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zero

zero

zero Sentence Examples

  • Dean pushed each of the four buzzers, with zero response.

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  • Zero is a cardinal number.

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  • The locks will open at zero four twenty-five.

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  • 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.

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  • Going from zero to one puppy might increase your utility a great amount.

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  • Both Deans agreed the letters were polite but of zero historical interest and strangely unloving.

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  • Both Deans agreed the letters were polite but of zero historical interest and strangely unloving.

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  • While the hum of the machines broke up the silence of the room, I was making zero progress.

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  • Therefore every form of degree 2, except of course that one whose weight is zero, is a perpetuant.

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  • Therefore every form of degree 2, except of course that one whose weight is zero, is a perpetuant.

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  • "It was zero this morning," he reminded her.

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  • There are zero personal memories.

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  • The micrometer is at zero when the two edges are brought exactly together.

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  • 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.

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  • 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.

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  • If s is any class and zero is a member of it, also if when x is a cardinal number and a member of s, also x-}-I is a member of s, then the whole class of cardinal numbers is contained in s.

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  • Or why they were here in the first place, as they expressed zero interest in the beauty of the area; Ouray's main attraction.

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

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  • One percent now is better than zero percent in three months.

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  • Theoretically the critical volume is three times the volume at absolute zero, i.e.

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  • This can be verified by equating to zero the five coefficients of the Hessian (ab) 2 axb2.

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  • St Petersburg, again, is connected with Greenwich by European systems of triangulation; and the Greenwich meridian is adopted by Russia as the zero for all her longitude values.

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  • The instrument therefore does not begin to read from zero current, but from some higher limit which, generally speaking, is about one-tenth of the maximum, so that an ammeter reading up to io amperes will not give much visible indication below i ampere.

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

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  • This can be verified by equating to zero the five coefficients of the Hessian (ab) 2 axb2.

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  • in the summer and 10° below zero in the winter.

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  • Day four, and he was zero for four.

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  • (1-20) The actual form of a perpetuant of degree 0 has been shown by MacMahon to be +1 K0_1+1 K 3+20-4 K2, 01, 0-2, 0-3, ...3, 2), K 0, Ke -1, ...K 2 being given any zero or positive integer values.

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  • t (22P11),; X 1 and 12 each assuming all integer (including zero) values.

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  • "That's nice," said Fred O'Connor, who had zero tradition, at least as far has Dean had learned in the fifteen years he'd lived with the old man.

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  • When the key is released the condensers and cables at once begin to return to zero potential, and if the key is depressed and released several times in rapid succession the cable is divided into sections of varying potential, which travel rapidly towards the receiving end, and indicate their arrival there by producing corresponding fluctuations in the charge of the condenser C3.

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  • On the whole, February and March continue to be cold, and their average temperatures rise above zero nowhere except on the Black Sea coast.

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  • The coil is so situated that, in its zero position when no current is passing through it, the plane of the coil is parallel to the direction of the lines of force of the field.

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  • If then the torsion head is provided with an index needle, and also if the movable coil is provided with an indicating point, it is possible to measure the torsional angle through which the head must be twisted to bring the movable coil back to its zero position.

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  • below zero and in August rises to loo°.

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  • Hot-wire ammeters are, however, liable to a shift of zero, and means are always provided by some adjusting screw for slightly altering the sag of the wire and so adjusting the index needle to the zero of the scale.

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  • Such instruments can be made to have equidivisional scales and to read from zero upwards.

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  • 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 +��� +aknAin, the value of which is zero when k is different from i, whilst it has the value A when k=i.

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  • = 0, we find that, eliminating x, the resultant is a homogeneous function of y and z of degree mn; equating this to zero and solving for the ratio of y to z we obtain mn solutions; if values of y and z, given by any solution, be substituted in each of the two equations, they will possess a common factor which gives a value of x which, corn bined with the chosen values of y and z, yields a system of values which satisfies both equations.

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  • It was an infuriating conversation, resulting in a big, fat zero.

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  • The survival rate on wounds like that are zero.

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  • Screw adjustments are provided for closing or opening the air gap between the electromagnets and armatures, for raising or lowering the siphon, and for adjusting the point of the siphon to the centre or side of the paper strip. The received signals are recorded on the paper strip in an undulating continuous line of ink, and are distinguished by the length of deviation from zero.

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  • He showed that in a simple Marconi antenna the variations of potential are a maximum at the insulated top and a minimum at the base, whilst the current amplitudes are a maximum at the top earthed end and zero at the top end.

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  • At a uniform speed on a level straight road 3, 5 and 6 are zero.

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  • above the zero of Fahrenheit; the lowest mean tem perature anywhere observed is about 4° Fahr., at Melville Island, north of the American continent.

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  • If any two rows or any two columns of a determinant be identical the value of the determinant is zero.

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  • anibll +an2b12+� �� +annbin a11b21+a12b22+��� +alnb2n, a21b21+a22b22+��� +a2nb2n, � � � ani b21 + a n2 b 22 + � � � +annb2n alib31+a12b32+���+ainb3n, a21b31+a22b32+���+a2nb3n, .�.a n lb 31 + a n2 b 32+ ��� +annb2n a ll b nl + a 12 b n2+ ��� + a ln b nn, a21bn1+a22bn2+�-�+a2nbnn, � � � ani b nl + a n2 b n2 +� � � +annbnn and all the elements of D become zero.

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  • Hence the product determinant has the principal diagonal elements each equal to A and the remaining elements zero.

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  • except that the elements of the leading diagonal are not all zero.

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  • A binary form which has a square factor has its discriminant equal to zero.

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  • By solving the equations of transformation we obtain rE1 = a22x1 - a12x1, r = - a21x1 + allx2, aua12 where r = I = anon-anon; a21 a22 r is termed the determinant of substitution or modulus of transformation; we assure x 1, x 2 to be independents, so that r must differ from zero.

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  • the i t " power of that appertaining to a x and b x multiplied by the j t " power of that appertaining to a x and c x multiplied by &c. If any two of the linear forms, say p x, qx, be supposed identical, any symbolic expression involving the factor (pq) is zero.

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  • To prove that this system is complete we have to consider (f, o) 2, 04') 1, (f,Q) 1, (f,Q) 2, (f,Q) 3, 0,Q) 1, (o,Q)2, and each of these can be shown either to be zero or to be a rational integral function of f, 0 Q and R.

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  • Restricted Substitutions We may regard the factors of a binary n ip equated to zero as denoting n straight lines through the origin, the co-ordinates being Cartesian and the axes inclined at any angle.

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  • Then a binary n", equated to zero, represents n straight lines through the origin, and the x, y of any line through the origin are given constant multiples of the sines of the angles which that line makes with two fixed lines, the axes of co-ordinates.

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  • if the determinant factors to be, each of them, either zero or unity.

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  • to be, each of them, either zero or unity.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 539) of demagnetizing a specimen by subjecting it to a succession of magnetic forces which alternated in direction and gradually diminished in strength from a high value to zero.

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  • dW F - d -v 1+ a 7rK dx dH (38) (34) [[[Magnetic Measurements]] If Ho is constant, the force will be zero; if Ho is variable, the sphere will tend to move in the direction in which Ho varies most rapidly.

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  • At a point whose distance from the axis of the wire is r the tangential magnetic force is H = 21r /a 2 (39) it therefore varies directly as the distance from the axis, where it is zero.'

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  • Plate 59), the magnetizing field Ho being first gradually increased and then diminished to zero.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • Mag., 1887, 23, 225) approached very much more nearly than Baur to the zero of magnetic force.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.'

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  • 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.

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  • 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.

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  • 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.

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  • (v.) An alternative method of obtaining the rule of transposition is to change the zero from which we measure.

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  • If r is greater than m or n (though of course not greater than m+n), some of the terms in (22) and (23) will be zero.

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  • It may be necessary to introduce terms with zero coefficients.

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  • +X) happens to be zero, X lies at infinity in a determinate direction; unless - aA is the barycentre of (3B, yC, ...

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  • 1n(n - I) distinct values, exclusive of zero.

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  • If r+s>n, a product such as E r E 3, worked out by the previous rules, comes out to be zero.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • It vanishes when u =mlr, m being any whole number other than zero.

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  • 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.

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  • The first root after zero is thus in the third quadrant, corresponding to m =1.

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  • 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.

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  • For a certain distance outwards this remains sensibly unimpaired and then gradually diminishes to zero, as the secondary waves become discrepant in phase.

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  • 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.

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  • The vibrations corresponding to the two parts are precisely antagonistic, since if both were operative the resultant would be zero.

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  • 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.

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  • (19), 1 abA) ' ' we may write 12= (cos 27rv 2 .dv) 2 + (f sin zirv 2 .dv) 2 (20), or, according to our previous notation, 12 = (2 - C 2 +(z - Sv)2= G2 +H2 Now in the integrals represented by G and H every element diminishes as V increases from zero.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • If w vanishes throughout the fluid at any instant, equation (I I) shows that it will always be zero, and the fluid motion is then called irrotational; and a function 4) exists, called the velocity function, such that udx+vdy-{-wdz =-d, (13) and then the velocity in any direction is the space-decrease or downward gradient of cp.

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  • 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.

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  • Over a concentric cylinder, external or internal, of radius r=b, 4,'=4,+ Uly =[U I - + Ui]y, (4) and 4" is zero if U 1 /U = (a 2 - b2)/b 2; (5) so that the cylinder may swim for an instant in the liquid without distortion, with this velocity Ui; and w in (I) will give the liquid motion in the interspace between the fixed cylinder r =a and the concentric cylinder r=b, moving with velocity U1.

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  • (io) The velocity q is zero in a corner where the hyperbola a cuts the ellipse a; and round the ellipse a the velocity q reaches a maximum when the tangent has turned through a right angle, and then q _ (Ch 2a-C0s 2(3).

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  • With a velocity function 49, the flow -f d 4 = 4)142, (2) (9) (to) (6) (22) Z Uy (I -a4,ic /r4), so that the flow is independent of the curve for all curves mutually reconcilable; and the circulation round a closed curve is zero, if the curve can be reduced to a point without leaving a region for which 4 is single valued.

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  • 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.

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  • = -dQ+1dg2, and integrating round a closed curve (udx+vdy+wdz) =0, and the circulation in any circuit composed of the same fluid particles is constant; and if the motion is differential irrotational and due to a velocity function, the circulation is zero round all reconcilable paths.

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  • 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.

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  • In the general motion again of the liquid filling a case, when a = b, 52 3 may be replaced by zero, and the equations, hydrodynamical and dynamical, reduce to d =- 2+ 2 J, = 2 x22111, d = 2 2`2 (+/'15-Om) (1 yy y n`t dt a +c dt a +c dt a +c) dc2, a2-1-c2 d122 a2 c2 dt ="2) +a2= G2y 71' dt = 121 1 - a 2 -c 2SJ, (19) of which three integrals are e +777 r z y 2= L -?2J2, (20) (a2 + c2) 2 2 121+14 =M+ 2c2(a2-c2)1 ' (21) 121+522hN = + x24 2,2 and then (dt / 2 = (a2 + c 2) 2(° v 2 - 12171) 2 4C4 2 2 - (+ c2)2?(E+77) (?

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  • For the 2 polygon has a right angle at a=a, a', and a zero angle at u = b, where 0 changes from o to 27/n and 1 - 2 increases by 21-rr/n; so that dSt A (b -a.b -a') a - (u -b),/ (u - a.u - a where A= tn (II) And the w polygon has a zero angle at u =o, oo, where 4, changes from o to m and back again, so that w changes by im, and du =B, where B=-.

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  • To determine x i the angular velocity P alone is introduced, and the conditions to be satisfied are (i.) 0 2 x1 = o, throughout the liquid; y l =mz - ny, at the surface of the moving body, but zero over a fixed surface, and at :infinity; the same for x 2 and x3.

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  • When the source S is inside the sphere and H outside, the line sink must extend from H to infinity in the image system; to realize physically the condition of zero flow across the sphere, an equal sink must be introduced at some other internal point S'.

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  • the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

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  • Thus the human element is reduced to zero, and the conception of prophecy becomes mechanical.

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  • We arbitrarily call the potential of the earth zero, since all potential difference is relative and there is no absolute potential any more than absolute level.

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  • Hence we see that if the whole surface of the sphere is divided into pairs of elements by cones described through any interior point, the resultant force at that point must consist of the sum of pairs of equal and opposite forces, and is therefore zero.

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  • p. 76, where Maxwell gives an elegant proof that if the force in the interior of a closed conductor is zero, the law of the force must be that of the inverse square of the distance.'

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  • Hence if the force is zero the potential V must be constant.

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  • 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.

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  • It must be such a potential distribution that the potential in the interior will be to constant, since the electric force must be zero.

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  • If then the outer cylinder be at zero potential the potential V of the inner one is V =A log (R 2 /R 1), and its capacity C =1/2 log R2/R1.

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  • It depends on the principle that if two condensers of capacity C I and C2 are respectively charged to potentials V I and V2, and then joined in parallel with terminals of opposite charge together, the resulting potential difference of the two condensers will be V, such that V = (C,V 2 -CiV2) /(C1+C2) (16); and hence if V is zero we have C I: C2 = V2 The method is carried out by charging the two condensers to be compared at the two sections of a high resistance joining the ends of a battery which is divided into two parts by a movable contact.'

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  • In general the dielectric constant is reduced with decrease of temperature towards a certain limiting value it would attain at the absolute zero.

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  • 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.

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  • But the force perpendicular to the curved surface of this cylinder is everywhere zero.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 5) a point-charge of positive electricity +q _q/ +q and an infinite conducting plate PO, shown in section, connected to earth and therefore at zero potential.

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  • 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.

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  • yet by any means can keep the identical surface occupied by it a plane of zero potential, the boundary conditions will remain the same, and therefore the field of force to the left of PO will remain unaltered.

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  • 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).

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  • 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.

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  • 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.

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  • 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.

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  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • Zero hour was to be 5:20 A.M.

    0
    0
  • Zero hour was at 5:20 A.M.

    0
    0
  • Zero hour was at 6:5 A.M.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 4) that Bessel had indicated, by notes in his handbooks, the following points which should be kept in mind in the construction of future heliometers: (I) The segments should move in cylindrical slides; b (2) the screw should be protected from dust; 6 (3) the zero of the position circle should not be so liable to change; 7 (4) the distance of the optical centres of the segments should not change in different position angles or otherwise; 8 (5) the points of the micrometer screws should rest on ivory plates; 9 (6) there should be an apparatus for changing the screen.'° Wilhelm Struve, in describing the Pulkowa heliometer,' 1 made The distances of the optical centres of the segments from the eye-piece are in this method as I; secant of the angle under measurement.

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    0
  • The maximum separation is consequently at 45° from zero.

    0
    0
  • The measures can be made on both sides of zero for eliminating index error.

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    0
  • 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.

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    0
  • 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.

    0
    0
  • This conception of the nature of heat leads at once to an absolute zero of temperature - a temperature of no heat-motion--which is identical, as will be seen later, with that reached in other ways, namely, about - 273° C.

    0
    0
  • 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.

    0
    0
  • To examine what is meant by a zero value of n we refer to formula (15).

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    0
  • below zero to 100° above) and marked local variations.

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    0
  • 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.

    0
    0
  • In the case of the triangle, for instance, b is zero, so that the area is lha.

    0
    0
  • Either or both of the bounding ordinates may be zero; the top, in that case, meets the base at that extremity.

    0
    0
  • 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.

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    0
  • In the winter the temperature descends below zero during exceptionally cold spells.

    0
    0
  • In the Puget Sound Basin an occasional cold east wind during a dry period in winter causes the temperature to fall below zero.

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    0
  • 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.

    0
    0
  • Since the resultant is zero, mU 2 sin 4) - T sin ct.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • or falls below zero.

    0
    0
  • 2 4 2m +2 2m+4; the function of zero order C is deduced by making m= o, and is equivalent to the series I -22 -}- 2-.4-, , &c. O.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • Mehler, who proved that a simple relation existed between the function of zero order and the zonal harmonic of order n.

    0
    0
  • that x-"' log x tends to zero as x tends to 00 for every positive value of m however small.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • in the general equation of the second degree the co-efficients of x 2 and y 2 are equal, and of xy zero.

    0
    0
  • Since the equation to a circle of zero radius is x 2 +y 2 =o, i.e.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • This formed the zero of the scale.

    0
    0
  • A solution containing to% of pure salt is used to indicate the zero of the scale, and the point at which the instrument floats when immersed in distilled water at to° R.

    0
    0
  • Each scale has its zero in the middle corresponding to 60° F.

    0
    0
  • 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? ?!

    0
    0
  • lower than the zero of the scale (60° F.) the a pl spirit must be reckoned stronger by the scale reading.

    0
    0
  • 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.

    0
    0
  • In Beck's hydrometer the zero of the scale corresponds to density 1 000 and the division 30 to density.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • intensity is zero, and this band is accompanied by a number of fainter images corresponding to the diffraction of a star image in a telescope.

    0
    0
  • 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.'

    0
    0
  • 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.

    0
    0
  • It arises from the ellipticity of the orbit, is zero at pericentre and apocentre, and reaches its greatest amount nearly midway between these points.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

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    0
  • 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.

    0
    0
  • 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.

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    0
  • ii.) that the abnormal values of the variation observed in the wood-built ships of his day was due to deviation of the compass caused by the iron in the ship; that the deviation was zero when the ship's head was near the north and south points; that it attained its maximum on the east and west points, and varied as the sine of the azimuth of the ship's head reckoned from the zero points.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • below the Amsterdam zero' in some of the drained lands in the western half of the country.

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    0
  • 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.

    0
    0
  • below the Amsterdam zero.

    0
    0
  • below the Amsterdam zero, but in the Noorderkwartier to the north, it reaches 102 ft.

    0
    0
  • below the Amsterdam zero, though the average is about I to 13 ft.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • (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.

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    0
  • If h also is zero, it becomes the equation of variable flow in the soil.

    0
    0
  • below zero; while their summers are delightful, with much sunshine and some hot days but pleasantly cool nights.

    0
    0
  • In summer the temperature varies from 70° to 90° F., and in winter from 50° above to 10° below zero.

    0
    0
  • Sleep is not exhaustion of the neuron in the sense that prolonged activity has reduced its excitability to zero.

    0
    0
  • 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.

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    0
  • 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.

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    0
  • Trans., 1900), The Atomic Heats Of Pure Nickel And Cobalt, As Determined From Experiments At The Boiling Points Of 02, And C02, Diminish So Rapidly At Temperatures Below O° C. As To Suggest That They Would Reach The Value 2.42 At The Absolute Zero.

    0
    0
  • 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.

    0
    0
  • In the next two days it reached zero magnitude, thus becoming the brightest star in the northern heavens, but after that it rapidly decreased.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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..

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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).

    0
    0
  • 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).

    0
    0
  • 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.

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    0
  • Zero >>

    0
    0
  • (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.

    0
    0
  • If we equate these to zero we get the co-ordinates of the instantaneous centre.

    0
    0
  • 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.

    0
    0
  • - the sum of the moments of the forces about each of the three points which are not collinear must be zero.

    0
    0
  • If they are not all parallel they must be concurrent, and their vectorsum must be zero.

    0
    0
  • 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).

    0
    0
  • 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.

    0
    0
  • If a line is a null-line with respect to the wrench (X, Y, Z, L, M, N), the work done in an infinitely small rotation about it is zero, and its coordinates are accordingly subject to the further relation Lf+M~+Nl+XX+Yp+Zvo, (5~

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • This may be described as a simple harmonic oscillation whose amplitude diminishes asymptotically to zero according to the law ehlr.

    0
    0
  • 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.

    0
    0
  • If A or B vanish we have an equiangular spiral, and the velocity at infinity is zero.

    0
    0
  • if in a line through G, and has therefore zero moment about any axis through G; hence in taking moments about such an axis we need only regard the velocities relative to G.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • gravity) have zero moment about G, w will be constant.

    0
    0
  • If the extraneous forces have zero moment about G the angular velocity 0 is constant.

    0
    0
  • This is the same as the motion about a fixed point under the action of extraneous forces which have zero moment about that point.

    0
    0
  • It frequently happens that the extraneous forces have zero moment about the axis of symmetry, as e.g.

    0
    0
  • qn differ from zero.

    0
    0
  • To apply this to liquids p must be made zero, and then StE = I, as is well known.

    0
    0
  • 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.

    0
    0
  • - -)Engelso In order that these conditions may obtain, the quantities in the brackets must be zero, since the factor aug is not zero.

    0
    0
  • in the south, and nearly zero in the Baltic provinces.

    0
    0
  • Even when the thermometer fell 6° below zero, all appeared in good spirits and vigorous health.

    0
    0
  • 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.

    0
    0
  • 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).

    0
    0
  • The total aberration of two or more very thin lenses in contact, being the sum of the individual aberrations, can be zero.

    0
    0
  • Consequently the powers of the two must be different (in order that 4) be not zero (equation 2)), and the dispersive powers must also be different (according to 4).

    0
    0
  • n qn qn-i - () gngn-1, and the limit of the right hand side is not necessarily zero.

    0
    0
  • The angle of contact of the first fluid is 180 and that of the second is zero.

    0
    0
  • For water in a clean glass tube the angle of contact is zero, and h= 2T/pgr.

    0
    0
  • 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.

    0
    0
  • - When the internal pressure is equal to the external, the film forms a surface of which the mean curvature at every point is zero.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • The limiting condition may be found by putting it equal to zero.

    0
    0
  • 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.

    0
    0
  • The thermometer rarely registers below zero F.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • The shearing stresses are zero along the lines of principal stress and reach a maximum on lines at 45° thereto.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • The lever, J, regains its zero position, and all is ready for another weighing.

    0
    0
  • 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.

    0
    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.

    0
    0
  • 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.

    0
    0
  • The zero adjust - ment is effected by means of levelling screws in the base of the frame.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • Consequently the motion of the mitre wheels is reversed and the poise is run back to zero.

    0
    0
  • 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.

    0
    0
  • or as low as zero.

    0
    0
  • (I) If the load is self-sustaining E' is zero or negative, and hence b -{- M/R must be equal to or greater than unity, and therefore it is impossible for the ratio of RÆ to rise to a greater value than (I - a)/2, and hence at least half the effort is wasted if the tackle 6.

    0
    0
  • 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.

    0
    0
  • To prevent confusion the zero or " nought " is introduced, so that the successive figures, beginning from the right, may represent ones, tens, hundreds,.

    0
    0
  • 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).

    0
    0
  • 5, the zero o falling into its natural place immediately before the commencement of the first unit.

    0
    0
  • 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.

    0
    0
  • is zero or divisible by I i.

    0
    0
  • Then, if this difference is zero or is divisible by 7, II or 13, the original number is also so divisible; and conversely.

    0
    0
  • 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.

    0
    0
  • are integers, and a is an integer or zero.

    0
    0
  • 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.

    0
    0
  • these resistances have values denoted by P, Q, R, and S, then when P: Q :: R: S, the current in the galvanometer circuit will be zero when an electromotive force is applied in the battery circuit.

    0
    0
  • any outside block with the central block, the current can only pass from the zero outer block to the central block by passing through a certain number of the resistance coils.

    0
    0
  • 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.

    0
    0
  • In summer the temperature may rise as high as 106° F., while in winter it often sinks to 13° or even 20° below zero.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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).

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • The line of lead is taken to be horizontal in the diagram, because the thermoelectric power, p, may be reckoned from any convenient zero.

    0
    0
  • Temperatures below zero are rare for any locality; and the same may be said of temperatures above 95° in summer.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • Losses due to absorption are almost zero when the lenses are very thin, as with lenses of small diameter.

    0
    0
  • the spectrum of zero order, can be admitted, no trace is generally found of the image of the grating.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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).

    0
    0
  • and after allowing for friction and other losses, is discharged at a temperature of 60° to 80° below zero F.

    0
    0
  • 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.

    0
    0
  • 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°.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • 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.

    0
    0
  • There are zero personal memories.

    0
    0
  • Then someone tries to kill one of you bushy tail bastards and I save your ass and get zero credit for doing so.

    0
    0
  • While the hum of the machines broke up the silence of the room, I was making zero progress.

    0
    0
  • My understanding was limited to knowing zero degrees latitude began at the equator and increased to ninety degrees at the poles.

    0
    0
  • 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.

    0
    0
  • Or why they were here in the first place, as they expressed zero interest in the beauty of the area; Ouray's main attraction.

    0
    0
  • "It was zero this morning," he reminded her.

    0
    0
  • One percent now is better than zero percent in three months.

    0
    0
  • 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.

    0
    0
  • "That's nice," said Fred O'Connor, who had zero tradition, at least as far has Dean had learned in the fifteen years he'd lived with the old man.

    0
    0
  • It was an infuriating conversation, resulting in a big, fat zero.

    0
    0
  • The locks will open at zero four twenty-five.

    0
    0
  • Dean pushed each of the four buzzers, with zero response.

    0
    0
  • The survival rate on wounds like that are zero.

    0
    0
  • Day four, and he was zero for four.

    0
    0
  • Therefore, zero or minimum tillage and direct seeding are important elements of conservation agriculture.

    0
    0
  • We now use matrix perturbation theory to compute the covariance of based on this zero approximation.

    0
    0
  • absolute zero?

    0
    0
  • absolute zero of temperature are dominated by quantum rather than thermal fluctuations.

    0
    0
  • Or is the ' moment ' a purely mathematical abstraction, that is, a zero of time?

    0
    0
  • adiabatic process is zero.

    0
    0
  • Therefore, coefficient alpha will be equal to zero.

    0
    0
  • amplitude of the primary oscillation has fallen to zero.

    0
    0
  • amplitude of the fluctuations, and the fact that the vacuum energy now, is incredibly near zero.

    0
    0
  • By redefining the zero of time the voltage amplitude can always be made real.

    0
    0
  • The wave amplitude varies from zero (nodes) to a maximum, half way between the nodes.

    0
    0
  • All results should ideally be zero, as the subjects should not be showing any atrophy.

    0
    0
  • When the pressure gage reaches zero wait one or two minutes before opening the autoclave.

    0
    0
  • If the input baud rate is set to zero, the input baud rate is specified by the value of the output baud rate.

    0
    0
  • I continued my search with it set on zero, knowing the Iron would give a double bleep.

    0
    0
  • To build a date or time string with field separators, a leading zero function should be used, to avoid code bloat.

    0
    0
  • With all the stalls and people milling around driver did a good job, and achieved a zero body count.

    0
    0
  • Particles with zero or integer spin are called bosons after Satyendra Bose, who together with Einstein described their kind of statistical mechanics.

    0
    0
  • caret position also cannot be set to less than zero, the beginning of the component's text.

    0
    0
  • Zero (0) is returned to indi- cate a zero value, rather than the null string.

    0
    0
  • cathode of the diode is earthed and the top of the output waveform is clamped to zero volts.

    0
    0
  • centric reflections have an E of zero.

    0
    0
  • Nancy is the Ground Zero of idle chit chat; which is odd considering what could be spread about her.

    0
    0
  • close to zero as you can without having toe over hang.

    0
    0
  • We recommend that gene sequences be numbered so that the first base of the first codon is numbered zero.

    0
    0
  • coexisting phases reduces to zero.

    0
    0
  • As for coke zero, it's coke zero, it's coke light under a different guise.

    0
    0
  • col height - it is zero.

    0
    0
  • If you are sharing the colorimeter with other groups, only the first group should zero it for each ' run ' ).

    0
    0
  • Residues with alternate conformations (using shelx occupancies) were getting marked as zero occupancy atoms.

    0
    0
  • The allocated colors in a shared colormap do not generally start at zero and they are not necessarily contiguous.

    0
    0
  • converge to zero at the dissociation limit?

    0
    0
  • Use of truncation toward zero in implicit conversion has not always been guaranteed in C either, by the way.

    0
    0
  • All vehicles replaced by hydrogen fuel cell vehicles with zero CO 2 emissions, powered by renewable, short-rotation coppice produced fuel.

    0
    0
  • The researchers can cool a beam of hydrogen atoms using a helium cryostat to just 10 degrees above absolute zero.

    0
    0
  • If the server's global debug level is greater than zero, then debugging mode will be active.

    0
    0
  • I'd never felt decadent enough to burn film that fast, but with digital there's zero marginal cost.

    0
    0
  • decrement instruction directly above them sets the zero flag anyway!

    0
    0
  • The payoff of mutual defection, DD, provides the baseline outcome that yields a payoff of zero to both participants.

    0
    0
  • Then for a given value of the optimum gain can be found by setting the partial derivative of with respect to to zero.

    0
    0
  • In addition, a technology park would be built alongside a ' Ground Zero Museum ' containing detritus and mementos from the Cold War.

    0
    0
  • A zero value occurring on the leading diagonal does not mean the matrix is singular.

    0
    0
  • The spectral leakage increases since zero padding introduces a discontinuity in the data stream.

    0
    0
  • The locations on the board at which zero vibration displacement occurs are called nodes, and the maximum displacement amplitudes occur at the antinodes.

    0
    0
  • diversion from landfill since introducing its own Zero Waste strategy in 1995.

    0
    0
  • dropped to zero right away?

    0
    0
  • effluent treatment, with the proportion of chemicals going to landfill being reduced, ideally to zero.

    0
    0
  • The system also allows for driving shorter distances with just electrical power and therefore zero emissions.

    0
    0
  • In a topologically trivial spacetime, one could make the electro static potential zero, by a gage transformation.

    0
    0
  • A perfect black body radiator has an emissivity of unity, so all other surfaces have emissivity between zero and one.

    0
    0
  • equal to zero suppresses major tickmarks entirely.

    0
    0
  • exception vector table are set to zero, together with all the registers.

    0
    0
  • A zero reference button is the only external control on the Encoder.

    0
    0
  • They played quite a few tracks from the latest album including my current fave Zero Friction.

    0
    0
  • Either zero or its contract with billion or more grabbed the checkered flag.

    0
    0
  • What would be the perfect foil for the Zero?

    0
    0
  • Its three and four wheeled electric forklifts offer reduced noise and zero emissions, making them ideal garden centers and greenhouses.

    0
    0
  • In the UK, board manufacturers are advertising low formaldehyde or zero formaldehyde emission boards made to the stringent German " E1 " standard.

    0
    0
  • Pixels where the two images were equal are zero, and appear as gray.

    0
    0
  • Options are also available for fire retardant formulas including low smoke zero halogen.

    0
    0
  • helium at a temperature just above absolute zero would be useful.

    0
    0
  • helium cryostat to just 10 degrees above absolute zero.

    0
    0
  • They take numbers as decimal unless starting with 0x (or 0X ), meaning hexadecimal; a leading zero does not mean octal.

    0
    0
  • histogram bins are reset to zero.

    0
    0
  • Diagnosis of secondary hypothyroidism can be done by measuring cTSH at zero and 30 minutes post TRH stimulation.

    0
    0
  • The Cuban youth illiteracy rate is zero, unmatched by any other Latin American country, where the average is 7% .

    0
    0
  • implode due to the zero growth rate mean assumption is still at work: slowly, big firms keep shrinking.

    0
    0
  • Fifteen years ago, its net foreign indebtedness was zero.

    0
    0
  • indefinite pronouns or the zero marking.

    0
    0
  • A zero length mark will make a hanging indent instead.

    0
    0
  • An ideal inductor presents zero resistance to the flow of Direct Current.

    0
    0
  • The rate of Dutch house-price inflation then slowed from 20% in 2000 to nearly zero by 2003.

    0
    0
  • initialized to zero (NULL ).

    0
    0
  • The key is for them to reduce their alcohol intake to zero, or near zero.

    0
    0
  • intangible personal property from taxation in 1984 by making the tax rate zero.

    0
    0
  • Parameter $ 0 is set from argument zero at shell invocation.

    0
    0
  • Whoever has the highest karma at the end of the week gets made moderator, then their karma gets reset to zero.

    0
    0
  • l p = h. If the momentum of the electrons is zero, then the wavelength they have is infinite.

    0
    0
  • lass="ex">l p = h. If the momentum of the electrons is zero, then the wavelength they have is infinite.

    0
    0
  • lagging power factor ensures that the devices in the inverter still turn on with zero voltage across them.

    0
    0
  • On the contrary 3 of the 4 zero anisotropy events identified are seen at heliographic latitudes greater than 42 degrees south.

    0
    0
  • The benefit is a dramatic reduction in spectral leakage, enabling any measure of zero padding to be used.

    0
    0
  • least squares do zero cycles.

    0
    0
  • For this is where the Earth's prime meridian, the line of zero degrees longitude, originates.

    0
    0
  • lowercase l for 1 (one) or the uppercase O for 0 (zero ).

    0
    0
  • macro invocation marks the buffer as interactive, a zero value as non-interactive.

    0
    0
  • A negative or reverse magnetic force applied for reducing magnetic induction to zero.

    0
    0
  • mango orchards was shown to reduce losses from 20% to zero.

    0
    0
  • The pri- Mary components are a stream head, a driver, and zero or more modules between the stream head and driver.

    0
    0
  • In quantum mechanics, a system can never have an energy of exactly zero.

    0
    0
  • For each reading, first set the instrument to read zero absorbance with a tube containing acidified methanol alone (the blank ).

    0
    0
  • In the calculation median seeing conditions are assumed, the zenith angle is zero, and the deformable mirror is conjugate to 6.5 km.

    0
    0
  • This " optical molasses " can slow millions of atoms to temperatures just millionths of a degree above absolute zero.

    0
    0
  • nonzero if the name is resolved; otherwise, it returns zero.

    0
    0
  • XSendEvent returns zero if the conversion to wire protocol format failed and returns nonzero otherwise.

    0
    0
  • 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.

    0
    0
  • octal escapes must always begin with a zero.

    0
    0
  • He hopes to compose the first oratorio to be performed in zero gravity.

    0
    0
  • The use of these blocks in mango orchards was shown to reduce losses from 20% to zero.

    0
    0
  • orientated policing, repeat offending zero tolerance and restorative justice approaches.

    0
    0
  • orthogonal transformation, Z, is applied to zero out the columns to the right of T.

    0
    0
  • Using the equation l p = h. If the momentum of the electrons is zero, then the wavelength they have is infinite.

    0
    0
  • Then for a given value of the optimum gain can be found by setting the partial derivative of with respect to to zero.

    0
    0
  • As a result, the collective payoff deteriorates, reaching the zero level around generation 120.

    0
    0
  • The peaks arise because the denominator will approach zero at sinusoidal frequencies, resulting in exceedingly sharp spectral peaks.

    0
    0
  • But Cambridgeshire CID wanted her to take zero tolerance a step further by giving them the names of the alleged dope peddlers.

    0
    0
  • The combination of ground temperatures only slightly below zero, high ice contents and steep slopes, makes mountain permafrost particularly vulnerable to changes.

    0
    0
  • personifyd continue to battle evil, often personified in the form of Dr. Zero.

    0
    0
  • plug the phono sockets into an AUX input and remember to turn the volume to zero before you try to play anything.

    0
    0
  • If pgid is zero, the process ID of the process specified by PID is used.

    0
    0
  • Catching everyone by surprise, the temperature suddenly plummeted to zero.

    0
    0
  • These zero percentage polarization values then result in zero polarized intensity values.

    0
    0
  • From their point of view zero popularity is a time wasting.

    0
    0
  • pore pressure is zero.

    0
    0
  • In basement reservoirs matrix porosity is effectively close to zero and most of the storage capacity and permeability is due to fractures.

    0
    0
  • positronium formation in positron collisions with atoms having zero threshold energy, Nucl.

    0
    0
  • Instead, upon notifying the affected product vendor, 3Com provides its customers with zero day protection through its intrusion prevention technology.

    0
    0
  • For this is where the earth's prime meridian, the line of zero degrees longitude, originates.

    0
    0
  • In a formal argument we claim the transition probability of OK to ERROR is zero.

    0
    0
  • pullout resistance and low smoke and fume, zero halogen seal onto the cables outer sheath.

    0
    0
  • push buttone Heidenhain to zero, press the push-button marked ` 0 ' at the left of the encoder display.

    0
    0
  • quantum mechanics, a system can never have an energy of exactly zero.

    0
    0
  • If the code is 4, and the second number is not zero, compute the quotient (first divided by second ).

    0
    0
  • The output of the expert system is a trust quotient, in the range from zero to one.

    0
    0
  • The output radix must be at least 2. The precision must be zero or greater.

    0
    0
  • raindrops caught in zero gravity can be a storm.

    0
    0
  • Zero Representation Another of the Home Secretary's Good Ideas is to limit the right of accused rapists to represent themselves in court.

    0
    0
  • Reactions may commonly be zero order, first order or second order with respect to a particular reactant.

    0
    0
  • redshift value of zero means that there is no measurement.

    0
    0
  • reduced to zero by last year.

    0
    0
  • remanent induction as the field is reduced to zero.

    0
    0
  • Higher order bits in pixel representations are assumed to be zero.

    0
    0
  • reset to zero at the time of powering up.

    0
    0
  • resonance frequency reaches 13 cycles we will be at a zero point magnetic field.

    0
    0
  • sail on a voyage to access the Zero Point Field at the end of this world.

    0
    0
  • saltation cannot be initiated within the vegetation, because of the zero wind velocity at the surface.

    0
    0
  • sandstorm blows up and visibility is cut to near zero, the team decides radical measures are called for.

    0
    0
  • set sail on a voyage to access the Zero Point Field at the end of this world.

    0
    0
  • The peaks arise because the denominator will approach zero at sinusoidal frequencies, resulting in exceedingly sharp spectral peaks.

    0
    0
  • shrinkthe distance to Andromeda will have shrunk to zero for the spacecraft.

    0
    0
  • southward turning as time zero.

    0
    0
  • spacesuit worn by the Darian ' Spirit ' originally appeared in the British space western feature Moon Zero Two (1969 ).

    0
    0
  • specious arguments over how close to zero a GM content is near enough GM-free.

    0
    0
  • Brachial systolic and diastolic pressure and ankle systolic pressures were measured using a Hawksley random zero sphygmomanometer and Doppler probe.

    0
    0
  • To get them for the starting model for the least squares do zero cycles.

    0
    0
  • The output shows however that the associated standard deviation is equal to zero.

    0
    0
  • sitting stationary is zero miles per gallon, switch off the engine whenever it is safe to do so.

    0
    0
  • subcritical testing is consistent with the zero yield CTBT.

    0
    0
  • The resulting vector, stored in the variable bad, contains the subscripts of the elements of data that are less than zero.

    0
    0
  • superposed epoch studies were carried out using the time of the southward turning as time zero.

    0
    0
  • sustains when both our circumstances without and our feelings within are at zero.

    0
    0
  • A blade that is radially symmetrical is said to have zero skew.

    0
    0
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