Further Deductions

The following rule should be clear in view of the discussion of Par. 6.5.5. 

Observation 6.1 If a single coronoid C has a hexagon in one of the addition modes, viz. 

then there must exist (at least) one single coronoid isomer C with the formula 

This rule is explained by the fact that C is generated by the appropriate addition of one hexagon to C. The addition modes are specified and characterized in Table 4. The following illustration, actually an extension of Fig. 5, is relevant. 

We can say more about C with the formulas given in Observation 6.1. There must exist such an isomer which possesses a fissure, bay, cove or fjord available for addition in the cases C 2H, and respectively. With regard to a coronoid C which has the 

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The first three columns, type of scattering, symmetry and type of reaction, give the inferences made from the actual diagrams. The final three columns, cross section, velocity in product and product energy, are then further deductions which come from the type of reaction which has been inferred. 

If one deducts the approximately 1 million unregistered emigrants from the 5.3 to 6 million victims that Benz claims he found, this leaves him with 4.3 to 5 million victims. From this, one must further deduct the difference between the Soviet Jews who appeared in Soviet statistics and the real number (some 1.5 million), the number of Jews who died in the Soviet Union from other causes (deportation, war, partisan warfare, at least 500,000), the number of statistically fabricated additional Polish Jews (some 700,000) as well as the number of Hungarian Jews who probably did not succumb in their entirety (300,000), in other words, a total of roughly 4 million. This would leave Benz with a remainder of at most 1.3 to 2 million unsolved cases. 

Having established the gross framework of the alkaloid, only the points of attatchment of the ethylamine bridge remained unsolved. Detailed analysis of previous work coupled with further deductive studies allowed Robinson to propose his ultimate structure, which explained and accounted for every prior and subsequent chemical investigation, including total synthesis. 

If the total mass of the sample e- pan [Pg.201]

Clearly, the choice of the functions E, H, A, or G is governed by the experimental conditions. For example, when temperature and pressure are under experimental control, one chooses the Gibbs free energy as the appropriate function of state from which to make further deductions. Processes carried out under adiabatic and constant pressure conditions are to be characterized by the enthalpy state function. We now show how the above functions of state may be determined experimentally, and how to choose the appropriate one with which to work under the selected operating conditions. 

Further deduction of the int ral to an ejqilicit form, and the subsequent evaluation of the equation of state of rubber-like elasticity are sra t-forward (2). One can easily show that /( . r/6) apjaroaches a Gaussian function for small r. 

Having narrowed the potential sources, it is usually possible to make further deductions from... 

Fault Tree Analysis. Fault trees represent a deductive approach to determining the causes contributing to a designated failure. The approach begins with the definition of a top or undesired event, and branches backward through intermediate events until the top event is defined in terms of basic events. A basic event is an event for which further development would not be useful for the purpose at hand. For example, for a quantitative fault tree, if a frequency or probabiUty for a failure can be deterrnined without further development of the failure logic, then there is no point to further development, and the event is regarded as basic. 

Applying the symmetry condition Eq. (13) to the third CGC implies that I + l+j = even. Along with the triangle rule this requires that I = I for the isotropic term j = 0, I = l l for j = 1, and I = I 2,0 for j = 2. These deductions determine the nature of the interference implicit in each of the angular parameters The fourth CGC in Eq. (12) further regulates... 

Testimony was further taken upon the question of any radical differences existing between the Asiatic and Caucasian races, and in the evidence will be found much valuable information upon this point peculiarly interesting to the ethnologist. The deduction from the testimony taken by the committee on this point would seem to be that there is not sufficient brain capacity in the Chinese to furnish motive power for self-government. Upon the point of morals, there is no Aryan or European race which is not far superior to the Chinese as a class.49... 

If the deductive process has stalled and no further progress seems possible or likely, then the iterative loop calls for application of inductive investigation methods such as a checklist or HAZOP. The inductive methods may also benefit from use of the fact/hypothesis matrix tool described in this chapter. 

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