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where the rst integral (for the light period) is given by Eq. 3-160 and the second integral (for the dark period) is given by Eq. 3-161. Evaluation of the integrals in Eq. 3-162 yields

conjunction with (as noted earlier) how rapidly the national debt was growing in the 1970 s and 1980 s, it is evident that the government was under severe pressure to reduce its financing costs The short-term market offered limited opportunity to cut these costs because British shortterm rates (see the next section) were generally as high as or higher than long-term rates in these years It was in this situation of financial desperation that the British government in 1981 introduced on a large scale the inflation-indexed bond (535) This was a financial innovation of considerable importance even though it failed to catch on in other leading countries where the government s financial situation was less desperate than in Britain These bonds offered to pay a fixed real rate of interest and to increase the principal value (and ultimate redemption value) each year at the rate of inflation.

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! M ts M 1 = M 2 M 1 = M s r 1 1 1 ln M s t 1 M 1 = M s 3-163

Following the bending diagram (refer to Figure 19-2), mark all locations you ll be soldering wires to (the wires that go to the IC connect to pins 6 and 8, counting over from the left). This time the two wires that go to the chance dial and trigger are soldered to the top wire on two arch-like components, making this connection a little easier than on the Casio SA-2.

Using Eq. 3-163 with Eqs. 3-160 and 3-161, one can calculate the ratio M = M s as a function of t=ts for a xed value of r. A semilog plot of such data for r 3 is shown in Fig. 3-11. To obtain ts the steady-state polymerization rate Rp s is rst measured at constant illumination (no pulsing). Then the average rate Rp is measured as a function of r and t. The data are plotted as the rate ratio Rp = Rp s versus log t. Alternately, one can plot the data as the rate ratio Rp = Rp 1 since this ratio is related to Rp = Rp s through Eq. 3-159. The theoretical plot (e.g., Fig. 3-11) for the same r value is placed on top of the experimental plot and shifted on the abscissa (x axis) until a best t is obtained. The displacement on the abscissa of one plot from the other yields log ts since the abscissa for the theoretical plot is log t log ts . The experimental determination of ts allows the calculation of kp , kt , ktr , and kz . kp =kt and 1=2 kp =kt , obtained from Eqs. 3-157 and 3-25 (non-steady-state and steady-state experiments, respectively), are combined to yield the individual rate constants kp and kt . Quantities such as

Initially the real yield at issue was less than 3%, although it rose to the 3 4% range along with real rates in the rest of the world in the mid- and later 1980 s Inflation was measured by the change in Britain s retail price index, to which the bond values were linked Hence, they are often termed index-linked gilts, gilts being short for gilt-edged bonds, as the English call their government s fixed-interest securities The advantage to the British government in issuing inflation-indexed bonds was at times considerable In the mid-1980 s, it could borrow on index-linked gilts at a real rate of about 3% At that time the inflation rate was about 5%, so the cost of financing was about 8% compared to new issue yields of 12 13% on non-indexed gilts.

Fig. 3-11 Semilog plot of 2[M]/[M]s versus t=ts . After Matheson et al. [1949] (by permission of American Chemical Society, Washington, DC).

Rt and M s are calculated from Eqs. 3-22 and 3-23, respectively. ktr and kz are calculated from the values of chain transfer and inhibition constants. The measurement of ts also allows an evaluation of the validity of the usual steady-state assumption in radical chain polymerization from the relationship [Flory, 1953]

M Rp tanh t=ts M s Rp s 3-164

Mark all hole locations with your pencil. Using a 1 8" drill bit, drill all your pilot holes. Open these holes to size with the hand reamer or, if the reamer s penetration is blocked, the careful use of a correctly sized burr bit mounted in your Dremel drill. Finish holes with your de-burrer.

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