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The emergence of Japan as an economic power, and the relatively recent liberalization of Japan s financial policies, including deregulation and the development of open markets, likely means that Japan is now entering the mainstream of interest rate history Table 76 brings forward from Table 11, 10, the lowest longterm rates there tabulated for each country by half-centuries from 1200 through 1700 To these old interest rates the modern long-term rates are added in two ways: in the form of half-century lows (usually the lowest decennial average) and also in the form of all decennial averages These various series are not based on identical credit instruments, but all are in varying degrees of long maturity The data in Table 76 are analyzed and charted in several ways in an effort to summarize (a) the trends of longterm interest rates; and (b) the differences in the trends between these various countries.

wx 1x 1 p 3 x 1 px 2 2 Xn Xw 2 1 p 2 p 1 p 3-191 3-192 3-193 3-194

For polymerizations where termination occurs by a combination of coupling, disproportionation, and chain transfer, one can obtain the size distribution by a weighted combination of the two sets of distribution functions presented above. Thus the weight distribution can be obtained as

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wx Ax 1 p 2 px 1 1 1 A x 1 p 3 x 1 px 2 2 3-195

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THE SUPRASECULAR TRENDS OF MEDIEVAL AND MODERN LONG-TERM INTEREST RATES BY FIFTY-YEAR PERIODS There was sufficient similarity in the long interest rate trends of all of these markets to encourage an attempt at generalization This has been done in Chart 78, not by averaging but by linking together by halfcenturies the lowest reported long rates in any one of these nine countries It has been the point of view of this history that the wide band of simultaneous interest rates has just one specific boundary, its minimum Sometimes the minimum boundary is higher or lower than at other times, and this is a reasonable way to define a trend The chart applies this principle internationally For years after 1700, the minima used are the lowest decennial averages, whenever they are available The suprasecular trends of ancient interest rates were charted and discussed in terms of national minima in Chart 1.

where A is the fraction of polymer molecules formed by disproportionation and chaintransfer reactions [Smith et al., 1966].

For many practical radical chain polymerizations, the reaction is carried out to high or complete conversion The size distributions for high-conversion polymerizations become much broader than those described above or those in step polymerizations Both the monomer and initiator concentrations decrease as a polymerization proceeds The polymer molecular weight depends on the ratio [M]/ I 1=2 according to Eq 3-98 In the usual situation [I] decreases faster than [M] and the molecular weight of the polymer produced at any instant increases with the conversion The overall molecular-weight distributions for high or complete conversion polymerizations are quite broad, with the X w =X n ratio being in the range 2-5 Broad molecular weight distributions are usually not desirable from the practical viewpoint, since most polymer properties show optimum values at speci c molecular weights.

Chart 2C traced medieval long-term rates in terms of half-century minima; the lines were determined.

Commercial polymerization processes often involve the addition of multiple charges of initiator and/or monomer during the course of the reaction to minimize the molecular weight broadening When autoacceleration occurs in polymerization there is even larger broadening of the 1=2 size distribution The large increases in the kp =kt ratio (Table 3-17) that accompany the gel effect lead to large increases in the sizes of the polymers being produced as the polymerization proceeds X w =X n values as high as 5 10 may be observed when the gel effect is present Excessive molecular-weight broadening occurs when branched polymers are produced by chain transfer to polymer Chain transfer to polymer can lead to X w =X n ratios as high as 20 50 This very extensive size broadening occurs because chain transfer to polymer increases as the polymer size increases Thus branching leads to even more branching as a polymerization proceeds.

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