Theory of residues

An alternative development may be to express the desired quantities in terms of contour integrals in the complex plane, using Cauchy s theory of residues, as described in E. Schrodinger, Statistical Thermodynamics, reprinted, Dover, New York, 1989. We have not explored this predominantly formal development. 

The solutions for the amplitudes Gb(E) are determined analytically. In order to get the amplitudes bn(t), we have used these solutions and have applied the theory of residues by countour integration in (5). For example, the resulting expressions for 62s(t) and 2p(t) are ... 

In 1839 another Frenchman, Charles Frederick Gerhardt (1816-1856), introduced his theory of residues, which stated that organic reactions could be considered to be the separation and rejoining of residues, which he regarded as being somewhat similar to radicals. This type of reaction he at first called copulation, but later he used the term double decomposition. Thus the nitration of benzene, a reaction first reported by Mitscherlich in 1833, was regarded as the elimination of part of each reactant to form water and the combination of the remaining parts (residues) to form nitrobenzene. In terms of a modem equation this would be represented as ... 

A. Rep.y x88 (1886), 945 iVoc. Roy. Soc.y x886, xl, 268-91 (Electrolytic Co uction in relation to Molecular Composition, Valency and the nature of Chemical Change being an Attepipt to Apply a Theory of Residual Affinity) Proc. Chem. Soc.y X887, iii, X27 J. Chem. iSoc.i 1888, liii, X25. 

It is seen from this table. .. that the point of view of the formation of the series in the types can be applied to ethers as to bases, to radicals as to aldehyde, and to bases as to amides. Gerhardt thus applied his theory of residues (see p. 417) to radicals in types, obtaining conjugated (conjug6s) or copulated (copulas) radicals. The acids are derived from water by substituting radicals for hydrogen (as Williamson had done, see p. 450) ... 

The theory of residual dipolar coupling between quadrupolar nuclei has been developed and applied to B-chlorocatecholborane using and 35/37Cl [26]. MAS and DOR NMR were applied to extract infor-... 

---