Revolutions

The remark in the last chapter that France was the scientifically acceptable culture of the 1700s may have caused a few curious second readings because in the last chapter we detailed the work of one Russian, two Scottish, one Swedish, and two English but no French chemists. The reason for this however was not a lack of material but rather such a surplus of material that it warrants a chapter unto itself. France was the center of European Enlightenment, and in France this passion for throwing off tradition took the extreme form revolution. France in the 1700s saw two revolutions—one political and one chemical. 

Politically speaking Enlightenment philosophy valued equality and freedom for individuals. In France there was a keen need for freedom and equality The country was in financial trouble, and those who were bearing the burden of the debt were powerless to do anything about 

In the midst of all this political strife, the philosophic debate on phlogiston also heated red hot. Scientists were polarized into phlogiston and antiphlogiston camps, basing their views on nationalistic and personal reasons as much as on experimentation. The debate was finally resolved, but with a resolution radical enough to constitute a revolution of its own. 

The Chemical Revolution was a revolution against the mysticism of the alchemists, the authority of the Scholastics, and the autocracy of the philosophy of the long-dead Aristotle. The weapons in this war were precise analytical measurement and precision in theoretical thought. The immediate result of the Chemical Revolution was to redefine chemical elements as separate materials with separate identities and prop- 

Lavoisier s family was part of the prosperous French bourgeois, and Lavoisier s youth consequently was comfortable. His father was a lawyer, his mother the well-dowered daughter of a lawyer, and Lavoisier was an adored, indulged, and idolized child. Though he was one of two children, his sister died in her teens, and when his mother died when he was 5 years old, his recently widowed maternal grandmother and a maiden aunt took over his care. 

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We should therefore conclude that refining will witness a very important evolution, without revolution, but which will affect both the processes and procedures utilized, the objective being to produce clean products in a clean , energy-efficient manner. 

Unfortunately, now that such methods have become available, such as the Time Of Flight Diffraction (TOFD) technique, this revolution does not happen. What we see instead is a much slower process towards quantitative NDT, in combination with adapted acceptance criteria for weld defects. 

Most of the situations encountered in capillarity involve figures of revolution, and for these it is possible to write down explicit expressions for and R2 by choosing plane 1 so that it passes through the axis of revolution. As shown in Fig. II-7n, R then swings in the plane of the paper, i.e., it is the curvature of the profile at the point in question. R is therefore given simply by the expression from analytical geometry for the curvature of a line... 

The general case has been solved by Bashforth and Adams [14], using an iterative method, and extended by Sugden [15], Lane [16], and Paddy [17]. See also Refs. 11 and 12. In the case of a figure of revolution, the two radii of curvature must be equal at the apex (i.e., at the bottom of the meniscus in the case of capillary rise). If this radius of curvature is denoted by b, and the elevation of a general point on the surface is denoted by z, where z = y - h, then Eq. II-7 can be written... 

As in the case of capillary rise, Sugden [27] has made use of Bashforth s and Adams tables to calculate correction factors for this method. Because the figure is again one of revolution, the equation h = a lb + z is exact, where b is the value of / i = R2 at the origin and z is the distance of OC. The equation simply states that AP, expressed as height of a column of liquid, equals the sum of the hydrostatic head and the pressure... 

The general analysis, while not difficult, is complicated however, the limiting case of the very elongated, essentially cylindrical drop is not hard to treat. Consider a section of the elongated cylinder of volume V (Fig. II-18h). The centrifugal force on a volume element is u rAp, where w is the speed of revolution and Ap the difference in density. The potential energy at distance r from the axis of revolution is then w r Apfl, and the total potential energy for the... 

Frenkel D and Mulder B 1985 The hard ellipsoid-of-revolution fluid. 1. Monte-Carlo simulations Mol. Phys. 55 1171-92... 

Schuster T M and Toedt J M 1996 New revolutions in the evolution of analytical ultracentrifugation Curr. Opinion Ceii. Bioi. 6 650-8... 

Tracing the arctan over a full revolution by the method described in Section rV and noting the factor 1 /2 in Eq. (171) establishes our result. (The case that E — m needs more careful consideration, since it leads to a breakdown of the adiabatic theorem. However, this case will be of no consequence for the results.)... 

The resonant timesteps of order n m (where n and m axe integers), correspond to a sampling of n phase-space points in m revolutions. This condition implies that... 

NMR IR UVVIS and MS) were obtained using pure substances It is much more common however to encounter an organic substance either formed as the product of a chemical reaction or iso lated from natural sources as but one component of a mixture Just as the last half of the twentieth cen tury saw a revolution in the methods available for the identification of organic compounds so too has it seen remarkable advances in methods for their separation and purification... 

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