about zero Centigrade and the activities of the denitrifying bacteria are practically suspended.
- If we form the product A.D by the theorem for the multiplication of determinants we find that the element in the i th row and k th column of the product is akiAtil+ak2A12 +Ã¯¿½Ã¯¿½Ã¯¿½ +aknAin, the value of which is zero when k is different from i, whilst it has the value A when k=i.
- For Two Forms The Seminvariants Of Degrees I, I Are Enumerated By 1 Z, And The Only One Which Is Reducible Is Ao 0 Of Weight Zero; 1 Hence The Perpetuants Of Degrees I, I Are Enumerated By 11 1 Ã¯¿½ Z 1Zz' And The Series Is Evidently A O B 1 Aibo, A 0 B 2 A B A2Bo, A O B 3 A L B 2 A 2 B 1 A3Bo, One For Each Of The Weights I, 2, 3,..Ad Infin.
- If instead of measuring from zero we measure from P, we find Q - R+ S = T-- P. The difference between this and (iii.) is that we transpose the first term instead of the last; the two methods corresponding to the two cases under (i.) of Ã¯¿½ 1 5 (2).
- The Poisson equation cannot, however, be applied in the above form to a region which is partly within and partly without an electrified conductor, because then the electric force undergoes a sudden change in value from zero to a finite value, in passing outwards through the bounding surface of the conductor.
- In the case of liquids and solids, comparison with water at 4Ã‚° C., the temperature of the maximum density of water; at o C., the zero of the Centigrade scale and the freezingpoint of water; at 15Ã‚° and 18Ã‚°, ordinary room-temperatures; and at 25Ã‚°, the temperature at which a thermostat may be conveniently maintained, are common in laboratory practice.
- The maximum separation is consequently at 45Ã‚° from zero.
- If, however, hinges or joints are introduced at the points of contrary flexure, they become necessarily points where the bending moment is zero and ambiguity as to the stresses vanishes.