# Modulus Sentence Examples

It will be observed that in the first process the value of the

**modulus**is in fact calculated from the formula.Hesse's canonical form shows at once that there cannot be more than two independent invariants; for if there were three we could, by elimination of the

**modulus**of transformation, obtain two functions of the coefficients equal to functions of m, and thus, by elimination of m, obtain a relation between the coefficients, showing them not to be independent, which is contrary to the hypothesis.Thus what have been called seminvariants are not all of them invariants for the general substitution, but are invariants for the particular substitution xl = X11 + J-s12, X 2 = 112 Again, in plane geometry, the most general equations of substitution which change from old axes inclined at w to new axes inclined at w' =13 - a, and inclined at angles a, l3 to the old axis of x, without change of origin, are x-sin(wa)X+sin(w -/3)Y sin w sin ' _sin ax y sin w a transformation of

**modulus**sin w' sin w' The theory of invariants originated in the discussion, by George Boole, of this system so important in geometry.The whole of the rod will therefore be subject to a compressive longitudinal stress P, the associated contraction R, expressed as a fraction of the original length, being R = P/M = (B 2 -H2)/87-M, where M is Young's

**modulus**.In nickel the maximum change of the elastic constants is remarkably large, .amounting to about 15% for Young's

**modulus**and 7% for rigidity; with increasing fields the elastic constants first decrease and then increase.Referring the reader to the article Elasticity for the theoretical and to the Strength Of Materials far the practical aspects of this subject, we give here a table of the "

**modulus**of elasticity," E (column 2), for millimetre and kilogramme.Let E be the bulk

**modulus**of elasticity, defined as increase of pressure = decrease of volume per unit volume where the pressure increase is so small that this ratio is constant, w the small increase of pressure, and - (dy/dx) the volume decrease, then E=e/(- dy/dx) or w Ã†= - dy/dx (I) This gives the relation between pressure excess and displacement.But if y is the displacement at A, dy/dx is the extension at A, and the force acting is a pull across A equal to Y&uodyldx, where Y is Young's

**modulus**of elasticity.Young's

**modulus**may be obtained for the material of a rod by clamping it in the middle and obtaining the frequency of the fundamental when Y = 412n2p.Owing to the yielding of joints when a beam is first loaded a smaller

**modulus**of elasticity should be taken than for a solid bar.AdvertisementIt follows that the density of the aether must exceed io 18, and its elastic

**modulus**must exceed Io 3, which is only about io s of the**modulus**of rigidity of glass.The second of these relations is an important one, as it shows that from a table of logarithms to base a, the corresponding table of logarithms to base b may be deduced by multiplying all the logarithms in the former by the constant multiplier i/logab, which is called the

**modulus**of the system whose base is b with respect to the system whose base is a.The two systems of logarithms for which extensive tables have been calculated are the Napierian, or hyperbolic, or natural system, of which the base is e, and the Briggian, or decimal, or common system, of which the base is io; and we see that the logarithms in the latter system may be deduced from those in the former by multiplication by the constant multiplier /loge io, which is called the

**modulus**of the common system of logarithms.The numerical value of this

**modulus**is o 4342944 81 9 03251 82765 11289..It follows from this property of the function that we cannot have for log x a series which shall be convergent for all values of x, as is the case with sin x and cos x, for such a series could only represent a uniform function, and in fact the equation log(I +x) =x -",, x2 +3x 3 -4x 4 + is true only when the analytical

**modulus**of x is less than unity.AdvertisementIf the logarithms are to be Briggian all the series in the preceding formulae must be multiplied by M, the

**modulus**; thus, log i o(I +x) = M(x-2x2+3x3-4x4+&c.), and so on.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.The constant -r is called the

**modulus**of decay of the oscillations; if it is large compared with 2irfa the effect of friction on the period is of the second order of small quantities and may in general be ignored.That least distance is called by Moseley the

**modulus**of stability.**Modulus**of a Machine.In the investigation of the properties of a machine, the useful resistances to be overcome and the useful work to be performed are usually given.AdvertisementThe result of this investigation, expressed in the form of an equation between this energy and the useful work, is called by Moseley the

**modulus**of the machine.The twist or surface-shear being proportional to the torque, the horse-power can be calculated if the

**modulus**of rigidity of the steel employed is known or if the amount of twist corresponding to a given power has previously been ascertained by direct experiment on the shaft before it has been put in place.Is this because cast gold has a higher, or lower,

**modulus**of elasticity compared to cobalt chromium?Residual measurements carried out on glass/polyester rods showed that the longitudinal tensile

**modulus**remains constant over the entire lifetime of the unidirectional composite.**Modulus**and strain to failure are measured using an extensometer (mechanical or non-contact ).AdvertisementAround t g there is a large fall in the value of the

**modulus**.Around T g there is a large fall in the value of the

**modulus**.The difference in the shear

**modulus**has been suggested as the main factor in determining the hardness of the multilayer system.To obtain a reliable estimate of indentation

**modulus**, each indentation**modulus**, each indentation experiment was repeated 20 times at 50 µm intervals.At least two tests were carried out at each temperature interval and the mean frequency value used to calculate the elastic

**modulus**.A - Yes, by overcoming the elastic

**modulus**, a new local memory can be induced.We have managed to explain, and quantify, the origin of the surprising negative gradient of the bulk

**modulus**in this model.The transfer function is the complex viscoelastic

**modulus**of the interface.The elastic

**modulus**is defined as a secant**modulus**at service load condition.In reality the values of shear

**modulus**G are much lower.To obtain a reliable estimate of indentation

**modulus**, each indentation experiment was repeated 20 times at 50 µm intervals.For a gas, the adiabatic bulk

**modulus**B = P, where P is the ambient pressure.The ratio of loss and storage

**modulus**, tan d, is also reported.Seat them down on a bead of clear low

**modulus**silicone sealer before the screws are inserted.Fix it to the base unit by bedding the sink onto beads of low

**modulus**silicone.The reduction factor for elastic

**modulus**of light gage steel is assumed to be identical to that of carbon steel.This sections starts by defining

**modulus**, tensile strength, elongation at break and yield strength on a typical stress-strain graph.Recommendations This method is inherently unsuitable for low

**modulus**polymeric material systems.No Australian timber in the foregoing list has a less

**modulus**than 13,100 lb per sq.Let E be the bulk

**modulus**of elasticity, defined as increase of pressure = decrease of volume per unit volume where the pressure increase is so small that this ratio is constant, w the small increase of pressure, and - (dy/dx) the volume decrease, then E=e/(- dy/dx) or w Ãƒâ€ = - dy/dx (I) This gives the relation between pressure excess and displacement.In portions of the structure liable to important changes of pressure from the rise, and fall of the water and subject to the additional stresses which expansion and contraction by changes of temperature and of moisture induce, and in view of the great difficulty of securing that the average

**modulus**of elasticity in all parts of the structure shall be approximately the same, it is probably desirable to limit the calculated load upon any external work, even of the best kind, to 15 or 20 tons per sq.The posts are made of a molybdenum- rhenium alloy that maintains a high

**modulus**of elasticity even at high temperatures.An example of estimating the elasto-plastic buckling stress through use of the material tangent

**modulus**is given.The bulk

**modulus**K ' relates the change in stress to the volumetric strain.The Luhn formula is sometimes referred to as the "

**modulus**10" or "mod 10" algorithm.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.In the theory of forms we seek functions of the coefficients and variables of the original quantic which, save as to a power of the

**modulus**of transformation, are equal to the like functions of the coefficients and variables of the transformed quantic. We may have such a function which does not involve the variables, viz.