One section of the law expresses the fact that the weights of two substances, not necessarily elements, that are equivalent in one reaction, are often found to be equivalent in a number of other reactions.
Bonnet's eminent contemporary, Buffon, held nearly the same views with respect to the nature of the germ, and expresses them even more confidently.
Such a system of classification, although convenient, is not the most natural one, and a sketch of the system which better expresses the relationships between the various subdivisions is given here.
The quality which Geoffrey Malaterra expresses by the word "effrenatissima" is also clearly marked in Norman history.
Equation (3), § I expresses the fundamental condition which must be satisfied when a locomotive is starting a train.
In all countries passenger trains must vary in weight according to the different services they have to perform; suburban Weight trains, for example, meant to hold as many pas ah d sengers as possible, and travelling at low speeds, do not weigh so much as long-distance expresses, which include dining and sleeping cars, and on which, from considerations of comfort, more space must be allowed each occupant.
Ezekiel, who borrowed both Jeremiah's language and ideas, expresses the same thought in the well-known words that Yahweh would give the people instead of a heart of stone a heart of flesh (Ezek.
Herodotus, who declines to commit himself as to the existence of Zalmoxis, expresses the opinion that in any case he must have lived long before the time of Pythagoras.
The " true mother of his mind as well as of his health " was a maiden aunt - Catherine Porten by name - with respect to whom he expresses himself in language of the most grateful remembrance.
He thus writes S+02=S02+7110o cal., which expresses the fact that the intrinsic energy of the quantities of sulphur and oxygen considered exceeds that of the sulphur dioxide derived from them by 71100 cal.
Expresses that under certain conditions the intrinsic energy of hydriodic acid is greater than the intrinsic energy of its component elements by 12200 cal., i.e.
The precise part these figures play is often idealized and expresses the later views of their prominence.
Whereas the Hebrew verb is devoid of real tenses, and only expresses an action as completed or as in process without indicating time past, present or future, Syriac has by the help of an auxiliary verb constructed a set of tenses.
But it is futile to seek the effect of much dealing in " futures " in the differences between price movements in the various markets, because (I) demand expresses itself in different ways-in Germany, for example, spinners buy to hold large stocks-and (2) the markets are in telegraphic communication, so that their price movements are kept parallel.
This equation, which is mathematically deducible from the kinetic theory of gases, expresses the behaviour of gases, the phenomena of the critical state, and the behaviour of liquids; solids are not accounted for.
The Rhine-daughter sings it in a childlike, indolently graceful way which well expresses the kind of toy the ring or the world itself would be to her.
Cuvier expresses the opinion that the dog exhibits the most complete and the most useful conquest that man has made.
Such is this famous work, full of obscurities, redundancies and contradictions, in which the thread of the argument is sometimes lost in a labyrinth of reasonings and citations, both sacred and profane, but which nevertheless expresses, both in religion and politics, such audacious and novel ideas that it has been possible to trace in it, as it were, a rough sketch of the doctrines developed during the periods of the Reformation and of the French Revolution.
Each of them satisfied by a common system of values; hence the equation R =o is derived on this supposition, and the vanishing of R expresses the condition that the equations can be satisfied by a common system of values assigned to the variables.
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,...
By the same law which expresses the power function s, in terms of the elementary functions a 1, a2, a3,...
Expresses s pg, ...
Which expresses the elementary functions in terms of the single bipart functions.
Hermite expresses the quintic in a forme-type in which the constants are invariants and the variables linear covariants.
- (aa) and then expresses the coefficients, on the right, in terms of the fundamental invariants.
If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.
Proceeding as we did in the case of the single binary form we find that for a given total degree 0+0', the condition which expresses reducibility is of total degree in the coefficients a and T; combining this with the knowledge of the generating function of asyzygetic forms of degrees 0, 0', we find that the perpetuants, of these degrees are enumerated by z26"'-11 -z.
If now the nti c denote a given pencil of lines, an invariant is the criterion of the pencil possessing some particular property which is independent alike of the axes and of the multiples, and a covariant expresses that the pencil of lines which it denotes is a fixed pencil whatever be the axes or the multiples.
The magnetic susceptibility expresses the numerical relation of the magnetization to the magnetizing force.
This expresses the retardation of the extreme relatively to the central ray, and is to be reckoned positive, whatever may be the signs of w, and 0 .
This therefore expresses the secondary disturbance at a distance r and in a direction making an angle cp with OZ (the direction of primary vibration) due to the element dS of the wave-front.
Savary expresses preference for this second plan, and makes the pertinent remark that in both these models " the rays of red light in the two solar images will be next to each other, which will render the sun's disk more easy to be observed than the violet ones."
In the preface Chillingworth expresses his new view about subscription to the articles.
With Horace and Tibullus he was on intimate terms, and Ovid expresses his gratitude to him as the first to notice and encourage his work.
Trajan in his reply (Epp. 97) expresses approval of Pliny's course of action in the case of the Christians brought before him.
Whether the first creed of the primitive Church was of the simple Christological character which confession of Jesus as the Lord expresses, or of an enlarged type based on the baptismal formula (Matt.
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..
The value of B is determined by observing the latent heat, Lo = F"o - F'0, which gives B =B" - B' =L0+(s' - So)00+(n+r)copo - bpo+dho (45) This constant may be called the absolute latent heat, as it expresses the thermal value of the change of state in a manner independent of temperature.
The first term on the right hand side expresses the energy of the surface electrification of the conductors in the field, and the second the energy of volume density (if any).
Opposition to present tyranny expresses itself in recurrence to the old popular ideal of the first simple Davidic kingdom (iv.
3-II); then, relieving their anxiety about his own prospects, he expresses the confident hope that he will be released and thus be able to return to them (i.12-26).
Aong after this date, when all scholars drew mainly from books, the old forms were still kept up. Tabari, for example, when he cites a book expresses himself as if he had heard what he quotes from the master with whom he read the passage or from whose copy he transcribed it.