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z Vd is in the range of 4 to 13 cm3 mol 1 , with most initiators being in the narrower range of 5 to 10 cm3 mol 1 [Luft et al, 1978; Neumann, 1972; Walling and Metzger, z 1959] The measured Vd for a particular initiator often varies with solvent viscosity z indicating that a large portion of Vd is due to increased pressure decreasing the ability of radicals to diffuse from the solvent cage This is further veri ed by the observation that z Vd determined by the disappearance of initiator is lower than that measured using radical z scavengers, which detect radicals only outside the solvent cage It is estimated that Vd would be 4 to 5 cm3 mol 1 for most initiators if there were no cage effect [Martin, z 1973].

Charts 1, 2C, and 78 can give a false impression of exact knowledge, which does not exist The discovery of a lower prevailing rate for any half-century other than the one employed would alter the shape of the curve The disqualification of one of the minimum rates employed would alter the shape of the curve The charts have nevertheless been presented because the story they tell seems correct in general and because they facilitate a review of the broad sweep of interest rates over history The assertion that there has been a long history of declining interest rates since the twelfth century does not rest upon the choice of statistics in Table 76 or on the particular method employed in creating Chart 78 There is ample evidence that interest rates declined on the average in the late Middle Ages and Renaissance.

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The volume of activation for propagation Vp is negative, since the reaction involves two species coming together (ie, a volume decrease occurs) in going to the transition state z Vp is in the range 15 to 24 cm3 mol 1 for most monomers [Beuermann and Buback, 2002; Brandrup et al, 1999; Ogo, 1984; Rzayev and Penelle, 2002; Weale, 1974] The volume of activation for bimolecular termination Vtz is positive with values that are generally in the range 13 to 25 cm3 mol 1 for most monomers At rst glance one would expect Vtz to be negative, since termination involves a decrease in volume when two radicals come together in the transition state However, since the termination step is diffusioncontrolled, increased pressure decreases kt by increasing the viscosity of the reaction medium [Nicholson and Norrish, 1956; O Driscoll, 1977, 1979].

(Another result of the increased viscosity is that the gel effect is observed at lower conversions at higher pressures) 3-12a-2 Rate of Polymerization.

The variation of the polymerization rate with pressure will depend on the variation of the ratio kp kd =kt 1=2 with pressure in accordance with Eqs. 3-32 and 3-196. This latter variation will be given by

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There is no doubt about the 3% rate for British consols in the eighteenth century and no doubt that this was well below fourteenth- and fifteenth-century long-term interest rates There is no doubt that the 247% decennial average for consols in the late nineteenth century was a new low for English rates and that the 231% average rate for long taxable US governments in the fifth decade of the twentieth century was a new low for American rates There were periods of easy money in the distant past the downtrend has not been smooth but twentieth-century lows have been below earlier lows, and twentiethcentury highs have been above earlier highs THE SECULAR TRENDS OF MODERN LONG-TERM INTEREST RATES The arrangement of the statistics in a succession of fifty-year minima obscures many very large fluctuations within these fifty-year periods.

3-197

3-198

The latter are traced in Table 76 and Chart 78 by a series based on minimum decennial averages from 1730 These are only English decennial averages until 1790 This decennial-average series shows that the suprasecular downtrend of interest rates during the last two centuries has been interrupted by three periods of secular increase: one during the late eighteenth century; the next during the early twentieth century; and the third following.

z The various terms are such that the value of VR is negative by 15 20 cm3 mol 1 for most 3 1 monomers (as high as 25 cm mol in some cases) and the rate of polymerization is z increased by high pressures (see Fig. 3-17). Thus, VR is 17.1, 17.2, 15.6, 26.3, and 17.5 cm3 mol 1 , respectively, for styrene, vinyl acetate, methyl methacrylate, butyl methacrylate, and ethylene [Buback and Lendle, 1983; Ogo, 1984]. It is worth noting that

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