A simple class of cases is that which deals with equivalence of sums of money in different currencies; these cases really come under § 120.
A special algebra is one which differs from ordinary algebra in the laws of equivalence which its symbols obey.
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.
The ultimate value of numerical inquiries must depend on the equivalence of the units on which they are based.
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.
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.
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.
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.
Petermann (Ann., 1869, 149, p. 129) provided the proof of the equivalence of the atoms 2 and 6 with respect to 1.
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.
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.
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)
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.
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.
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.
Joule's experiments on the equivalence of W and H were not sufficiently precise to decide the question.
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 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.
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.
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.