Aaron Todd Taylor was charged in 14 counts of a 23-count indictment with offenses relating to the distribution of LSD and marijuana and to witness tampering. Taylor was accused of being a principal supplier to a large LSD distribution conspiracy managed by Seth Ferranti. The conspiracy of at least nine persons operated for over two years between 1989 and July 1991, distributing in excess of 100,000 doses of LSD, mainly to high school and college students. Each dose had a street value of $3 to $5. The jury found Taylor guilty on Count 1 for conspiracy in violation of 21 U.S.C. § 846; on Counts 10, 12, 14, and 16, for distributing LSD in violation of 21 U.S.C. § 841(a)(1); and on Count 22 for possession of LSD with intent to distribute in violation of 21 U.S.C. § 841(a)(1). The jury acquitted Taylor on four counts and the government dismissed the remaining four counts. Taylor was sentenced to 235 months imprisonment on the conspiracy count and 120 months on each of the remaining counts, all sentences to be served concurrently. On appeal, he raises a diverse array of issues, challenging virtually every phase of his trial. For the reasons that we give hereafter, the judgment of the district court is affirmed.

* Taylor contends first that, despite legal obligations imposed on the government to produce exculpatory and impeachment evidence (Brady material), the government failed to disclose a psychological evaluation about Christopher Novak, a government witness, that revealed a learning disability affecting Novak's ability to recall details of past events. Taylor argues that the government's failure could not have been an oversight because he served a specific discovery request for the timely production of such evidence.

The government contends that because the part of the report relating to Novak's substance abuse and addictive behavior was revealed to Taylor several days before trial and the psychological evaluation was provided to him during trial in time for cross-examination, the information was timely provided. The government further points out that Novak's testimony related principally to conduct of a coconspirator, Christopher Buckley, whose attorney vigorously crossexamined Novak on the basis of the report. Arguing that no prejudice was caused by any late production, it notes that the jury ultimately acquitted Buckley. The government argues also that, even if the production of the information was late, the delay did not and could not have changed the outcome of Taylor's trial. See United States v. Bagley, 473 U.S. 667, 678, 682 (1985) (holding that the government's failure to disclose impeachment information mandates reversal only if the evidence is material, and the evidence is material "only if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different").

Although it is established that if the requested information potentially could assist the defendant in challenging the credibility or competence of a prospective government witness, it must be provided, see id. at 674-78, we do not need to resolve that debate between the parties in this case because we conclude that the information was provided to defendant's counsel in time for effective cross-examination. While we do not hold that such a late production of discovery immediately before cross-examination generally satisfies the government's obligation to provide Brady material timely, in this case no prejudice was shown. Because Novak testified principally against Buckley and other substantial evidence was offered and relied on to establish Taylor's guilt, we cannot conclude that, had the material been provided earlier, a reasonable probability existed that Taylor would have been acquitted. We share Taylor's concern about the government's failure to respond earlier to the specific document request, and our decision should not be interpreted as approving the timing of production. Nevertheless, any failure on the government's part in this case did not prejudice Taylor and therefore was harmless.

Taylor next contends that the district court erred in evidentiary rulings that permitted the government to use a chart under Fed. R. Evid. 1006 and that limited cross-examination of government witnesses Meg Dudley, Kristi Johnson, and Richard Miclick.

In providing testimony about the import of a large number of telephone calls made among persons involved in this case, the government utilized a chart summarizing information contained in voluminous telephone toll records, invoking Fed. R. Evid. 1006 to show the chart to the jury. The telephone records had been provided to Taylor before trial and were available for inspection at trial. Taylor objected to use of the chart, arguing that the actual telephone records had not been introduced into evidence and the chart was therefore the "rankest form of hearsay." No contention has been made that the records were not relevant or that the chart did not fairly summarize them.

We believe that the defendant has misconceived the function and operation of Rule 1006. The rule requires only that the telephone records from which the summary is made be "made available for examination or copying" and, only if the court so orders, that they be "produced in court." Although the rule does not require that the records actually be put into evidence absent a court order, we have held that the underlying documents must nevertheless be admissible in evidence. See United States v. Strissel, 920 F.2d 1162, 1164 (4th Cir. 1990) ("[W]e require only that the underlying evidence be admissible and available to the opponent so that a proper cross-examination may be had.").

The telephone records in this case would undoubtedly qualify as business records admissible under Fed. R. Evid. 803. Furthermore, even if the records were not admissible or if the chart did not accurately summarize them, the defendant made no objection. He only contended at trial that the court should have required that telephone records be admitted into evidence before the chart could be used. We therefore find that no error was committed by the district court under Rule 1006.

Similarly we find no error in the district court's limiting the crossexamination of certain government witnesses. Having carefully examined the record, we find no abuse of discretion. Cross-examination of the witnesses was not denied but rather only repetitive crossexamination was limited.

Taylor next contends that he was improperly denied a bill of particulars. The indictment presented in this case is 30 pages long, charging 22 separate counts, each describing a crime committed at a particular location, on a particular date, and by particular defendants. The conspiracy count is described yet in more detail and runs nine pages, describing the necessary facts to identify 23 separate overt acts. We believe that this indictment fairly and fully apprises the defendant of the charges against him. To require more detailed information in this case through a bill of particulars would be nothing more than a direction that the government provide the defendant with discovery, which is not the office of a bill of particulars. See United States v. Automated Medical Laboratories, Inc., 770 F.2d 399, 405 (4th Cir. 1985) ("A bill of particulars is not to be used to provide detailed disclosure of the government's evidence in advance of trial.") We therefore reject Taylor's argument that he was entitled to a bill of particulars.

Taylor contends that the district court erred in instructing the jury on the government's burden of proof to the effect that the government had to present proof "of such a convincing character that a reasonable person would not hesitate to rely and act upon it in the most important of his or her other affairs." As for the instruction, we have noted that attempts to define "proof beyond a reasonable doubt" are not useful and should not be attempted, see United States v. Love, 767 F.2d 1052, 1060 (4th Cir. 1985), cert. denied, 474 U.S. 1081 (1986), but to do so does not per se constitute reversible error. In this case no evidence suggests any confusion by the jury or prejudice to the defendant.

Finally, Taylor challenges his sentence, objecting to a finding that 520 grams of LSD were involved. He contends that he should have had the benefit of the government's agreement with co-conspirators that only 78 grams be attributed to the conspiracy for sentencing or, alternatively, that he was denied equal protection by the disparate sentences. He also objects to the inclusion of the medium (blotter paper) in the calculation of the weight of the LSD.

The facts in the record adequately support the district court's finding that more than 520 grams should be attributable to Taylor for sentencing. There is direct evidence of transactions with Taylor or for which Taylor supplied the LSD which showed more than 300 grams of LSD were involved. Only this amount is required to be shown to reach the level under the Sentencing Guidelines at which Taylor was sentenced. When an application of the Guidelines turns on a factual determination, as it did here, we will not reverse the sentence unless it was clearly erroneous. See United States v. Daughtrey, 874 F.2d 213, 217 (4th Cir. 1989). The sentence imposed on Taylor by the district court was substantially supported by the record and will not be disturbed by this court. The defendant moreover cannot claim the benefit of an agreement reached by co-conspirators with the government, not having himself negotiated such an agreement.

On the issue of whether the blotter paper containing the LSD should be included in calculating its weight, the Supreme Court has put the issue to rest in Chapman v. United States, 111 S. Ct. 1919, 1924 (1991), ruling that "the entire mixture or substance is to be weighed when calculating the sentence." See also United States v. Lauzon, 938 F.2d 326, 328 & n.1 (1st Cir. 1991), cert. denied, 112 S. Ct. 450 (1991).

In summary, we find no reversible error in the proceedings before the district court, and accordingly we affirm its judgment.