# In-terms-of sentence example

in-terms-of

- All kinds of energy are ultimately measured in terms of work.
- In the case of close double stars he estimated the distance in terms of the disk of the components.
- webs serve not only for pointing on stars to determine their coordinates (in manner afterwards described), but also for estimating the diameters of the star-images in terms of these 4" intervals.
- Estimate the diameter of the star's image in terms of the 4" intervals of the movable webs.
- materia, matter), in philosophy, the theory which regards all the facts of the universe as explainable in terms of matter and motion, and in particular explains all psychical processes by physical and chemical changes in the nervous system.Advertisement
- The galvanometer being so adjusted that a current of definite strength through one of the coils gives a definite deflection of the needle, the amount of leakage expressed in terms of the insulation resistance of the wires is given by the formula.
- At the end of May the pope, in an allocution to the cardinals, had spoken of Italy in terms of unusual cordiality, and had expressed a wish for peace.
- Thus we might restate our grouping of philosophies in terms of the views they take regarding necessity.
- The element of naturalism stands for science with a leaning towards materialism (" explanation in terms of matter and motion ").
- Davis, who classifies land surfaces in terms of the three factors - structure, process and time.Advertisement
- Spencer's grandiose cosmic formula in terms of mechanism.
- The relation between the b.h.p. and the torque on the driving-axle is 55 o B.H.P. =Tu., (9) It is usual with steam locomotives to regard the resistance R as including the frictional resistances between the cylinders and the driving-axle, so that the rate at which energy is expended in moving the train is expressed either by the product RV, or by the value of the indicated horse-power, the relation between them being 55 0 I.H.P. =RV (Io) or in terms of the torque 55 0 I.H.P.X€=RVe=TW (II) The individual factors of the product RV may have any value consistent with equation (to) and with certain practical conditions, so that for a given value of the I.H.P. R must decrease if V increases.
- which the area represents from the following formula, which is expressed in terms of the absolute temperature T, of the steam at the steam-pipe, and the temperature T2= 461°H-212° =673° absolute corresponding to the back pressure: - Maximu per pound oflsteaelwork =U=(T - T) (i -f -Lr--.1) - T2loge.Tr--2.
- Pepys, a far more trustworthy judge, speaks of him invariably in terms of respect and approval as a " grave, serious man," and commends his appointment as treasurer of the navy as that of " a very notable man and understanding and will do things regular and understand them himself."
- Though his method is throughout scholastic, he covers the same ground, and Grotius speaks of him in terms of high respect.Advertisement
- It has been proposed to adopt the joule, with the symbol j, as thermochemical unit for small quantities of heat, large amounts being expressed in terms of the kilojoule, Kj =100o j.
- As to the style and literary character of Jordanes, every author who has used him speaks in terms of severe censure.
- In a modern industrial community it is possible to express this standard fairly accurately for the purposes of economic investigation in terms of money.
- From this fact arises the ground of political obligation, for the institutions of political or civic life are the concrete embodiment of moral ideas in terms of our day and generation.
- Certain elements present themselves in feeling which seem stubbornly to resist any attempt to explain them in terms of thought.Advertisement
- It is the Church which creates the Carolingian empire, because the clergy thinks in terms of empire.
- AMPEREMETER, or Ammeter, an instrument for the measurement of electric currents in terms of the unit called the ampere.
- The size of a globe is usually given in terms of its diameter.
- Also, as the Cartesian geometry shows, all the relations between points are expressible in terms of geometric quantities.
- These entities are not created by mathematicians, they are employed by them, and their definitions should point out the construction of the new entities in terms of those already on hand.Advertisement
- So accurate and convenient is this determination that it is now used conversely as a practical definition of the ampere, which (defined theoretically in terms of magnetic force) is defined practically as the current which in one second deposits i '18 milligramme of silver.
- With regard to a great many rivers we know only the position of their mouths and their approximate lengths estimated by natives in terms of a day's march.
- P. Gordan first proved that for any system of forms there exists a finite number of covariants, in terms of which all others are expressible as rational and integral functions.
- +amam Expanding the right-hand side by the exponential theorem, and then expressing the symmetric functions of al, a2, ...a m, which arise, in terms of b1, b2, ...'
- Further we find x=aX+a'Y+a"Z, y=bX z= cX+c'Y+ c"Z, and the problem is to express the nine coefficients in terms of three independent quantities.Advertisement
- In general in space of n dimensions we have n substitutions similar to X l = a11x1 +a12x2 + ï¿½ ï¿½ ï¿½ + ainxn, and we have to express the n 2 coefficients in terms of Zn(n - I)i independent quantities; which must be possible, because X1+X2+..."IL Xn =xi+x2 +x3 +...+4.
- If al, a2, ...a, n be the roots of f=o, (1, R2, -Ai the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) ï¿½ ï¿½;f (Nn) = 0; so that Rf,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4..
- Now by the theory of symmetric functions, any symmetric functions of the mn values which satisfy the two equations, can be expressed in terms of the coefficient of those equations.
- Hence, finally, the resultant is expressed in terms of the coefficients of the three equations, and since it is at once seen to be of degree mn in the coefficient of the third equation, by symmetry it must be of degrees np and pm in the coefficients of the first and second equations respectively.
- af Expression in Terms of Roots.-Since x+y y =mf, if we take cx any root x 3, y1, ofand substitute in mf we must obtain, y 1 C) zaZ1 ï¿½; hence the resultant of and f is, disregarding numerical factors, y,y2...y,,.Advertisement
- the sum of the n th powers of the quantities, is expressible in terms of functions which are symbolized by separations of any partition (n"1n'2n'3...) 1 !
- ) j1+j2+j3+..ï¿½ (J1+ j2 +j3+...-1)!/T1)?1(J2)72 (J 3)/3..., j11j2!j3!... ?.1 for the expression of Za n in terms of products of symmetric functions symbolized by separations of (n 1 1n 2 2n 3 3) Let (n) a, (n) x, (n) X denote the sums of the n th powers of quantities whose elementary symmetric functions are a l, a 2, a31ï¿½ï¿½ï¿½; x 1, x2, x31..; X1, X2, X3,...
- in terms of dl, d 2, d 3, ..., products denoting successive operations, by the same law which expresses the ele mentary function a s in terms of the sums of powers s l, s 2, s3,...
- Further, we can express d 8 in terms of Dl, D 2, D3, ...
- by the same law which expresses the power function s, in terms of the elementary functions a 1, a2, a3,...Advertisement
- All symmetric functions are expressible in terms of the quantities ap g in a rational integral form; from this property they are termed elementary functions; further they are said to be single-unitary since each part of the partition denoting ap q involves but a single unit.
- The partitions with one bipart correspond to the sums of powers in the single system or unipartite theory; they are readily expressed in terms of the elementary functions.
- which expresses the elementary functions in terms of the single bipart functions.
- = (A11+A22)n by the substitutions 51 = A l, E1+ï¿½1 2, 52 = A2E1+ï¿½2E2, the umbrae Al, A2 are expressed in terms of the umbrae al, a 2 by the formulae A l = Alai +A2a2, A2 = ï¿½la1 +ï¿½2a2ï¿½ We gather that A1, A2 are transformed to a l, a 2 in such wise that the determinant of transformation reads by rows as the original determinant reads by columns, and that the modulus of the transformation is, as before, (A / .c).
- is expressed in terms of new quantities X, Y, Z, ...Advertisement
- is expressed in terms of other new quantities X', Y', Z', ....
- + ï¿½ï¿½ï¿½, Z = v16+v2%/+v3" +ï¿½ï¿½ï¿½, wherein it should be noticed that new quantities are expressed in terms of the old, as regards the latter set, and not vice versa."
- If u, a quantic in x, y, z, ..., be expressed in terms of new variables X, Y, Z ...; and if, n,, ..., be quantities contragredient to x, y, z, ...; there are found to exist functions of, n, ?, ..., and of the coefficients in u, which need, at most, be multiplied by powers of the modulus to be made equal to the same functions of E, H, Z, ...
- We cannot, however, say that it is an invariant unless it is expressible in terms of the real coefficients.
- When either of the forms is of an order higher than the first (ab), as not being expressible in terms of the actual coefficients of the forms, is not an invariant and has no significance.Advertisement
- It will be shown later that all invariants, single or simultaneous, are expressible in terms of symbolic products.
- - (aa) and then expresses the coefficients, on the right, in terms of the fundamental invariants.
- a irl aï¿½ 2 a a3 ...Ev 1 02 2 ?3 3 ...; and, if we express Ea l v2 2 0-3 3 in terms of A2, A3 i ..., and arrange the whole as a linear function of products of A2, A3,..., each coefficient will be a seminvariant, and the aggregate of the coefficients will give us the complete asyzygetic system of the given degree and weight.
- Solving the equation by the Ordinary Theory Of Linear Partial Differential Equations, We Obtain P Q 1 Independent Solutions, Of Which P Appertain To S2Au = 0, Q To 12 B U =0; The Remaining One Is Ab =Aobl A 1 Bo, The Leading Coefficient Of The Jacobian Of The Two Forms. This Constitutes An Algebraically Complete System, And, In Terms Of Its Members, All Seminvariants Can Be Rationally Expressed.
- The substitution for x, y in terms of X, Y is the most general linear substitution in virtue of the four degrees of arbitrariness introduced, viz.
- The number of different symbols a, b, c,...denotes the the covariants are homogeneous, but not in general isobaric functions, of the coefficients of the original form or forms. Of the above general form of covariant there are important transformations due to the symbolic identities: - (ï¿½b) 2 2)2 = a b - a b; (xï¿½ = as a consequence any even power of a determinant factor may be expressed in terms of the other symbolic factors, and any uneven power may be expressed as the product of its first power and a function of the other symbolic factors.
- Since the poles of different magnets differ in strength, it is important to agree upon a definite unit or standard of reference in terms of which the strength of a pole may be numerically specified.
- After pointing out that, since the magnetization of the metal is the quantity really concerned, W is more appropriately expressed in terms of I, the magnetic moment per unit of volume, than of B, he suggests an experiment to determine whether the mechanical work required to effect the complete magnetic reversal i Phil.
- Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.
- The most important are: (I) To express the time of describing an elliptic arc under the Newtonian law of gravitation in terms of the focal distances of the initial and final points, and the length of the chord joining them.
- combine the separate quantities or numbers expressed in terms of x as unit into a single quantity or number so expressed, obtaining sx =10.
- Let X and Y be the related quantities, their expressions in terms of selected units A and B being x and y, so that X=x.A, Y = y.
- This latter process, however, is itself based on a definition of division in terms of multiplication (ï¿½ï¿½ 15, 16).
- As in quaternions, so in the extensive calculus, there are numerous formulae of transformation which enable us to deal with extensive quantities without expressing them in terms of the primary units.
- If 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular resolving power is given by X/2 D sin a = X/2 R (3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.
- Comparing the expressions for C, S in terms of M, N, and in terms of G, H, we find that G = z (cos u+sin u)-M, H = z (cos u-sin u) +N.
- 11,1r; and we get in terms of v 1 1.3.5 1.3.5.7.9 C ' ?
- (b2V2 + n2) (a2 - b 2) = - z It will now be convenient to introduce the quantities a l, a 2', 7731 which express the rotations of the elements of the medium round axes parallel to those of co-ordinates, in accordance with the equations Ty - 1 = dz ' 3= - dy 2 = dx - In terms of these we obtain from (7), by differentiation and subtraction, (b 2 v 2 + n 2) 7,3 = 0 (b 2 0 2 +n 2) .r i = dZ/dy (b 2 v 2 +n 2)', , 2 = - dZ/dx The first of equations (9) gives 3 = 0 (10) For al we have ?1= 47rb2, f dy e Y tkr dx dy dz
- The intensity of light is, however, more usually expressed in terms of the actual displacement in the plane of the wave.
- The difficulty, however, is more apparent than real, and in this sense, that if we start with a diseased organ as our subject of inquiry, we can quite properly, and without committing a solecism, treat of the functions of that organ in terms of its diseased state.
- Hero's expressions for the areas of regular polygons of from 5 to 12 sides in terms of the squares of the sides show interesting approximations to the values of trigonometrical ratios.
- It is in this book that Hero proves the expression for the area of a triangle in terms of its sides.
- Fraunhofer further initiated the specification of refraction and dispersion in terms of certain lines of the spectrum, and even attempted an investigation of the effect of chemical composition on the relative dispersion produced by glasses in different parts of the spectrum.
- Uniplanar motion alone is so far amenable to analysis; the velocity function 4 and stream function 1G are given as conjugate functions of the coordinates x, y by w=f(z), where z= x +yi, w=4-Plg, and then dw dod,y az = dx + i ax - -u+vi; so that, with u = q cos B, v = q sin B, the function - Q dw u_vi=g22(u-}-vi) = Q(cos 8+i sin 8), gives f' as a vector representing the reciprocal of the velocity in direction and magnitude, in terms of some standard velocity Q.
- In this capacity he exhibited an almost feverish activity; he perpetually appeared at the bar of the assembly on behalf of the commune; he announced the massacres of September in the prisons in terms of apology and praise; and he sent off the famous circular of the 3rd of September to the provinces, recommending them to do likewise.
- Until recently these spherical lenses were numbered in terms of their focal length, the inch being used as the unit.
- It appears, therefore, that Spencer ultimately describes the Knowable in terms of the mechanical conceptions of matter and motion, and that this must give a materialistic colouring to his philosophy.
- But the attempt to interpret, in terms of this Asiatic diagram, the actual distribution of dialects and peoples in European Greece, led to difficulties.
- In the next place we must notice that electrification is a measurable magnitude and in electrostatics is estimated in terms of a unit called the electrostatic unit of electric quantity.
- On the other hand there are numerous methods by which the capacities of condensers may be compared and a relative measurement made in terms of some standard.
- Kelvin had previously proposed to define an absolute scale of temperature independent of the properties of any particular substance in terms of Carnot's function by making F'(t) constant.
- (3) This relation may be interpreted in two ways, according as we require the heat absorbed in terms of the change of pressure or volume.
- The equation to these lines in terms of v and 0 is obtained by integrating dE=sd0+(Odp/de - p)dv = o .
- The equation to the lines of constant total heat is found in terms of p and 0 by putting dF=o and integrating (it).
- The value of the angular coefficient d(pv)/dp is evidently (b - c), which expresses the defect of the actual volume v from the ideal volume Re/p. Differentiating equation (17) at constant pressure to find dv/do, and observing that dcldO= - nc/O, we find by substitution in (is) the following simple expression for the cooling effect do/dp in terms of c and b, Sdo/dp= (n+I)c - b..
- In the modified Joule-Thomson equation (17), both c and n have simple theoretical interpretations, and it is possible to express the thermodynamical properties of the substance in terms of them by means of reasonably simple formulae.
- The values of the partial differential coefficients in terms of n and c are as follows: - Substituting these values in equations already given, we find, from (6) S - s =R(I +nc/V)2 (24) „ (9) dE/dv (o const) =ncp/V .
- Changes of entropy must be calculated in terms of quantities of heat, and must be interpreted in a similar manner.
- The final state of the substance, when equilibrium has been restored, may be deduced from this condition, if the energy can be expressed in terms of the co-ordinates.
- Assuming the function G to be expressed in terms of p and 0, this condition represents the relation between p and 0 corresponding to equilibrium between the two states, which is the solution of the relation (v" - v')dp/dO=L/D, (5).
- (39) dG"/dp (D const) =v, dJ"/dv (0 const) = p. (40) And all the properties of the substance may be expressed in terms of G or J and their partial differential coefficients.
- No sooner had the Characteristics appeared than they were welcomed, in terms of warm commendation, by Le Clerc and Leibnitz.
- The hypothesis that the state was steady, so that interchanges arising from convection and collisions of the molecules produced no aggregate result, enabled him to interpret the new constants involved in this law of distribution, in terms of the temperature and its spacial differential coefficients, and thence to express the components of the kinetic stress at each point in the medium in terms of these quantities.
- The relative densities of gases are usually expressed in terms of the standard gas under the same conditions.
- He earnestly admonished Leo, for his own sake and for Florence, to found a permanent and free state system for the republic, reminding him in terms of noble eloquence how splendid is the glory of the man who shall confer such benefits upon a people.
- The religious views of Servetus, marked by strong individuality, are not easily described in terms of current systems. His denial of the tripersonality of the Godhead and the eternity of the Son, along with his anabaptism, made his system abhorrent to Catholics and Protestants alike, in spite of his intense Biblicism, his passionate devotion to the person of Christ, and his Christocentric scheme of the universe.
- In point of fact it is found that the properties which are most easily explained are those connected with the gaseous state; the explanation of these properties in terms of the molecular structure of matter is the aim of the " Kinetic Theory of Gases."
- The point of view which has now been gained enables us to interpret most of the thermal properties of solids in terms of molecular theory.
- The kinetic theory of gases attempts to give a mathematical account, in terms of the molecular structure of matter, of all the non-chemical and non-electrical properties of gases.
- But Landen's capital discovery is that of the theorem known by his name (obtained in its complete form in the memoir of 1775, and reproduced in the first volume of the Mathematical Memoirs) for the expression of the arc of an hyperbola in terms of two elliptic arcs.
- it is representation in terms of a unit.
- the direct measurement of certain magnitudes (usually lengths) in terms of a unit, and the application of a formula for determining the area or volume from these data.
- It might, therefore, be described as that branch of mathematics which deals with formulae for calculating the numerical measurements of curved lengths, areas and volumes, in terms of numerical data which determine these measurements.
- This use of formulae for dealing with numbers, which express magnitudes in terms of units, constitutes the broad difference between mensuration and ordinary geometry, which knows nothing of units.
- The failure seems (§ 2) to be due to difficulty in realizing the numerical expression of an area or a solid in terms of a specified unit, while the same difficulty does not arise in the case of linear measure or liquid measure, where the number of units can be ascertained by direct counting.
- When an area has been calculated in terms of square feet, primes and square inches, the primes and square inches have to be reduced to square inches; and similarly with the calculation of volumes.
- - In § 23 the area of a right trapezium has been expressed in terms of the base and the two sides; and in § 34 the area of a somewhat similar figure, the top having been replaced by an arc of a parabola, has been expressed in terms of its base and of three lengths which may be regarded as the sides of two separate figures of which it is composed.
- This would involve p and q; but, for our purposes, the data are the sides pa+q and pb+q and the base b - a, and the expression of the integral in terms of these data would require certain eliminations.
- The province of mensuration is to express the final result of such an elimination in terms of the data, without the necessity of going through the intermediate processes.
- If the area of the cross-section, in every position, is known in terms of its distance from one of the bounding planes, or from a fixed plane A parallel to them, the volume of the solid can be expressed in terms of the area of a trapezette.
- The volume of a briquette can be found in this way if the area of the section by any principal plane can be expressed in terms of the distance of this plane from a fixed plane of the same set.
- The top is then a parabola whose axis is at right angles to the base; and the area can therefore (§ 34) be expressed in terms of the two bounding ordinates and the midordinate.
- Denoting the areas of the three strips by A, B, and C, and introducing the middle ordinate ug, we can express A + B; B -{- C; A + B -FC; and B in terms of uo, u 1, u 2; u 1, u2, u3; uo, u, u 3; and u 1, ug, u 2 respectively.
- The general formulae of § 54 (p being replaced (i) by 2m) may in the same way be applied to obtain formulae giving the area of the trapezette in terms of the mid-ordinates of the strips, the series being taken up to b 2f ul m or /th 2J ug m at least, where u is of degree 2f or 2f + I in x.
- Hence, for the case of a parabola, we can express the area in terms of the bounding ordinates of two strips, but, if we use mid-ordinates, we require three strips; so that, in each case, three ordinates are required.
- It follows that, by taking two ordinates in a certain position with regard to the bounding ordinates, the area of any parabolic trapezette whose top passes through their extremities can be expressed in terms of these ordinates and of the breadth of the trapezette.
- This is a particular case of a general theorem, due to Gauss, that, if u is an algebraical function of x of degree 2p or 2p + I, the area can be expressed in terms of p -}- i ordinates taken in suitable positions.
- To extend these methods to a briquette, where the ordinate u is an algebraical function of x and y, the axes of x and of y being parallel to the sides of the base, we consider that the area of a section at distance x from the plane x = o is expressed in terms of the ordinates in which it intersects the series of planes, parallel to y=o, through the given ordinates of the briquette (§ 44); and that the area of the section is then represented by the ordinate of a trapezette.
- The volume of a frustum of a cone, for instance, can be expressed in terms of certain magnitudes by a certain formula; but not only will there be some error in the measurement of these magnitudes, but there is not any material figure which is an exact cone.
- The terms quadratureformula and cubature-formula are sometimes restricted to formulae for expressing the area of a trapezette, or the volume of a briquette, in terms of such data.
- Thus a quadrature-formula is a formula for expressing [A x .24] or fudx in terms of a series of given values of u, while a cubature-formula is a formula for expressing [[Vx, 0 .
- u]] or ffudxdy in terms of the values of u for certain values of x in combination with certain values of y; these values not necessarily lying within the limits of the integrations.
- The first, which is the best known but is of limited application, consists in replacing each successive portion of the figure by another figure whose ordinate is an algebraical function of x or of x and y, and expressing the area or volume of this latter figure (exactly or approximately) in terms of the given ordinates.
- The - - 4X + g tangential area may be expressed in terms of chordal areas.
- Some of the formulae obtained by the above methods can be expressed more simply in terms of chordal or tangential areas taken in various ways.
- The following are some examples of formulae of this kind, in terms of chordal areas.
- There are similar formulae in terms of the tangential areas T1, Thus (iii) of § 68 may be written A -a -1-(9T 1 - T3).
- We have therefore B in the first place to see whether the difference can be expressed in terms of the directions of the tangents.
- = x0 To apply these, the differential coefficients have to be expressed in terms of differences.
- The following are the results (for the formulae involving chordal areas), given in terms of differential coefficients and of central differences.
- One method is to construct a table for interpolation of x in terms of u, and from this table to calculate values of x corresponding to values of u, proceeding by equal intervals; a quadrature-formula can then be applied.
- Even where u is an explicit function of x, so that f x udx may be expressed in terms of x, it is often more convenient, for construction of a table of values of such an integral, to use finite-difference formulae.
- The formulae may be used for extending the accuracy of tables, in cases where, if v represents the quantity tabulated, hdv/dx or h 2 d 2 v /dx 2 can be conveniently expressed in terms of v and x to a greater degree of accuracy than it could be found from the table.
- Then u/U = - dy/dx (2) This gives the velocity of any particle in terms of the displacement.
- Equating (I) and (2) u/U = wÃ† (3) which gives the particle velocity in terms of the pressure excess.
- We have c3 and u expressed in terms of the original length dx and the displacement dy so that we must y put dE= (dx+dy = (I +dy/dx)dx, and U dy p = .l o (w+pu t) I dx.
- § 311) gives the pressure variations in the incident waves in terms of those in the resonator, and so the pressure variation and the amplitude of vibration in the waves to be measured were determined.
- The integration can be performed when M is expressed in terms of x.
- The value of the American dollar, in terms of AustroHungarian paper kronen with legally fixed value, varied in fact, as shown by the Swiss exchange market, as follows: - State Finances.
- The view that our knowledge in such cases may be completely represented by means of laws of action at a distance, expressible in terms of the positions (and possibly motions) of the interacting bodies without taking any heed of the intervening space, belongs to modern times.
- Although, however, gravitation has formed the most perfect instance of an influence completely expressible, up to the most extreme refinement of accuracy, in terms of laws of direct action across space, yet, as is well known, the author of this ideally simple and perfect theory held the view that it is not possible to conceive of direct mechanical action independent of means of transmission.
- They were content with a knowledge of the truth of the principle of gravitation; instead of essaying to explain it further by the properties of a transmitting medium, they in fact modelled the whole of their natural philosophy on that principle, and tried to express all kinds of material interaction in terms of laws of direct mechanical attraction across space.
- If material systems are constituted of discrete atoms, separated from each other by many times the diameter of any of them, this simple plan of exhibiting their interactions in terms of direct forces between them would indeed be exact enough to apply to a wide range of questions, provided we could be certain that the laws of the forces depended only on the positions and not also on the motions of the atoms. The most important example of its successful application has been the theory of capillary action elaborated by P. S.
- A little earlier had begun the practice of partial Indulgences, which are always expressed in terms of days or years.
- Among the ancients the Epicureans expressed all eudaemonia in terms of pleasure.
- The term potentiometer is usually applied to an instrument for the measurement of steady or continuous potential difference between two points in terms of the potential difference of the terminals of a standard voltaic cell of some kind, such as a Clark or Weston cell.
- Instead of adjusting in this manner the electromotive force of any form of cell, if we pass any constant current through a known resistance and bring wires from the extremities of that resistance into connexion with the slider and the galvanometer terminal, we can in the same way determine the fall of potential down the above resistance in terms of the electromotive force of the standard cell and thus measure the current flowing through the standard resistance.
- From the potential terminals of the strip, wires are brought to the potentiometer so as to determine their potential difference in terms of the electromotive force of the standard Clark cell.
- In the absence of the actual standards of ancient times the units of measure and of weight have to be inferred from the other remains; hence unit in this division is used for any more or less closely defined amount of length or weight in terms of which matter was measured.
- -- The metric equivalents of the units of the metric system in terms of the imperial system, as recalculated in 1897, are as follows: -
- This quantity may readily be expressed in terms of the refractive indices for the three colours, for if A is the angle of the prism (supposed small) bc=(/1c - I)A, bD =(/ AD - OA, F - I)A, where µc, A n, µ F are the respective indices of refraction.
- A voltmeter isan instrument for measuring difference of electric potential in terms of the unit called a volt.
- gives us at once an expression for the diameter in terms of the circumference by means of an infinite series.'
- As far as the circlesquaring functions are concerned, it would seem that Gregory was the first (in 1670) to make known the series for the arc in terms of the tangent, the series for the tangent in terms of the arc, and the secant in terms of the arc; and in 1669 Newton showed to Isaac Barrow a little treatise in manuscript containing the series for the arc in terms of the sine, for the sine in terms of the arc, and for the cosine in terms of the arc. These discoveries 1 See Euler, ” Annotationes in locum quendam Cartesii," in Nov.
- Immediately preceding this very piece in his collected works is a carol written in terms of the utmost simplicity.
- He had specially prepared himself, as he thought, for "teaching imaginative men, and political men, and legal men, and scientific men who bear the world in hand"; and he did not attempt to win their attention to abstract and worn-out theological arguments, but discussed the opinions, the poetry, the politics, the manners and customs of the time, and this not with philosophical comprehensiveness, not in terms of warm eulogy or measured blame, but of severe satire varied by fierce denunciation, and with a specific minuteness which was concerned primarily with individuals.
- A generalization of Galileo's results takes the form that under constant conditions of this kind, force (defined in terms of motion) is constant, and that the superposition of two sets of conditions, if their independence can be secured, results in superposition of the forces associated with them separately.
- The case of electro-magnetic forces between two conductors carrying electric currents affords an example of a statement of motion in terms of force of a highly artificial kind.
- In this connexion a statement in terms of force is apt to be displaced by more direct and more comprehensive methods, and the attention of physicists is directed to the intervention of the ether.
- Such general statements of the theory of motion as that of Lagrange, while releasing us from the rather narrow and strained view of the subject presented by detailed analysis of motion in terms of force, have also suggested a search for other forms which a statement of elementary principles might equally take as the foundation of a logical scheme.
- The solubilities of solids may be expressed in terms of the mass of solute which will dissolve in loo grammes of water.
- It is possible to state the conditions of solubility in terms of the theory of available energy, but the result comes to little more than a re-statement of the problem in other terms. Nevertheless, such a re-statement is in itself sometimes an advance in knowledge.
- The possibility of these phenomena should be borne in mind when attempts are made to interpret the structure of crystalline bodies in terms of the theory of equilibrium.
- According to the Memoirs of Sir James Melville, both Lord Herries and himself resolved to appeal to the queen in terms of bold and earnest remonstrance against so desperate and scandalous a design; Herries, having been met with assurances of its unreality and professions of astonishment at the suggestion, instantly fled from court; Melville, evading the danger of a merely personal protest without backers to support him, laid before Mary a letter from a loyal Scot long resident in England, which urged upon her consideration and her conscience the danger and disgrace of such a project yet more freely than Herries had ventured to do by word of mouth; but the sole result was that it needed all the queen's courage and resolution to rescue him from the violence of the man for whom, she was reported to have said, she cared not if she lost France, England and her own country, and would go with him to the world's end in a white petticoat before she would leave him.
- When, in the course of centuries, the exhaustion of richer ores shall have forced us to mine, crush and concentrate mechanically or by magnetism the ores which contain only 2 or 3% of iron, then the cost of iron in the ore, measured in terms of the energy needed to mine and concentrate it, will be comparable with the actual cost of the copper in the ore of the copper-mines of to-day.
- He succeeded more nearly than any of his predecessors in expressing or suggesting ideas and emotions which might have been supposed to be capable of translation only in terms of music. " The unconscious self, or rather the sub-conscious self," says Emile Verhaeren, " recognized in the verse and prose of Maeterlinck its language or rather its stammering attempt at language."
- If Q is expressed in terms of this unit in equation (I), it is necessary to divide by c, or to replace k on the right-hand side by the ratio k/c. This ratio determines the rate of diffusion of temperature, and is called the thermometric conductivity or, more shortly, the diffusivity.
- The heat transmitted should be measured calorimetrically, and not in terms of the uncertain emissivity.
- No calorimetric observations are required, but the results are obtained in terms of the thermal capacity of unit volume c, and the measurements give the diffusivity klc, instead of the calorimetric conductivity k.
- The quantity of heat absorbed by the stratum (x' x") in the interval considered can also be expressed in terms of the calorimetric conductivity k.
- The advantage is that the quantities of heat are measured directly in absolute measure, in terms of the current, and that the results are independent of a knowledge of the specific heat.
- (9) By a property of the parabola, the mean temperature is 3rds of the maximum temperature, we have therefore (R - R 0)/aRo =1C 2 Ra/12gk, (io) which gives the conductivity directly in terms of the quantities actually observed.
- The last expression in terms of k/k' is very simple, but the first is more useful in practice, as the quantities actually measured are E, C, 1, q, and the difference of temperature.
- His scheme was first to work out, in a separate treatise De corpore, a systematic doctrine of Body, showing how physical phenomena were universally explicable in terms of motion, as motion or mechanical action was then (through Galileo and others) understood - the theory of motion being applied in the light of mathematical science, after quantity, the subject-matter of mathematics, had been duly considered in its place among the fundamental conceptions of philosophy, and a clear indication had been given, at first starting, of the logical ground and method of all philosophical inquiry.
- The subsequent process, the warrant directing a messenger-at-arms to charge the debtor to pay or perform in terms of the letters, was called "letters of horning."
- But the peculiar way in which it enforces its morals in terms of the Platonic contrast between the spiritual and sensuous worlds, as archetype and temporal manifestation, suggests a special local type of theology which must be taken into account in fixing its provenance.
- On the day of his capture Monmouth wrote to James in terms of the most unmanly contrition, ascribing his wrong-doings to the action of others, and imploring an interview.
- Many of the properties of such series, and the methods of describing them, are dealt with elsewhere (see Probability: Law of Error); and the frequency with which the mean value or any deviation from the mean value of a character occurs in a race of animals or of plants may probably always be expressed in terms of one or other of the series there described.
- Themselves giving up this world as hopeless, and looking for salvation in the next, they naturally thought the Buddhists must do the same, and in the absence of any authentic scriptures, to correct the mistake, they interpreted Nirvana, in terms of their own belief, as a state to be reached after death.
- The climate of eastern Bokhara and Darwaz is delightful in summer, and Dr Regel writes of its Alpine scenery and flora in terms of enthusiastic admiration.
- The normal value, for example, of the post-war exports of Bahrein should be more nearly £3,000,000 than £ I,000,000, owing to the enhanced value in terms of money of pearls, and the export trade of Bandar 'Abbas should likewise be more in a normal post-war than in a pre-war year.
- When Essex returned to England, Chichester rendered valuable service under Mountjoy in the war against the rebellious earl of Tyrone, and in 1601 Mountjoy recommended him to Cecil in terms of the highest praise as the fittest person to be entrusted with the government of Ulster.
- Let it be supposed that two positive lenses of equal curvature powers are made out of these two glasses, then in order to represent the combined dispersion of the two together the two 0µ's for each spectral region may be added together to form 0'µ as in the line below, and then, on again expressing the partial z'µ in terms of L'µ (C to F) we get the new figures in the bottom row beneath the asterisks.
- Suppose now, for the moment, that the readings of the levels k and l are identical in both observations, we have then, in the difference between the micrometer readings north and south, a measure of the difference of the two zenith distances expressed in terms of the micrometer screw; and, if the "` value of one revolution of the micrometer screw" is known in seconds of arc we have for the resulting latitude FIG.
- The value of "one revolution of the screw in seconds of arc" can be determined either by observing at transit the difference of zenith distance of two stars of known declination in terms of the micrometer screw, the instrument remaining at rest between their transits; or by measuring at known instants in terms of the screw, the change of zenith distance of a standard star of small polar distance near the time of its greatest elongation.
- All the gods, great and small, had their places assigned to them in the heavens, and facts, including such as fell within the domain of political history, were interpreted in terms of astral theology.
- The astral theology of the Babylonian-Assyrian religion, while thus bearing the ear-marks of a system devised by the priests, succeeded in assimilating the beliefs which represented the earlier attempts to systematize the more popular aspects of the religion, and in this way a unification of diverse elements was secured that led to interpreting the contents and the form of the religion in terms of the astral-theological system.
- Quantities of heat may be measured indirectly in a variety of ways in terms of the different effects of heat on material substances.
- But the specific heat of water is often stated in terms of other units.
- The difficulties arise in connexion with the determination of the quantities of ice melted or steam condensed, and in measuring the latent heat of fusion or vaporization in terms of other units for the comparison of observations.
- The weight of steam condensed on the body gives a means of calculating the quantity of heat required to raise it from the atmospheric temperature up to ioo° C. in terms of the latent heat of vaporization of steam at zoo° C. There can be no appreciable gain or loss of heat by radiation, if the admission of the steam is sufficiently rapid, since the walls of the enclosure are maintained at too C., very nearly.
- Joly has himself determined the mean specific heat of water between 12° and zoo° C. by this method, in terms of the latent heat of steam as above given, and finds the result 9952.
- The British engineer prefers to state results in terms of foot-pounds of work in any convenient latitude per pound-degree-Fahrenheit of heat.
- Hirn's method of measuring the work expended in terms of the torque and the number of revolutions, still possess value as experimental evidence.
- 4.197 4.188 4.181 4.1764.1 75 4.177 These Are Expressed In Terms Of The Hydrogen Scale, But The Difference From The Nitrogen Scale Is So Small As To Be Within The Limits Of Experimental Error In This Particular Case.
- Gannon For The Determination Of The Specific Heat Of Water In Terms Of The International Electric Units (Phil.
- The Difference Of Potential E Between The Ends Of The Tube, And The Electric Current C Through It, Are Measured On An Accurately Calibrated Potentiometer, In Terms Of A Clark Cell And A Standard Resistance.
- But For The Determination Of Relative Values Of Specific Heats In Terms Of A Standard Liquid, Or Of The Variations Of Specific Heat Of A Liquid, The Method Depends Only On The Constancy Of The Standards, Which Can Be Readily And Accurately Tested.
- Many Of The Uncertainties In The Reduction Of Older Experiments, Such As Those Of Regnault, Arise From Uncertainty In Regard To The Unit In Terms Of Which They Are Expressed, Which Again Depends On The Scale Of The Particular Thermometer Employed In The Investigation.
- We May Probably Take The Tabulated Values As Showing Correctly The Rate Of Variation Between 110° And 190° C., But The Values In Terms Of Any Particular Thermal Unit Must Remain Uncertain To At Least 0.5% Owing To The Uncertainties Of The Thermometry.
- Regnault Himself Adopted The Formula, S = I 0 00004T 0.0000-0091 2 (Regnault), (3) For The Specific Heat S At Any Temperature T C. In Terms Of The Specific Heat At O° C. Taken As The Standard.
- 6, Show A Minimum At 25° C., And A Maximum At 87° C., The Values Being 9935 And 1.0075 Respectively In Terms Of The Mean Specific Heat Between O° And 100° C. He Paid Great Attention To The Thermometry, And The Discrepancies Of Individual Measurements At Any One Point Nowhere Exceed O 3%, But He Did Not Vary The Conditions Of The Experiments Materially, And It Does Not Appear That The Well Known Constant Errors Of The Method Could Have Been Completely Eliminated By The Devices Which He Adopted.
- Assoc. Report, 1899, with a slight modification Specific Heat Of Water In Terms Of Unit At 20° C. 4.180 Joules to allow for the increase in the specific heat below 20° C. This was estimated in 1899 as being equivalent to the addition of the constant quantity 0.020 to the values of the total heat h of the liquid as reckoned by the parabolic formula (5).
- For This Reason The Definition Of The Thermal Unit Will In The End Probably Be Referred To A Scale Of Temperature Defined In Terms Of A Standard Platinum Thermometer.
- The Following Formulae Represent His Results For The Specific Heat S At Constant Volume In Terms Of The Density D In Gms. Per C. C.: Air, S = 0.1715 0 028D, C02, S = 0.165 0.213D } O 34D2.
- de Tocqueville, who spoke of them in terms of the highest praise.
- Forms are qualities and activities expressed in terms of the ultimates of nature, i.e.
- normally in terms of collocations of matter or modes of motion.
- Mill seems most often to think of the former, while tending to formulate in terms of the latter.
- That the unit for logic is the concept and not the judgment has proved a stumblingblock to those of Lotze's critics who are accustomed to think in terms of the act of thought as unit.
- The step he took is really nothing more than the kinematical principle of the composition of linear velocities, but expressed in terms of the algebraic imaginary.
- From a different point of view, equation (12) may be applied to determine the specific heat of steam in terms of the rate of variation of the total heat.
- Employing this type of equation, all the thermodynamical properties of the substance may conveniently be expressed in terms of the diminution of volume c due to the formation of compound or coaggregated molecules, (v - b) =RO/p - co(Oo/O) n =V - c. .
- In the following list, which contains a few typical examples, the different formulae are arranged to give the logarithm of the saturation-pressure p in terms of the absolute temperature 0.
- It is generally called Dupre's formula in continental text-books, but he did not give the values of the coefficients in terms of the difference of specific heats of the liquid and vapour.
- The Path may also be described in terms of the "seven principles."
- St Anselm denied that any penalty was due to the devil, and in terms of feudal honour restated the problem.
- With a less thorough-going intellectualism other scholars reinterpret Christianity in terms of current scientific phraseology.
- They all sought to explain the material universe as given in sensible perception; their explanation was in terms of matter, movement, force.
- The earliest thinkers down to Heraclitus endeavoured to find a material substance of which all things consist; Heraclitus, by his principle of universal flux, took a new line and explained everything in terms of force, movement, dynamic energy.
- Being is intelligible only in terms of Becoming.
- The value in terms of arc of the scale of the record can be obtained by measuring the distance between the magnet mirror and the recording drum, and in most observations it is such that a millimetre on the record represents one minute of arc. The time scale ordinarily employed is 15 mm.
- The displacement is thus expressed in terms of the six independent quantities E, 1~, ~, X, u, 1-.
- This, theorem, also due to Lagrange, enables us to express the mean square of the distances of the particles from the centre of mass in terms of the masses and mutual distances.
- This may be expressed in terms of the product of inertia with respect to parallel planes through G by means of the formula (14); viz.:
- The following table gives the period, for various amplitudes a, in terms of that of oscillation in an infinitely small arc about a vertical axis half-way between the points of attachment of the upper string.
- which expresses the internal kinetic energy in terms of the relative velocities of the several pairs of particles.
- Rotating Pieces: Couples of Forces.It is often convenient to express the energy exerted upon and the work performed by a turning piece in a machine in terms of the moment of the couples of forces acting on it, and of the angular velocity.
- It may be noted here that, while Cavendish adhered to the phlogistic doctrine, he did not hold it with anything like the tenacity that characterized Priestley; thus, in his 1784 paper on "Experiments on Air," he remarks that not only the experiments he is describing, but also "most other phenomena of nature seem explicable as well, or nearly as well," upon the Lavoisierian view as upon the commonly believed principle of phlogiston, and he goes on to give an explanation in terms of the antiphlogistic hypothesis.
- We are on firmer ground when simply describing the phenomena of primitive religion than when seeking to account for these in terms of natural law - in whatever sense the conception of natural law be applicable to the facts of the mental life of man.
- We thus find V in terms of the constant and the difference of the two screw readings.
- The difference of potentials is thus determined in terms of a weight, an area and a distance, in absolute C.G.S.
- The expression for these coefficients in terms of the constants of the optical system, i.e.
- It would seem that, in the extreme spiritual vicissitudes of his life, conscious alternately of personal weakness and of the largest speculative grasp, he at times threw himself entirely on the consolations of evangelical faith, and at others reconstructed the cosmos for himself in terms of Neo-Platonism and the philosophy of Schelling.
- The consul may even defray the expenses of maintaining, and forwarding to their destination, passengers taken off or picked up from wrecked or injured vessels, if the master does not undertake to proceed in six weeks; these expenses becoming, in terms of the Passenger Acts 1855 and 1863, a debt due to His Majesty from the owner or charterer.
- The experiments on solids lead to certain laws of elasticity expressed in terms of coefficients, the values of which can be determined only by experiments on each particular substance.
- This explanation of the action of the solid is equivalent to that by which Gauss afterwards supplied the defect of the theory of Laplace, except that, not being expressed in terms of mathematical symbols, it does not indicate the mathematical relation between the attraction of individual particles and the final result.
- In more recent times the method of Gauss has been modified so as to take account of the variation of density near the surface, and its language has been translated in terms of the modern doctrine of the conservation of energy.'
- We have next to determine the value of x in terms of the action between one particle and another.
- We may also write ur 1 = I +zu 1+ &c., since z is very small compared with u, and expressing u in terms of w by (25), (we find l 21- mv i fi(z) i I +z(c R w + ' R 2 w) do) = 27rmoti(z) I -f-ZZ (Ki + R2/ This then expresses the work done by the attractive forces when a particle m is brought from an infinite distance to the point P at a distance z from a stratum whose surface-density is a, and whose principal radii of curvature are R 1 and R2.
- As Laplace has shown, the values for K and T may also be expressed in terms of the function cs, with which we started.
- [In order to express the dependence of the tension at the interface of two bodies in terms of the forces exercised by the bodies upon themselves and upon one another, we cannot do better than follow the method of Dupre.
- Laplace does not treat systematically the question of interfacial tension, but he gives incidentally in terms of his quantity H a relation analogous to (47).
- This equation, which gives the pressure in terms of the principal radii of curvature, though here proved only in the case of a surface of revolution, must be true of all surfaces.
- I or the curvature of any surface at a given point may be completely defined in terms of the positions of its principal normal sections and their radii of curvature.
- Now that the length of a division has been estimated a priori, it is perhaps preferable to reverse Plateau's calculation, and to exhibit the frequency of vibration in terms of the other data of the problem.
- It is interesting, however, to notice that Bacon (De Principiis) assigns to him his true place in the history of thought, and points out that both in his own day and later "in the times of Roman learning" he was spoken of in terms of the highest praise.
- Thus, Hasdrubal's devotion and valour at the battle on the Metaurus are described in terms of eloquent praise; and even in Hannibal, the lifelong enemy of Rome, he frankly recognizes the great qualities that balanced his faults.
- The composition of the alloy is stated in terms of its "fineness," the proportion of silver in 1000 parts of alloy.
- Kirchhoff's contributions to mathematical physics were numerous and important, his strength lying in his powers of stating a new physical problem in terms of mathematics, not merely in working out the solution after it had been so formulated.
- But the relation of subordination of one state to another was generally expressed in terms of feudal law.
- Moreover, every statement of fact involves certain general notions and theories, so that the "facts" of the separate sciences cannot be stated except in terms of the conceptions or hypotheses which are assumed by the particular science.
- Just four years later he wrote to her in terms of such calculated harshness and imposed such conditions as to make further intercourse virtually impossible.
- In Lange's Logische Studien, which attempts a reconstruction of formal logic, the leading idea is that reasoning has validity in so far as it can be represented in terms of space.
- It preserved the monotheistic idea yet afforded a description of the Divine activity in terms of Hellenic thought; the Word of the Old Testament is one with the X6yos of the Stoics.
- thick of a monolithic dam, subject to the pressure of water against its vertical side to the full depth ab= d in feet, the horizontal _ eL 2 pressure of water against the section of the dam, inI creasing uniformly with the depth, is properly represented by the isosceles right-angled triangle abe, in which be is the maximum water-pressure due to the Cent full depth d, while the area 2 abe = d is t h e total hor12 d3 6 If x be the width of the base, and p the density of the masonry, the weight of the masonry in terms of a cubic foot of water will be acting at its centre of gravity g, situated at 3x from the outer toe, and the moment of resistance to overturning on the outer toe, p x 2 d (2) In countries where good clay or retentive earth cannot be obtained, numerous alternative expedients have been adopted with more or less success.
- Where a number is expressed in terms of various denominations, a cardinal number usually begins with the largest denomination, and an ordinal number with the smallest.
- In order to apply arithmetical processes to a quantity expressed in two or more denominations, we must first express it in terms of a single denomination by means of a varying scale of notation.
- To express the quantity in terms of £, it ought (20) (12) to be written £254 13 v 6; this would mean £254 1202 or £(254+20 20 + 6 12), and therefore would involve a fractional number.
- Comparison, Addition and Subtraction of Fractions.-The quantities 4 of A and 7 of A are expressed in terms of different units.
- To compare them, or to add or subtract them, we must express them in terms of the same unit.
- is a mixed quantity, being expressed in pounds and shillings; to express it in terms of pounds only we must write itL3-1-70-.
- This number, expressed in terms of the fraction ioo, T oor 0001, would be 271530.
- 1665; and of, would be 271.530, but expressed in terms of ioo it would be 271530.
- The pth root of a number (§43) may, if the number is an integer, be found by expressing it in terms of its prime factors; or, if it is not an integer, by expressing it as a fraction in its lowest terms, and finding the pth roots of the numerator and of the denominator separately.
- When a mixed quantity or a mixed number has to be multiplied by a large number, it is sometimes convenient to express the former in terms of one only of its denominations.
- in determining the rate of a " dividend "), approximate expression of the divisor in terms of the largest unit is sufficient.
- The following tables are given as illustrations of the arrangement adopted elsewhere in this article; the entries in any column denote multiples or submultiples of the unit stated at the head of the column, and the entries in any row give the expression of one unit in terms of the other units.
- Hence when x = o, P: Q = R :S and the value of R can be determined in terms of P, Q and S.
- It is easy to derive the further forms - = 3(n - m), 2 (7-5) =(n - m) (n +m -9), (+3) - 5-2K = 2n(n-i--3) - T-2c, (so) 2 (M I) (ni -2) - - 2(n - (n-2) (II, 12) m 2 -2 5 -3K = n2 -2T -31, =m +n, - (6) the whple system being equivalent to three equations only; and it may be added that using a to denote the equal quantities 3m+c and 3 n + everything may be expressed in terms of m,n,a.
- Edward Baliol surrendered it in 1 334 in terms of his compact with Edward III., but the Scots regained it in 1339.
- At Alexandria, Clement and his great pupil Origen state Christianity in terms of philosophy.
- Thus far the outcome of what Locke teaches about matter is, that it is Something capable of being expressed in terms of mathematical.
- quantity, and also in terms of our own sensations.
- It will easily be seen that the connecting link between the old and the new calendars is very slight indeed and that the expression of a date in one calendar in terms of the other is a matter of some difficulty.
- Good as a true universal can only be realized by a true self, and both imply a principle of unity not wholly expressible in terms of the particulars which it unifies.
- that the good is defined in terms of self-realization and selfrealization in terms of the good, it may be doubted whether any rational system of ethics can avoid a similar imputation.
- When, following the preceding method, the variations of the elements are expressed in terms of the time, they are found to be of two classes, periodic and secular.
- Not only the grosser facts concerning radial velocity, but variations in it so small as a mile, or less, per second, have been recorded and interpreted in terms of deep meaning.
- Plana (1781-1864), effected the integration by expressing the time in terms of the moon's true longitude.
- Then, by inverting the series, the longitude was expressed in terms of the time.
- By the second general method the moon's co-ordinates are obtained in terms of the time by the direct integration of the differential equations of motion, retaining as algebraic symbols the values of the various elements.
- We have just mentioned the four small quantities e, e', y and m, in terms of the powers and products of which the moon's co-ordinates have to be expressed.
- It is obvious that the co-ordinates of any point on an ellipse may be expressed in terms of a single parameter, the abscissa being a cos q4, and the ordinate b sin 43, since on eliminating 4 between x = a cos and y = b sin 4) we obtain the equation to the ellipse.
- The determination of the curves of constant retardation depends upon expressing the retardation in terms of the optical constants of the crystal, the angle of incidence and the azimuth of the plane of incidence.
- (38) The function J" may be expressed in terms of 0 and v by writing for p its value, namely, RD/(v+c - b).
- Dewar and Fleming, working at very low temperatures, were compelled to use the platinum thermometer, and expressed their results in terms of the platinum scale.
- - The method employed by the writer, to which allusion has already been made, consisted in observing the change of distribution of temperature in terms of the resistance along a wire heated by an electric current, when the heating current was reversed.
- dE, namely, dE =dP+(s' - s")dT = (P/T)dT = pdT = (p" - p')dT, in which the coefficient, P, of the Peltier effect, and the thermoelectric power, p, of the couple, may be expressed in terms of the difference of the thermoelectric powers, p and p", of the separate metals with respect to a neutral standard.
- Many were also very adroit in terms of choosing a school.
- The consequences of security breaches can be disastrous in terms of the public profile and the operation of your business.
- The program was retained in the BBC archives, but never commercially exploited in terms of either a DVD or VHS release.
- The problems were immense in terms of wasted opportunities for economic growth and social justice.
- The reign of the king marks the high point of the 26th dynasty in terms of wealth and prosperity.
- advantageous in terms of self-employment taxes in comparison to LLCs.
- aeonen we realize more that it takes eons to develop right understanding we shall be less inclined to think in terms of progress.
- It sets out a challenging agenda for Departments in terms of identifying their major impacts, planning improvements, and monitoring and reporting performance.
- Of course Weber was right in terms of operating policy - the ECB does not target a monetary aggregate.
- The film succeeds not only in terms of action and suspense but as cautionary fable, historical allegory, social satire and moral disquisition.
- allowing complete flexibility in terms of investment.
- Scotland has much to offer in terms of top quality wild trout angling.
- The Church of England, certainly in terms of its leadership, is marked by " craven apologetics and moral and cultural relativism.
- Everything I've said here can be understood in terms of the polarity of precision and meaning discussed in the previous article.
- These early signs are poorly articulated in terms of handshape, location and movement.
- articulated where necessary in terms of constitutive conventions or implicit codes of practice.
- aspheric surfaces are presented, with an interpretation in terms of spatial frequencies.
- aspiring to achieve is at least match your existing terms in terms of performance or to increase them.
- As described in this extremely authoritative book: " In terms of business continuity, immediate physical damage is not the most important concern.
- averse in terms of strict eligibility criteria for training courses.
- What can we do in terms of a code of conduct to stop you from getting a savage beating?
- The topic remains controversial especially in terms of international trade of hormone-treated beef.
- This will bring great benefits in terms of getting officers back out on the streets in the shortest possible time.
- The existence of primitive thought habits makes a great deal of sense in terms of evolutionary biology.
- Employe loyalty is defined in terms of turnover intentions and managers ' ratings of the employees ' loyal boosterism, a type of OCB.
- Students will know exactly how close to class borderlines they are, at least in terms of overall performance.
- First, many engineering systems have performance requirements naturally stated in terms of the upper bounds on the steady-state variance values.
- bring great benefits in terms of getting officers back out on the streets in the shortest possible time.
- The former is thought to be more significant in terms of calorie burning than the latter.
- calibrated in terms of casualty data for 1997 from the STATS19 national accident reporting system.
- categorized in terms of problem page types.
- For them, the landscape is brought into knowledge and representation in terms of the cultural centrality of the court.
- In order to accommodate chancy causation, Lewis (1986c) defines a more general notion of causal dependence in terms of chancy causation, Lewis (1986c) defines a more general notion of causal dependence in terms of chancy counterfactuals.
- chronological narratives that explain the present in terms of the past.
- The statement is given in terms of intersecting great circles on a sphere.
- These experiences are now described in terms of brain circuitry.
- The good bits were good but they were too overshadowed by the big clangers that were made in terms of camera work and script.
- It also helped achieve greater clarity for me in terms of what I'm personally looking for.
- Bully tactics Men use power in terms of financial clout.
- The angular integral of the reduced matrix element is expressed in terms of recoupling coefficients and coefficients of fractional parentage.
- column header of the field you'd like the summary to be sorted in terms of.
- CRD commentary The review question was clear in terms of the study design, intervention, participants and outcomes.
- common denominator in terms of users ' knowledge.. .
- commonwealth war cemetery in the world in terms of burials.
- The website also shows what the next steps are in terms of implementing the compact for Devon 2005/2006.
- In the country, you simply have to make do with what you've got, in terms of the human companionship.
- Intrusive research is defined in terms of whether consent would be required of a person who is mentally competent.
- comprehensible in terms of a more general kind of emergence.
- The pros probably outweigh the cons in terms of what it will do for her socially.
- conceived narrowly in terms of either ' patrimonialism ' or coercive authoritarianism.
- conceived solely in terms of the grammatical possibilities which the system offered.
- conceptualized in terms of sheer temporal sequences and causal dependencies, the latter cannot.
- considerable in terms of a richer cultural experience, educational resources and employment opportunities.
- Should we think in terms of a linear expansion of western consumerism ending in global convergence?
- contextualize climate information in terms of other biophysical, socio-economic and cultural information for the area of its application.
- cost-effective in terms of smaller openings.
- costly in terms of time and money.
- couched in terms of the optimal size of institutions.
- counterproductive in terms of sound motor learning.
- AMP is a lovely company, however in terms of choreography its artistic credo is not firm.
- These results cannot be fully explained in terms of simple cross-pollination.
- Music is now a major strength of the school, in terms of the enthusiasm engendered in a wide cross section of pupils.
- curvaceous arms and sumptuously deep cushions have instant appeal in terms of both look and comfort.
- deceptive in terms of angles, which you will have to be aware of.
- deconstruction in terms of the masculine subject, then ' woman ' becomes a metaphor for unrealized possibility.
- He also granted decree for removing against the defender in terms of the second crave of the initial writ.
- defensible in terms of reducing anxiety rather than reducing risk.
- defined in terms of indigenous social judgements.
- They consolidated their hold on what were, in terms of western European norms of the time, unusually large demesnes.
- The theory of causation in terms of chains of causal dependence can handle this sort of example.
- described in terms of coupled partial equations in two dimensions.
- For this reason, the course will seek to explore specific dimensions of world cinema in terms of historical and social contexts of production.
- disability rights legislation in terms of public service management?
- disastrous in terms of the public profile and the operation of your business.
- However, there is some reluctance in that sms isn't reliable in terms of delivery, thus discouraged in emergencies.
- A similar proof using discrete Abel summation delivers a variant of the theorem in terms of ls instead of li.
- I'm definitely not pleased with the first half in terms of us being very very disjointed.
- It is not wilful disobedience - it is just that people get biased in terms of making money.
- disparate in terms of subject matter.
- The tariffs have however been highly disruptive in terms of their overall effect on world trade.
- disruptive in terms of their overall effect on world trade.
- diverse in terms of their look and feel, there are many sites that serve similar roles.
- However, dune buggies have become more diversified in terms of the terrain they can handle.
- downside in terms of battery power: little more than 60 minutes for intensive tasks.
- But both speak in terms of such a fundamental dualism.
- A comparison is also made with cycle 22, which is ' paired ' with cycle 23 in terms of the solar dynamo.
- earthquake hazard maps like this are more often expressed in terms of ground acceleration.
- economical in terms of energy expended per meter of distance traveled.
- efficient in terms of road space and energy per passenger than cars.
- Can you explain the above problem in terms of digital electronics?
- The Ipswich carving is limited both in terms of narrative excitement and decorative embellishment.
- enormous in terms of patient numbers, the global TB market is estimated at only US $ 500 million.
- entangledy the entangling power of permutations, given in terms of a combinatorial formula.
- She also eschews interpretation of the statute in terms of her own policy preferences.
- Archbishop Giffard gave his assent, on account of their penury, in terms of warm eulogy as to their devout life.
- The impact on people's mental health was clearly evident in terms of the high emotions in some of the responses.
- exacting requirements in terms of size, styling and finishing.
- Argos was proclaimed simply the best in terms of performance and genuine all-round excellence.
- natural explanation is provided in terms of precedent events, causal laws, or necessary conditions that invoke natural existents.
- exorbitant price you can pay for worry in terms of your health.
- This was the era of CND and I saw the key battle in terms of the West versus soviet expansionism.
- explicable in terms of age or verbal IQ.
- Another bit of good news is that, in terms of a personality disposition it's very important, extroversion is going up dramatically.
- What will next year bring in terms of engineering feats?
- fibrew twitch fibers are fatigue resistant and are therefore used for sustained exercise; in terms of lactate they are best suited to clearance.
- Competition in terms of overall national strength is becoming increasingly fierce.
- fifteenth in the world in terms of the UN's Gender Empowerment Measure (GEM ).
- first-rate in terms of the theory of art.
- Also I am totally flabbergasted that SCCC would accept this shoddy piece of programming which could cost them dearly in terms of lost subscriptions.
- formulated in terms of these four aims.
- gasoline generator can be assessed in terms of usage.
- gas turbines with fuel cells on ships, both in terms of design and propulsion.
- However, in terms of actual practices in the working environment, this is clearly too generalized to be of much use.
- generous in terms of space and each has an en-suite shower and toilet with wheelchair access.
- sediment geochemistry may also be interpreted in terms of the different element concentrations associated with particular grain sizes.
- bumblebee gobies: In terms of care, similar to the knight goby, but needing proportionately smaller foods.
- I think in terms of health and nutrition now and not greasy food products anymore.
- In 2002, Kaohsiung harbor was the fifth largest harbor in the world in terms of the volume of container cargo processed.
- But in terms of military hardware, they dwarfed the Germans in all areas.
- These attacks on an almost hard-wired complacency are vital in terms of grabbing the audience and demanding that they listen.
- headlamp nacelle is the major departure in terms of new bits, and leads to many other details.
- heterogeneous in terms of other components.
- holistic perspective tended to view clients in terms of potential health.
- homogeneous in terms of the number of lanes closed during an incident.
- homogenous in terms of street widths.
- This small area of North London is largely homogenous in terms of street widths.
- Similar binding sites in terms of surface shape and properties, but which have low homology with the reference structure, may also exist.
- This approach is analyzed in terms of its ability to reliably identify, and provide good alternatives for, incorrectly hypothesized words.
- iceberg in terms of the appearances of the Golden Ratio in the arts.
- The child is considered illegitimate in terms of intestacy.
- illegitimate in terms of intestacy.
- These establish the indigenous discourse of insanity, which saw madness in terms of an externally imposed affliction.
- impoverished in terms of diversity as might be expected from the lack of underlying plant structure.
- inconclusive in terms of an evaluation.
- UNIT has been a wildly inconsistent series in terms of both style and the quality of the stories.
- individuates mental states in terms of their causes and effects.
- EXECUTE is limited by two factors: The need to compile the string at runtime makes EXECUTE inefficient in terms of speed.
- inefficient in terms of their energy use.
- infancy in terms of uptake, the operational reasons for implementation can be clear.
- inferior in terms of quality and efficacy to wild harvested materials.
- inflexible in terms of both road safety and the rule of law.
- As a relatively small employer in terms of resource availability it is not possible to offer a full range of diverse training in-house.
- innovate in terms of technical skill and style throughout the 2nd half of the century.
- intensive in terms of maintenance and raise issues about sustainability.
- It may be design-led, in pursuit of human-computer interaction goals evaluated in terms of utility or esthetics.
- intercropping maize with kale for silage production can have advantages in terms of yield and weed suppression over the crops grown alone.
- H Understand and be able to describe interference effects in terms of constructive and destructive interference.
- This relation can, first of all, be characterized in terms of the notion of partial isomorphism.
- Automatically inflating jackets are the best in terms of comfort.
- Diagrams and words show why - in terms of moments and center of mass - the new javelin doesn't travel so far.
- jewelleryiamond jewelry is manufactured in Mumbai in India, and offers superb quality, both in terms of workmanship and fine crafting.
- justifiable in terms of left principle.
- knock-on effect in terms of access to quality legal advice for asylum-seekers.
- It also allowed much more latitude in terms of plot.
- It can be solved analytically in terms of the statistical mechanics of spin lattices.
- least in terms of response time.
- Three surviving stone lecterns are described and analyzed in terms of their petrography and sculptural style.
- leeway in terms of car design is limited, making it a fairly level playing field that we are entering.
- Even with a well-developed feminist movement, the United States has been a laggard in terms of women legislators.
- Most importantly we must take into account the costs in terms of the ' whole life cycle ' of the product.
- First, they have tended to see the global in terms of an essentially linear process, or linear processes, of globalization.
- It is likely to go absolutely loony in terms of numbers.
- I feels very low-key there in terms of the police.
- However, his stance must never become the mainstream in terms of progressive opinion.
- Would the likely cost in terms of failures and/or malformations inevitable in developing a program of human reproductive cloning be ethically acceptable?
- manageable in terms of the way in which IWG work would be undertaken.
- The requirements for testing using the cylindrical mandrel are the same as the conical mandrel in terms of dimensions.
- But please bear in mind that in terms of light output, they can't compete with incandescent mantles or filaments.
- Explain this in terms of removing harmful microorganisms from the mouth.
- minnow in terms of mass.
- mismatch between expectations, in terms of the speed at which an investment is made.
- This group exhibition brings together a diverse mix of artists, both in terms of personal geography and artistic preoccupation.
- modest in terms of worldly wealth and influence, and he had no advantage in that respect.
- PDF can incorporate multimedia content, and can support interactivity in terms of data gathering through PDF forms.
- oil multinationals Nigeria is rich and the Delta is truly opulent in terms of its raw materials and natural resources.
- The headlamp nacelle is the major departure in terms of new bits, and leads to many other details.
- negligible in terms of their effect on action inertia.
- This is important in terms of it acting as a community focus in an otherwise nondescript residential environment.
- Contemporary with the vases, Pindaric odes also describe agonistic triumph in terms of desire and its consummation.
- onerous in terms of expenditure.
- optional extras in terms of activities arranged by the school to take place wholly outside school hours.
- organized thematically in terms of broad chronological groupings.
- Management of in terms of high tibial osteotomy vs Uni.
- The Germans were completely outclassed in terms of Ultra.
- outset in terms of budgeting such projects; multimedia projects are expensive and time consuming.
- For people in good health who are not severely overweight 5 the benefits in terms of improved appearance are usually greater than the disadvantages.
- The scenarios have also been interpreted in terms of a ' blame matrix ' for human exposure to secondary particulates.
- What can orange offer you in terms of career path?
- payback in terms of job satisfaction is massive.
- classroom pedagogy is conceptualized in terms of learner active engagement.
- genuine penitence and faith are seen in terms of justice and caring love.
- Ol - I think In terms of what got me into piano it was my jazz piano teacher.
- pivotal in terms of my preparation for my job interview.
- politic in terms of obstacles to the realization of citizenship are similarly widespread.
- preconception care differed between studies, for example in terms of contraceptive, dietary and insulin advice.
- predecessor in terms of your DJing, you're much more of a turntables.
- Augustine had taught only the predestination of the elect which he understood in terms of God's positive choice to redeem.
- EP thus attempts to explain human nature exclusively in terms of evolved predispositions to behave in a particular way.
- prescriptive in terms of what kind of community network you might wish to set up.
- prest study was in terms of " Europeanisation.
- priceless in terms of the art.
- TRY is one pass through the main loop, being defined in terms of simpler primitives to perform the required task.
- proactive in terms of gathering the evidence base.
- The presence of SCC does not necessarily indicate a poor prognosis in terms of duration of survival.
- prohibitive in terms of cost.