Analyst, January 1995, Vol. 120 35 Routine Lead Isotope Determinations Using a Lead-207-Lead-204 Double Spike: a Long-term Assessment of Analytical Precision and Accuracy Jon. D. Woodhead Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia F. Volker Institute of Petrography and Geochemistry, University of Karlsruhe, Karlsruhe, Germany M. T. McCulloch Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia Lead-isotope data obtained on a multicollector mass spectrometer over a four year period using a 207PP04Pb double spike to correct for the effects of mass discrimination, are reported. Considerable improvements in both precision and accuracy over conventional correction procedures were noted, without recourse to rigorous loading or run conditions.An external precision in 206Pb/204Pb, 207PbPPb and 208PbP”Pb ratios +0.003,0.003 and 0.01 (2 X standard deviation), respectively, is routinely obtainable independent of minor variations in loading and run parameters. Keywords: Lead isotope analysis; double spike technique Introduction In the determination of radiogenic isotope ratios, particularly within the Earth Sciences, a correction is usually made for the isotope mass fractionation effects encountered during thermal ionization mass spectrometry (mass discrimination) by normalization to an accepted ratio of two non-radiogenic isotopes; e.g., for Sr, the ratio *6Sr/g*Sr = 0.1194 is commonly employed. However, of the naturally occurring Pb isotopes only 204Pb is non-radiogenic whereas 2WPb, 207Pb and Pb208 are daughter products from the radioactive decay of U and Th.Consequently, the analytical precision and accuracy of Pb isotope determinations has always been limited by an inability to make such a correction. The recent advent of a ‘new generation’ of multi-sample, multicollector mass spectrometers has led to a rapid proliferation in both the number and quality of Sr and Nd isotope determinations available, highlighting an increased requirement for more accurate and precise Pb isotope data with which to address scientific problems requiring fine resolution. Many factors contribute to mass spectrometer induced fractionation; in particular, relatively subtle variations in filament loading and run conditions can produce marked variations in mass-fractionation characteristics.Although it has been demonstrated that rigorously controlled loadinghnning parameters can produce considerable improvements in precision,’ for whole rock samples such an approach is often not possible or indeed desirable. The usual approach employed is to determine a mass discrimination factor by analysis of a Pb standard with well-known isotopic composition and then apply the same correction factor to all unknowns. With geological materials, however, even if a consistent discrimination factor can be established by a given operator with reference to a Pb isotopic standard [usually National Bureau of Standards (NBS) (now National Institute of Standards and Technology) Standard Reference Material (SRM) 981 (natural lead)], real rock samples rarely run under identical conditions of mass fractionation, for at least two reasons.The first reason is the relative ‘impurity’ of sample Pb compared with standard Pb. Even with very ‘clean’ column chemistry (two column passes, blanks <lo0 pg), trace contaminants such as Cd, Zn and organics affect the performance of the silica gel substrate, often resulting in markedly different behaviour on the filament. This issue is rarely addressed as the ‘real’ values for rock samples are not known; it is simply assumed that a correction factor derived for the standard can be applied to the sample. However, it will be shown below that this may not always be the case. The second reason in contrast to the running of standard Pb, with real samples there is often a lack of prior knowledge of the exact amount of Pb being analysed. This problem is particularly acute for samples that have been acid-leached as a precaution to remove surficial contaminants (these problems have been discussed by McDonough and Chauvel2 and Volker et al.,3 for example), and with very low-level or small samples that are not readily amenable to X-ray fluorescence analysis of Pb content. The resultant variation in both amount of Pb loaded and Pb: silica gel ratio often limits the utility of reference to isotopic standards to determine mass fractionation. Fortunately, these problems are surmountable. DodsonJ showed that a rigorous correction for the effects of mass discrimination was possible by spiking a second sample aliquot with an artificial solution, highly enriched in two isotopes, thereby simulating the presence of two non-radiogenic iso- topes, and Compston and Oversbys and Cooper and Richards6 first routinely applied this ‘double spike’ method to Pb isotope analysis. The technique was not widely adopted at the time but, foreseeing the arrival of multicollector machines and the need for increasingly precise data, Hamelin et al.7 have made a re-evaluation of the Pb double spike procedure.These workers concentrated in particular on the optimization of run parameters and provided an analysis of error propagation in relation to spike: sample ratios but presented little data. We have been using a zo7Pb-204Pb double spike for Pb isotope36 Analyst, January 1995, Vol.120 15.6 n a 4 3 a w 15.5 analysis routinely in our laboratory3,x-lI and here present the first long-term (four year) evaluation of its performance in conjunction with a Finnigan MAT 261 multicollector mass spectrometer. ' Analytical Details Lead was separated from geological materials by conventional HBr/HCI techniques using Teflon microcolumns,'2 Dowex AG 1x8 anion-exchange resin, and two column passes for sample purification. We stress, however, the advantage of using rock chips rather than powders and the need for preliminary acid washing before dissolution to remove any non-magmatic contaminants. Such an approach cannot be applied to older materials where individual mineral phases may have developed different isotopic compositions with time but we believe it should be used without exception for samples of recent age.Total procedural blanks are typically in the range 20-50 pg and always less than 100 pg. Although a 2osPbA02Pb double spike is the theoretical ideal as both isotopes do not occur in natural samples,13 the prohibitive cost and difficulty of obtaining very 'clean' samples of these enriched isotopes makes such a spike unsuitable for routine analytical work. A 207PV04Pb double spike of similar composition to DSII of Compston and Oversby5 was used here (206Pb/204Pb = 0.237, 207Pb/2(]4Pb = 8.714, 2ogPb/204Pb = 0.443). Samples were split for spiking immediately prior to filament loading and mass spectrometry, thus, avoiding potential problems due to variable blank levels in spiked- and unspiked-runs which have hampered previous attempts to use the double spike method.14 Following the methodology of Hamelin et al.,7 in order to control error propagation, the ratio of 204Pb"nknown/2'4Pbspike, designated Q , in the spiked run is maintained within the limits 0.02 < Q < 1, although an exact knowledge of Q (i.e., by weighing) is not necessary unless simultaneous Pb concentration data are required from the analysis. Samples were loaded on single Re filaments with silica gel-H3P04 in a clean air hood. This procedure takes 1-2 h for a carousel of 13 samples and, although a disciplined method is adopted, in particular to avoid blank problems, the rigorous loading and heating sequences advocated by experienced Pb isotope workers, are not necessary (any perturbations in fractionation are corrected by the double spike analysis). Again, during mass spectrometry, precisely controlled heating procedures under manual control or the use of automated heating sequences15 are only necessary in so far as a stable ion beam must be established; the accuracy of the result is in no way compromised.All samples were run on a Finnigan MAT 261 mass spectometer, operated in static multicollector mode. Data acquisition was usually at a filament temperature of about 1100-1200 "C and, typically, consisted of four blocks of data per run, each comprising twelve 8 s integrations (thus, 96 s integration time per block). Baselines were measured every two blocks and gain calibrations every three or four samples. It is difficult to generalize about the degree of within-run precision obtained for each sample run as the speed at which a given sample moves along a mass discrimination trend depends on both the amount of Pb loaded and the condition of the silica-gel substrate through which the sample essentially 'distils'.Hence, low-level samples will tend to move more rapidly along the mass discrimination vector resulting in relatively larger values for within-run precision. With relatively large loads (100 ng), it has been found that four blocks of data are sufficient to provide an internal precision (2 x standard error) of k0.002 or better on 206Pb/204Pb but we do not believe that larger values of within-run precision produce any significant degradation in the final result, after double spike correction. Spiked- and unspiked-aliquots were usually run on the same carousel, each machine 'run', thus, providing six complete analyses plus one blank or standard run. A number of different mathematical solutions for the double spike unmixing analysis have been formulated.16-18 Our data reduction was performed by an iterative technique using a computer program developed for the Macintosh, further details of which can be found in the Appendix. It is relatively easy to perform 26 analyses ( i . e . , two carousels) within 1 d, thus providing 12 unknown analyses plus a standard or blank. Analytical Accuracy for NBS SRM 981 As a preliminary test of the ability of the double spike technique to correct for highly variable degrees of mass fractionation, a single filament load of 40 ng of NBS SRM 981 was run repeatedly to exhaustion (three blocks of data per run), turning up the filament current between runs to exaggerate mass discrimination effects.The resulting raw data are shown in Fig. 1, together with data corrected in conjunc- tion with a single NBS SRM 981 + double spike analysis, run under 'normal' fractionation conditions. These data show that the correction procedure is efficient over a very wide range of mass discrimination , far outside that normally encountered in routine analysis. The method only appears to break down for extreme mass fractionation (point 'x', with corresponding corrected value, point 'y', in Fig. l), presumably as a result of the severe degradation of the signal intensity at this point producing error in the measurement of the 204Pb peak and result ant 206Pb/204P b , 207P b P P b and 20sP bP4P b ratios .As a measure of the long-term accuracy of the double spike technique, raw and double spike corrected data for NBS SRM 981, obtained at the Australian National University over a 37.4 t- 37.2 9 > 37.0 a a 0 0 0 0 ox V 36.6 1 8 Certified/preferred value I I I I ~ ox 0 0 - mooy @Certified value 15.4 I I I I I 16.90 16.95 17.00 17.05 17.10 206 Pbfo4 P b Fig. 1 Results of an experiment in which a single filament load of 40 ng of NBS SRM 981 was run repeatedly to exhaustion, turning up the filament current between runs to exaggerate mass discrimination effects (open circles). Filled circles represent the same data after correction with a single 'double spike' analysis (a mixture of NBS SRM 981 plus ~07PbJ04Pb tracer).See text for details.Analyst, January 1995, Vol. 120 37 period of four years from 1989 to 1993, have been collated in Fig. 2. It is important to note that the dispersion displayed in the uncorrected data does not represent the degree of consistency obtainable by any one analyst under normal conditions; rather it is a compilation of data for seven operators who have used the laboratory, over a period of time in which three different batches of silica gel have been used, and includes early tests of the double spike technique, therefore, encompassing many different analytical situations in terms of sample loading and run conditions. However, this array can be usefully regarded as covering the maximum range in mass discrimination ever likely to be encountered by any one laboratory, and certainly far more than that for any one individual.When the double spike correction is applied to the data using the corresponding double spike runs, most of this dispersion disappears, with all of the resulting corrected data 36.80 36.70 n n > 36.60 0 36.50 36.40 Certified value k 2 SD Doubl6 spike corrected data 15.52 Certified value 2 2 SD, 15.50 a 15.44 204 I .J.w 16.86 16.88 16.90 16.92 16.94 16.96 2wPb/204Pb Fig. 2 Compilation of NBS SRM 981 uncorrected (open circles) and double spike corrected (filled circles) data from this laboratory over the period 1989-93. The uncorrected data represent a compilation for seven operators, over a period of time in which three different batches of silica gel were used and include a number of early experimental runs; thus, they cover a range in mass discrimination far greater than that normally encountered by any one individual. Note, however, that the double spike corrected values all fall within the 2 x s uncertainty assigned to the NBS SRM values.See text for further details. falling well within the range of uncertainty assigned to SRM 981 by the NBS. Note that a residual error visible in these data, and shown in Fig. 2 , does not coincide with the mass fractionation vector; this is in fact a ‘204 error’ line, associated with errors in the measurement of the relatively small 204Pb peak if the beam intensity is low: some of this dispersion could, thus, be reduced further by running larger amounts of Pb to produce beam intensities in the region of = 3 V 2f18Pb or more.These two sets of data, taken in conjunction, firmly establish the validity of the double spike method in producing highly accurate data over an exceptionally wide range of mass discrimination, far beyond that normally encountered in routine analysis. We believe the double spike procedure is particularly powerful when applied to relatively low-level samples (<20 ng). In conventional Pb work, these can cause significant problems, not only because of the potential importance of the blank, but also because the relatively low levels of Pb being run often follow different mass fractionation versus time paths to the standard, resulting in an inappropriate fractionation correction being applied. Analytical Precision (Reproducibility of the Double Spike Correction) The NBS SRM 981 data shown in Fig.2 also provide what might be termed a ‘worst case’ estimate of the analytical reproducibility possible with the double spike method because the uncorrected data cover such a large range of fractionation effects. Table 1 contains a full statistical analysis of the corrected data, from which it is clear that even with the considerable dispersion in uncorrected data, application of the double spike correction results in an external precision, expressed as +2 X standard deviation (s), of 0.004,0.005, and 0.013 on the 206PbPPb, 207PbP4Pb and 208PbP4Pb ratios, respectively. In order to determine whether the technique could provide improvement on data obtained in laboratories where very stringent run conditions are imposed, different aliquots of NBS SRM 981 and a whole-rock sample were processed through the normal chemistry and loading procedures in our laboratories (in addition the whole-rock chips were individually acid-washed prior to dissolution) in an identical way.Each split was then run at the same temperature (1100 “C), with the same heating sequence. These data, shown in Table 2, provide some estimate of the levels of reproducibility possible under ideal conditions using conventional Pb isotope techniques; again an ‘end-member’ situation as, in routine analysis, it is unlikely that such consistency in the amount of Pb loaded could be achieved. The data for the NBS SRM are less dispersed than those for the rock sample and, as both have experienced the same chemistry, this cannot be attributed to blank effects (which are in any case negligible); it must reflect either very minor isotopic heterogeneity in the rock or mass fractionation effects due to trace amounts of contaminants from the rock sample affecting the performance of the silica gel substrate as noted above.Although the reproducibility Table 1 Statistical analysis of double spike corrected NBS SRM 981 data (n = 109), obtained under many different run conditions, i.e., covering a very large range in mass discrimination effects Re 1 at i ve Standard Standard standard Maximum - Isotope ratio Mean deviation error deviation (%) Minimum Maximum minimum 0.010 206Pb/204Pb 16.937 0.0020 0.0002 0.012 16.932 16.942 207 PbF04Pb 15.492 0.0024 0.0002 0.016 15.485 15.497 0.012 208PbFmPb 36.708 0.0064 0.0006 0.017 36.692 36.721 0.02938 Analyst, January 1995, Vol.120 here is excellent, application of the double spike correction provides further improvement by a factor of two, with external precision o n the corrected data for the rock sample -7(]6Pb/ZO4Pb, -7(17Pb/"]JPb and ?08Pb/Z()JPb ratios of 0.0026, 0.0034 and 0.0096, respectively (again expressed as k 2 X s). Comparison of the rock and NBS SRM data in Table 2 confirms our belief that sample Pb, prepared and run under identical conditions to standard Pb, behaves in a different manner during mass spectrometry. Processing for both these Table 2 Replicate analyses (total procedure) for individual samples, under optimum conditions (although the data are reported to three decimal places, statistics were calculated on values to four decimal places) (1) NBS SRM 981, 150 ng loads, with chemistry (two column passes), identical run conditions- Raw data (uncorrected) Double spike corrected Sample 206Pb/ 207pb/ 2OXpb/ ?OhPb/ 207Pb/ 2OXpb/ No. 204Pb 204Pb 204Pb 204Pb 204Pb 204Pb 1 16.887 15.424 36.490 16.937 15.492 36.707 2 16.885 15.422 36.482 16.937 15.493 36.707 3 16.886 15.423 36.486 16.936 15.492 36.704 4 16.886 15.422 36.485 16.936 15.490 36.702 5 16.888 15.424 36.494 16.936 15.491 36.703 Mean 16.886 15.423 36.487 16.936 15.492 36.705 SD * 0.0010 0.0012 0.0043 0.0007 0.001 1 0.0024 SET 0.0004 0.0005 0.0019 0.0003 0.0005 0.0011 RSDt 0.006% 0.008% 0.012% 0.004% 0.007% 0.007% (2) 32 NG 0124 Andesite, Western Bismarck arc, P.N.G.b- Raw data (uncorrected) Double spike corrected Sample 206Pb/ 207Pb/ 2OSpb/ 206pb/ 207pb/ 20Spb/ No.204pb 204pb 204Pb 204Pb 204pb 7-04pb 1 18.632 15.489 38.217 18.695 15.568 38.477 2 18.634 15.492 38.227 18.697 15.570 38.485 3 18.634 15.492 38.228 18.695 15.568 38.478 4 18.629 15.486 38.209 18.693 15.566 38.473 5 18.628 15.485 38.204 18.697 15.570 38.484 6 18.633 15.490 38.221 18.695 15.568 38.477 Mean 18.632 15.489 38.218 18.695 15.568 38.479 18.6877 15.5587 38.4487 SD* 0.0024 0.0031 0.0099 0.0013 0.0017 0.0048 SEt 0.0010 0.0013 0.0040 0.0005 0.0007 0.0020 RSDt 0.013% 0.020% 0.026% 0.007% 0.010% 0.012% (3) K-feldspars, Berridale and Bega batholiths, S . E. Australia(I- Raw data (uncorrected) Double spike corrected Sample 20hPb/ 207Pb/ *"SPb/ 206Pb/ 207Pb/ 208Pb/ BB104 18.099 15.552 37.939 18.153 15.621 38.163 Duplicate 18.087 15.537 37.892 18.153 15.622 38.169 KB22 18.171 15.562 38.022 18.226 15.633 38.253 Duplicate 18.IS9 15.554 37.996 18.222 15.635 38.260 MG-19 18.111 15.503 37.782 18.169 15.577 38.023 Duplicate 18.1 11 15.507 37.805 18.167 15.579 38.039 No. 204pb 204pb 204Pb 204pb 204Pb 204pb ' SD = Standard deviation. + SE = Standard error. -I RSD = Relative standard deviation. 11 Ratios obtaincd by conventional correction procedures, using a mass discrimination factor calculatcd from the NBS SRM 981 data in part (1) on this table. Note the comparison with the double spike corrected data, highlighting the potential loss of accuracy by the use of conventional correction procedures. + Ref.19. 11 Ref. 9. sets of analyses was identical, including the column chemistry and loading procedure. Similar amounts of Pb were loaded on to the filaments in each instance and all were run at about 1100 "C. Reproducibility between individual runs for each sample is excellent, but the NBS SRM and whole-rock samples have experienced consistently different degrees of mass fractionation with values of E (the mass discrimination factor per u) of 0.00149 and 0.00170, respectively. This, coupled with the observation that beam intensities were lower for the same amount of rock Pb, suggests suppression of the ion beam by trace amounts of impurities which were not adequately removed by the chemistry. This is a clear demonstration that, even under optimum conditions, conventional correction procedures for mass discrimination effects are likely to result in some loss of accuracy and, we believe, a strong argument for the application of the double spike technique.It is most unlikely that routine Pb isotope analyses will approach the precison obtained here under these ideal circumstances. However, comparison of the corrected data from both Tables 1 and 2 shows that the double spike technique provides a very high degree of precision, essentially independent of the extent of mass fractionation, producing, for geological samples run under routine conditions, external precision in 206Pb/204Pb, 207Pb/204Pb and 208PbP4Pb ratios of +0.003,0.003 and 0.01 (2 x s), respectively. A brief survey of the literature indicates that most laboratories quote errors on the mass discrimination factor for Pb isotope analyses of about 0.02-0.03% per u.2,12,20,*1. Based on this error, a simplistic calculation using maximum and minimum discrimination factors translates into a range on measured 206Pb/204Pb, 207PbPPb and 2osPb/204Pb ratios of k0.01,0.014, and 0.044, respectively.We conservatively estimate, therefore, that use of the double spike increases precision by a factor of three over conventional mass fractionation correction procedures. Conclusions The use of a 207PbXO4Pb double spike for correction of mass fractionation effects during routine Pb isotope analysis offers increased analytical accuracy and precision without recourse to excessively rigorous loading or run conditions; indeed, tests show that this appears to be largely independent of minor variations in loading/run parameters.An improvement in precision by a factor of three over conventional methods appears to be easily obtainable. In view of the increased requirement for high precision Pb isotope data, and the relatively rapid analysis time offered by modern multicollector mass spectrometers, we consider use of the double spike to be far more advantageous than the use of 'conventional' correc- tion methods. We thank L. Kinsley, G. Mortimer, M. Fanning and J. Richards, all of whom have been involved at various stages in the gradual refinement of our double spike procedures at the Research School of Earth Sciences. J. Hergt, G. Mortimer and two anonymous reviewers provided constructive comments on the original manuscript.Appendix Data Reduction Although exact solutions can be obtained from double spike analysis,17 an iterative method is presented here, which has the advantage that a more complex fractionation law can be incorporated in the solution (in this instance we have used a power law). As described previously, two mass spectrometerAnalyst, January 199.5, Vol. 120 39 runs are required, one being a mixture of the sample and z"7PV04Pb tracer (termed 'mix') and the other an analysis of the unknown sample (termed 'Sa'). The program first determines the apparent 204Pb/207Pb tracer composition in the mixture run [i.e., (204Pb/207Pb)ta mix] using the following spike-sample unmixing equation: (2"Pb/207Pb),, = (204Pb/207Pb)mix - [(204Pb/2'7Pb)sa - (2"4Pb/207Pb) mix] x [ (208Pb/207Pb) mix - (208Pb/207Pb)t]/ [ ( 208Pb/2"7Pb)sa - ( 2"8Pb/207Pb)mix] (1) where the subscripts mix and Sa refer to the measured composition in the mixture and sample runs, respectively, and t is the known ratio in the tracer.A first estimate of the mass discrimination factor in the mixture run (Dmix) is then obtained using Dmix = [(204PbP07Pb),, mix)/(204Pb/207Pb),]*'3 (2) The measured ratios in the mixture run are then corrected for mass fractionation using the above estimate for Dmix. The 208Pb/206Pb ratio of the sample in the mixture run, minus the spike contribution (2°8Pb/206Pbsa mix) is then calculated from an analogous equation to (1) above. Using this corrected ratio an estimate of the mass fractionation in the unspiked sample can then be obtained from the relationship: Ds, = [(20'Pb/206Pb)sa/(20'Pb/206Pb)Sa mix]'" (3) where (208Pb/206Pb)sa) is the ratio measured in the unspiked sample run.This calculation scheme is then iterated several times until the change in the value of Dmix is less than 10-6. If spiking is within the range Q = 0.02-1, then the convergence is rapid within 3 4 iterations. Further details can be obtained from the authors. 2 McDonough, W. F.. and Chauvel, C., Earth Planet. Sci. Lett., 1991, 105, 397. 3 Volker. F.. McCulloch. M. T., and Altherr. R.. Geophys. Res. Lett., 1993, 20, 927. 4 Dodson, M., J. Sci. Instrum., 1963,40,289. 5 Compston. W., and Oversby. V. M., J. Geophys. Res., 1969, 74. 4338. 6 Cooper, J. A., and Richards, J. R., in Hot Brines and Recent Heavy Metal Deposits in the Red Sea, eds. Degens, E. T., and Ross, D. A., Springer-Verlag, New York, 1969, pp. 499-511. 7 Hamelin, B., Mahnes, G., Albarede, F., and Allkgre, C. J., Geochim. Cosmochim. Acta, 1985,49, 173. 8 Richards, J. P., McCulloch, M. T., Chappell, B. W., and Kerrich, R., Geochim. Cosmochim. Acta, 1991,55, 565. 9 McCulloch, M. T., and Woodhead, J. D., Geochim. Cosmo- chim. Acta, 1993, 57, 659. 10 Woodhead, J. D., and Devey, C. W., Earth Planet. Sci. Lett., 1993, 116, 81. 11 Woodhead, J. D., and Johnson, R. W., Contrib. Mineral. Petrol., 1993, 113,479. 12 Manhes, G., Minster, J. F., and Allkgre, C. J., Earth Planet. Sci. Lett., 1978, 39, 14. 13 Todt, W., Cliff, R. A., Hanser. A., andHofmann, A. W., Terra Cognita, 1984, 4, 209. 14 Oversby, V. M., Geochim. Cosmochim. Acta, 1973,37,2593. 15 Gulson, B. L., Korsch, M. J., Cameron, M., Vaasjoki, M., Mizon, K., Porritt, P., Carr, G. R., Kamper. C., Dean, J. A., and Calvez, J.-Y., Int. J. Mass Spectrom. Ion Process., 1984.59, 125. 16 Dodson, M., Geochim. Cosmochim. Acta, 1970, 34, 1241. 17 Gale, N. H., Chem. Geol., 1970, 6, 305. 18 Hofmann, A. W., Earth Planet. Sci. Lett., 1971, 10, 397. 19 Woodhead. J. D., and Johnson, R. W., unpublished work. 20 Galer, S. J. G., MacDougall, J. D., and Erickson. D. J., 111, Geophys. Res. Lett., 1989, 16, 1301. 21 Tatsumoto, M.. Basu, A. R., Wankang, H., Junwen, W., and Guanhong, X . , Earth Planet. Sci. Lett., 1992, 113, 107. References Richards, J. R., Trans. Geol. SOC. S . Afr., 1986, 89, 285. 1 Paper 4/01 4 7 7 0 Received March 14, 1994 Accepted July 29, 1994