Witt’s theory

Witt s theory of solid solutions in dyeing loses its only support as soon as one postulates that textiles and mordants may act as ionizing adsorbents. 

Toxophor-Auxotox Theory. The theory of toxophors and auxotoxes, first elaborated by Ehrlich for toxic substances and later applied by Nekrassov to the war gases, attributes the physiopathological properties of these substances to special atoms or radicles in a similar manner to Witt s theory regarding the colour of organic substances. 

The first publication of importance regarding the relationship between odour and chemical constitution per se, is that of Klimont, who attempted an explanation on the lines of Witt s colour theory. Elimont introduced the term aromataphore to designate groups which carry a pleasant odour with them. ... 

Itishould be noticed that the similarity between the osmophore theory and Witt s chromophore colour theory does not extand much beyond the initial conception and there seems to be no connection between the odour and the colour of a body, it is indeed quite the exception for a body to have both a strong odour and a strong colour. Two prolific sources of colour, viz. the diazo group and a large molecule have no counterpart as regards odour, and it is probably only by chance that quinone and chroman both have pronounced odours and are the sources of colour. 

A further effort to establish a relationship between explosive properties and structure has been made more recently by Piets [2]. He proposed a theory of ex-plosophores and auxoploses in a way analogous to Witt s suggested chromo-phores and auxochromes in the dyes, and Ehrlich s suggested toxophores and autotoxes in chemotherapeutics. 

In contrast to this Witt s older theory bore, however, a purely phenomenological character. Chromophors or colour-carriers were distinguished, usually unsaturated groups such... 

However, Nekrassov s theory cannot be applied so generally to the war gases as Witt s to coloured substances. 

A good check for the theory is van de Witte s chloroform/ methanol mixes used for his extensive work on membranes [9a-. The RED number is calculated to be 1 for a 40 60 ratio, not far from the 55 45 ratio typical of the mixes at cloud point (which corresponds to a radius of 8.6). Of course, the issue of crystallinity plays a big role in van de Witte s work. As mentioned earlier, the radius of crystalline polymers is smaller and the cloud points shift to a 65 35 ratio, corresponding to a radius of 7.4. 

To round off this section we note a few unusual applications of Polya s Theorem an application to telecommunications network [CatK75], and one to the enumeration of Latin squares [JucA76]. In pure mathematics there is an application in number theory [ChaC82], and one to the study of quadratic forms [CraT80], being the enumeration of isomorphism types of Witt rings of fields. Finally, we note a perhaps unexpected, but quite natural, application in music theory to the enumeration of chords and tone rows for an n-note scale [ReiD85]. In the latter paper it is shown that for the usual chromatic scale of 12 semitones there are 80 essentially different 6-note chords, and 9,985,920 different tone rows. 

In 1938, Brunauer, Emmett and Teller(12) and Emmett and de Witt(13) developed what is now known as the BET theory. As in the case in Langmuir s isotherm, the theory is based on the concept of an adsorbed molecule which is not free to move over the surface, and which exerts no lateral forces on adjacent molecules of adsorbate. The BET theory does, however, allow different numbers of adsorbed layers to build up on different parts of the surface, although it assumes that the net amount of surface which is empty or which is associated with a monolayer, bilayer and so on is constant for any particular equilibrium condition. Monolayers are created by adsorption on to empty surface and by desorption from bilayers. Monolayers are lost both through desorption and through the adsorption of additional layers. The rate of adsorption is proportional to the frequency with which molecules strike the surface and the area of that surface. From the kinetic theory of gases, the frequency is proportional to the pressure of the molecules and hence ... 

Pearl J (2000) Causality Models, Reasoning and Inference. Cambridge University Press, Cambridge. Pearson K, Lee A, Bramley-Moore L (1899) Mathematical contributions to the theory of evolution. VI. Genetic (reproductive) selection inheritance of fertility in man, and of fecundity in thoroughbred racehorses. Philosophical Transactions of the Royal Society A 192 257-330. Piantadosi S, Wittes J (1993) Politically correct clinical trials. Controlled Clinical Trials 14 562-567. 

Detailed theory and application ean be found in Cook, R. D., Malkus, D. S., Plesha, M. E., Witt, R. J. Concepts and Applications of Finite Element Analysis, Wiley Text Books, New York, 2001 Chandrupatala, T. R. Introduction to Finite Element in Engineering, Prentice Hall, Englewood Cliffs, NJ, 1991. 

Quick, B.L., Stephenson, M.T., Witte, K., Vaught, C., Booth-Butterfield, S. and Patel, D. 2008. An examination of antecedents to coal miners hearing protection behaviors A test of the theory of planned behavior. Journal of... 

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