The equivalence of the four hydrogen atoms of methane rested on indirect evidence, e.g.
A special algebra is one which differs from ordinary algebra in the laws of equivalence which its symbols obey.
Equivalent terms, which are not necessarily identical or literal translations, were adopted for the English, French and German languages, the equivalence being closest and most systematic between the English and German terms.
A simple class of cases is that which deals with equivalence of sums of money in different currencies; these cases really come under § 120.
For in the latter case we possess, according to Hume, no standard of equivalence other than that supplied by immediate observation, and consequently transition from one premise to another by way of reasoning must be, in geometrical matters, a purely verbal process.
The law of reciprocal proportions, or, as it might well be named, the law of equivalence, cannot be adequately enunciated in a few words.
disclosures strengthened the Federalists, until these, mistaking the popular resentment against France for a reaction against democracy - an equivalence in their own minds - passed the alien and sedition laws.
is not a statement of equality of the same kind as the statement " 153 X 20=3060," but only a statement of equivalence for certain purposes; in other words, it does not convey an absolute truth.
Force, naturally expansive and operating on the homogeneous atoms which constitute elemental matter, is subject to the law of equilibrium, or equivalence of action and reaction.
The law of reciprocal proportion, of which some examples have been already given, is part of a larger law of equivalence that underlies most of our chemical methods and calculations.
The ultimate value of numerical inquiries must depend on the equivalence of the units on which they are based.
Joule's experiments on the equivalence of W and H were not sufficiently precise to decide the question.
Thirdly we have the limiting cases of this in the inductive syllogism 5ui 7riu'mw, 7 a syllogism in the third figure concluding universally, and yet valid because the copula expresses equivalence, and in analogy 8 in which, it has been well said, instances are weighed and not counted.
Petermann (Ann., 1869, 149, p. 129) provided the proof of the equivalence of the atoms 2 and 6 with respect to 1.
From the equivalence of a small rotation to a localized vector it follows that the rotation ~ will be equivalent to rotations E,ii, ~ about Ox, Oy, Uz, respectively, provided = le, s1 = me, i nc (I) and we note that li+,72+l~Z~i (2)
Hence the positions occupied by the nitro groups in the two different nitrobrombenzoic acids must be symmetrical with respect to the carboxyl group. In 1879, Hubner (Ann., 1 95, p. 4) proved the equivalence of the second pair, viz.
15); but we are yet in need of evidence as to the exact equivalence of margins, axis, &c., obtaining between the lung-book of Scorpio and the gill-book of Limulus.
On the other hand a map drawn on the surface of a sphere representing a terrestrial globe will prove true to nature, for it possesses, in combination, the qualities which the ingenuity of no mathematician has hitherto succeeded in imparting to a projection intended for a map of some extent, namely, equivalence of areas of distances and angles.
Ampere's experimental and theoretical investigation of the mutual action of electric currents, and of the equivalence of a closed circuit to a polar magnet, the latter suggesting his celebrated hypothesis that molecular currents were the cause of magnetism.
The evidence of the exact equivalence of the segmentation and appendages of Limulus and Scorpio, and of a number of remarkable points of agreement in structure, was furnished by Ray Lankester in an article published in 1881 (" Limulus an Arachnid," Quart.
The evidence for this view, that all these agencies are at bottom connected together and parts of the same scheme, was enormously strengthened during the latter half of the 19th century by the development of a relation of simple quantitative equivalence between them; it has been found that we can define quantities relating to them, under the names of mechanical energy, electric energy, thermal energy, and so on, so that when one of them disappears, it is replaced by the others to exactly equal amount.
Again, there are many theories of the equivalence of different cubic cubits of water with various multiples of talents (2, 3, 18, 24, 33); but connexion by lesser units would be far more probable, as the primary use of weights is not to weigh large cubical vessels of liquid, but rather small portions of precious metals.
The fundamental character of energy in material systems here comes into view; if there were any other independent scalar entity, besides mass and energy, that pervaded them with relations of equivalence, we should expect the existence of yet another set of qualities analogous to those connected with temperature.
But instead of returning to the concrete fact of the equivalence of momentum, by which each body moving makes the other move oppositely, he denied that bodies do reciprocally act on one another, and even that bodies as mutually resisting substances press one another apart in collision.
The object of the present article is to illustrate the practical application of the two general principles - (I) Joule's law of the equivalence of heat and work, and (2) Carnot's principle, that the efficiency of a reversible engine depends only on the temperatures between which it works; these principles are commonly known as the first and second laws of thermodynamics.
Beside the equivalence of the hon to 5 utens weight of water, the mathematical papyrus (35) gives 5 besha = (2/3)cubic cubit (Revillout's interpretation of this as 1 cubit cubed is impossible geometrically; see Rev. Eg., 1881, for data); this is very concordant, but it is very unlikely for 3 to be introduced in an Egyptian derivation, and probably therefore only a working equivalent.
A large number of their statements are rough (2, 18, 33), being based on the working equivalence of the bath or epha with the Attic metretes, from which are sometimes drawn fractional statements which seem more accurate than they are.
This is usually regarded as being, like (ii.), a statement of equivalence.
However, equivalence questions for the deterministic case, whether two grammars or pushdown automata generate the same language or tree are open.
If we adopt a conception of meaning where truth-conditional equivalence is sufficient for synonymy, we have an apparent counterexample to compositionality.
equivalence of qualifications may be obtained from the Academic Registrar.
Double devolution, by linking the two changes together, implies an equivalence that might not emerge in practice.
The use of mathematical models to demonstrate safety equivalence is therefore becoming more important.
Sample size was calculated on the basis of establishing equivalence of the two modes of care.
The logic makes use of purely operational concepts, such as observational equivalence of program fragments.
Compositional equivalence also provides strong evidence that no unintended changes have taken place.
The current system relies too heavily on a test of ' substantial equivalence ' .
Their denotational semantics are fully abstract with respect to contextual equivalence.
Make sure your kid gets a better education than you seem to have, with your pathetic attempts at moral equivalence.
Identifying strategies by some kind of behavioral equivalence we expect to receive a linear category.
equivalence relation in the domain of living things.
equivalence class may not be an endpoint of a range.
equivalence ratio is applied in this method.
equivalence formula would also benefit from adherence to key principles.
The external behavior of entities is characterized using the notion of a bisimulation equivalence.
Homotopy equivalence of spaces also has a relative version.
Do you agree with our proposals for changes to the guidance on the method of calculation for commission equivalence?
In order to resolve stimulus equivalence, stimuli can be combined into classes whenever a unique behavior is required.
motor control: Mechanisms of motor equivalence in handwriting.
finite approximations approaching strict equivalence in the limit.
interpretive resemblance is put forward instead of the traditional one of equivalence.
naive assumption of symbolic equivalence.
notable for the absence of any discussion of level or equivalence.
notions of equivalence.
Does not this condition alone, in the absence of equivalence or exchange, in itself involve the nullity of the act?
observational equivalence of program fragments.
operate within the national framework of equivalence.
Simultaneously with the discussions of Kekule, Ladenburg, Claus, Baeyer and others as to the merits of various plane formulae of the benzene complex, there were published many suggestions with regard to the arrangement of the atoms in space, all of which attempted to explain the number of isomers and the equivalence of the hydrogen atoms. The development of stereo-isomerism at the hands of ' Victor Meyer and G.
Every ordinary algebraic quantity may be regarded as of the form a+0 - I, where a, 6 are " real "; that is to say, every algebraic equivalence remains valid when its symbols of quantity are interpreted as complex numbers of the type a-1-(-V - I (cf.
The general purpose is to give something like an equivalence of importance to divisions or branches indicated by the same term, but it is not intended to imply that every phylum has the Ursprung der Wirbelthiere (Leipzig, 1875); and Lankester, Degeneration (London, 1880),, ti, ae / .r ?
From it Spencer proceeds to deduce the indestructibility of matter and energy, the equivalence and transformation of forces, the necessity of a rhythm, of Evolution (i.e.
Note the equivalence of orthogonal arrays with affine resolvable designs.
Paulsen, The German Universities, pp. 344-345)1; (vii.) examinations of several hundred candidates at a time cannot be rationally conducted so as to be equally fair to the individuality of all candidates; the individual test is the only complete one (it is admitted that examinations on a large scale necessarily involve a margin of error; but this error may be reduced to a minimum, especially by a combination of oral and practical with written work); (viii.) the multiplicity of school examinations required for different reasons produces confusion in our secondary education (there is a growing tendency to admit equivalence of " schoolleaving " and entrance examinations; thus entrance examinations of Oxford, Cambridge and London, and the Northern Universities Joint Board are interchangeable under certain conditions); (ix.) the multiplicity of examinations tends to " underselling " (the success of the London examinations in medicine proves that a high standard attracts candidates as well as a low one; possibly intermediate standards may be killed in the competition; it is by no means obvious that a uniform system of examinations would conduce to efficiency); (x.) examinations produce physical damage to health, especially in the case of women-students (on this point more statistical evidence is needed; see, however, Engelmann quoted by G.
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