Defendant Aaron Lowden appeals from the sentence imposed by the district court following his plea of guilty to distribution of LSD, a violation of 21 U.S.C. § 841(a)(1). Lowden had sold to an undercover agent three sheets of blotter paper and a vial of liquid, both of which mediums contained LSD.

At the sentencing hearing, Lowden established that the net weight of the LSD was significantly less than the gross (combined) weight of the paper, liquid and LSD contained therein. With respect to the gross weight, the district court received evidence of three different measurements of the contraband. First, the presentence report, based on a government chemist's September 1989 analysis, stated that the gross weight of the LSD-impregnated blotter paper was 2 grams, and that of the LSD-bearing liquid 5.7 grams, for a total of 7.7 grams. A second analysis, performed for the government in December 1989, found the gross weight of the paper to be 2.0 grams and of the liquid 4.03 grams, for a total of 6.03 grams. The third analysis, performed by a chemist for the defense in May 1990, found the gross weight of the paper to be 1.9 grams and of the liquid 4.1 grams, for a gross total of 6.0 grams.

The district court rejected Lowden's argument that only the net weight of the LSD found in the paper and liquid should be considered in sentencing. And in determining the gross weight, the court found that the gross weight given in the presentence report was correct. The latter conclusion was based on the defense chemist's testimony that some of the liquid and paper could have been consumed during the first government chemist's analysis, and that some of the liquid could have evaporated between the first analysis and the second and third.

The district court accordingly found Lowden to have possessed 7.7 grams of substances containing LSD, which meant that his base offense level was 30. Had the court accepted the reports of either of the other two chemists, the total weight of the substances would have been less than 7 grams, and the offense level 28. Finally, the district court rejected Lowden's argument that it should depart downward because the counting of the carrier medium would lead to the disparate sentences the Guidelines were designed to eliminate. Although agreeing that two defendants with the same amount of LSD could hypothetically receive different sentences depending solely on the weight of the carrier medium with which they mixed the LSD, the district court did not find this possibility to be a basis for departure. The district court sentenced Lowden to 87 months (slightly more than seven years), the lowest sentence for his guideline range. We affirm.

Lowden argues that the standard of proof for determining the weight of the substances is "beyond a reasonable doubt," and that, because there was insufficient evidence to find that they weighed 7.7 grams, his conviction violated due process. Assuming, arguendo, that the argument for a "reasonable doubt" standard was properly preserved for appeal, it is clearly without merit. See United States v. Wright, 873 F.2d 437 (1st Cir.1989) (citing McMillan v. Pennsylvania, 477 U.S. 79, 106 S. Ct. 2411, 91 L. Ed. 2d 67 (1986)) ("[c]ase law clearly establishes that the government need not prove the facts used for sentencing 'beyond a reasonable doubt.' The Supreme Court has held that the 'preponderance standard satisfies due process' "). Under the preponderance standard, there was more than ample evidence from which the district court could have concluded that the combined weight of the liquid, paper and LSD was 7.7 grams. District court findings of fact in a sentencing hearing may be overturned only if clearly erroneous. United States v. Diaz-Villafane, 874 F.2d 43 (1st Cir.1989). Given the first chemist's analysis measuring the gross weight of 7.7 grams, and the testimony explaining how later analyses might have found a lower gross weight, the district court's finding was not clear error.

Lowden further argues that including the weight of the two carrier mediums for purposes of determining his sentence violated the due process clause of the federal Constitution, because such inclusion could result in the arbitrary imposition of different sentences on defendants dealing in identical amounts of LSD, depending on the carrier medium used.1 It does not appear that Lowden raised this constitutional argument below. Although he did claim that the use of gross weights was arbitrary, he did so solely in order to buttress a request that the court depart from the guidelines. Lowden never contended below that the arbitrariness rose to the level of a constitutional violation. That argument is, therefore, waived. See United States v. La Guardia, 902 F.2d 1010 (1st Cir.1990).

Assuming, arguendo, that we may consider Lowden's constitutional challenge for the first time on appeal under the "plain error" doctrine, we find no plain error here. In Chapman v. United States, the Supreme Court specifically held that sentencing based on the weight of blotter paper containing LSD did not violate due process. --- U.S. ----, 111 S. Ct. 1919, 1927-29, 114 L. Ed. 2d 524 (1991). Lowden argues that the Court left open the possibility that due process would be violated where a carrier heavier than paper, such as the liquid here, was used. To be sure, the Court stated that "hypothetical cases can be imagined involving very heavy carriers and very little LSD," but it went on to note that "those cases are of little import in considering a claim by persons such as petitioners, who used a standard LSD carrier." Id. 111 S.Ct. at 1928. Even assuming that Chapman left room for a constitutional challenge in a case involving a particularly heavy or unusual carrier, this is not that case. Blotter paper appears to be the "carrier of choice" for LSD, id., and Lowden has pointed to no evidence that the liquid here (apparently water) was in any way an unusual medium within which to mix LSD. Compare United States v. Mahecha-Onofre, 936 F.2d 623 (1st Cir.1991) (including weight of acrylic chemically bonded with cocaine so as to make a suitcase); United States v. Lopez-Gil, 1992 WL 764, No. 90-2059 at 6-12 (1st Cir. Jan. 3, 1992) (applying Mahecha-Onofre to a cocaine-fiberglass suitcase). We think it safe to say that a substantially heavier or more unusual medium than the water used here would be required in order to raise a due process argument of substance.

Lowden's final argument is that his sentence violates the Eighth Amendment because it is disproportionate to the seriousness of his crime. Again, this challenge was not raised below, but even assuming it can be considered under the plain error doctrine, we reject it. In Harmelin v. Michigan, --- U.S. ----, 111 S. Ct. 2680, 2686, 115 L. Ed. 2d 836 (1991), two justices (Justice Scalia, joined by Chief Justice Rehnquist) concluded that the Eighth Amendment contains no proportionality guarantee and hence would abandon the "general principle of disproportionality" stated in Solem v. Helm, 463 U.S. 277, 103 S. Ct. 3001, 77 L. Ed. 2d 637 (1988). Three other justices (Justice Kennedy, joined by Justices O'Connor and Souter) accepted a narrow application of the Solem test, strictly limiting the comparison of the sentence received with sentences for similar crimes in the same or other jurisdictions and forbidding only "extreme sentences that are 'grossly disproportionate' to the crime." 111 S. Ct. at 2705. See Tart v. Massachusetts, 949 F.2d 490, 503 n. 16 (1st Cir.1991). It is significant for present purposes that these three justices cited with seeming acceptance and approval the Court's 1982 decision in Hutto v. Davis, 454 U.S. 370, 102 S. Ct. 703, 70 L. Ed. 2d 556, upholding a sentence of 40 years imprisonment for possessing with intent to distribute nine ounces of marijuana. Id. 111 S.Ct. at 2706. The present sentence--seven years for distribution of 7.7 grams of LSD, an amount sufficient to produce 550 dosage units of a far more potent drug--seems clearly less severe in comparison.

Even if inter-jurisdictional comparison still remains material under Harmelin, a doubtful proposition, Lowden could have received up to ten years (he actually received seven) if prosecuted in a Maine court. See Me.Rev.Stat.Ann. tit. 17-A, § 1252. Thus even by that standard his sentence was not disproportionate. In Harmelin itself the Supreme Court sustained a sentence to life in prison without possibility of parole for possession of 672 grams of cocaine. Lowden's seven-year sentence for distribution of 7.7 grams of LSD was considerably shorter. True, the number of doses of cocaine in Harmelin was also much greater (32,500 to 65,000 doses compared with 550), but still we see no possibility under Harmelin for sustaining Lowden's Eighth Amendment claim.

The sentence imposed by the district court is affirmed.