Defendants Beverly Powell, Raymond Williams, and Kevin Wilson appeal their jury convictions and sentences for conspiring to distribute cocaine and cocaine base in violation of Title 21 U.S.C. §§ 846 and 841(a)(1). The issues raised in this appeal are (1) whether the district court erred in denying defendant Powell's motion to suppress evidence obtained when police stopped the vehicle in which she was a passenger and subsequently searched her purse, (2) whether the district court erred in denying defendant Powell's request for production of Special Agent Dodson's original handwritten notes, (3) whether defendant Williams was denied a fair trial by failure on the part of the government to timely file a bill of particulars and by a prejudicial variance between the bill of particulars and the proof offered at trial, (4) whether the district court erred in determining for sentencing purposes that defendants Wilson and Williams were leaders or supervisors of the conspiracy, (5) whether the district court erred in determining for sentencing purposes the amount of drugs for which defendant Wilson was responsible, (6) whether 21 U.S.C. § 841(b)(1)(B)(iii) is void for vagueness because of a failure to define "cocaine base," and (7) whether the treatment of one gram of crack cocaine for sentencing purposes as the equivalent of 100 grams of cocaine powder pursuant to 21 U.S.C. § 841(b) violates Equal Protection guarantees of the Fifth Amendment. For the reasons that follow, we affirm.

Johnny Henderson was the government's star witness at trial and at the subsequent sentencing hearing. Much of his testimony was corroborated by other witnesses. Henderson testified to the following: Henderson, Malcolm Wilson, and defendants Kevin Wilson, Beverly Powell, and Raymond Williams were members of a cocaine conspiracy that sold approximately 400 to 500 kilograms of cocaine in the Flint, Michigan area from 1985 to 1989. Henderson first met Kevin Wilson in 1985 when he and Wilson discussed Henderson's business of running crack houses in Flint, Michigan. Henderson showed Wilson how he made powder cocaine into crack and sold the crack at his crack houses. Wilson formed a business deal with Henderson to supply Henderson with cocaine in order to convert it into crack.

On at least one occasion, Henderson saw Wilson with several kilograms of cocaine. Malcolm Wilson, Kevin Wilson's brother, worked with Kevin to supply Henderson with cocaine. During 1985 to 1987, Malcolm Wilson sold Henderson two kilograms of cocaine a week. When Kevin Wilson was out of town, Henderson paid Malcolm Wilson for the cocaine. Kevin Wilson had his own crack houses, and he hired others to manage the crack houses for him.

On occasion, Malcolm Wilson, Kevin Wilson, and Henderson discussed ways in which they could raise the prices at their crack houses and exchanged information about how to evade the police who were investigating them. They also discussed how they should communicate with each other and agreed to use pager devices rather than the telephone because the telephone lines might be tapped. Kevin Wilson also provided cocaine to at least three other members of the conspiracy who are not involved in this appeal.

In accordance with an agreement between Henderson and Kevin Wilson, at least 90 percent of the cocaine that Henderson acquired from Kevin Wilson was converted into crack. Kevin Wilson once told Henderson that he had made over $400,000 from the sale of cocaine, and Henderson made as much as $10,000 a day from just one of his crack houses. On some occasions, Kevin Wilson and Henderson travelled together to Detroit to buy cocaine for distribution to their crack houses and to other members of the conspiracy.

In 1986, Beverly Powell became active in the cocaine distribution business. She occasionally accompanied Henderson to Detroit to buy cocaine. In addition, other people worked for her and assisted her in picking up cocaine and storing it at various locations. Most of the cocaine that Henderson bought from Kevin and Malcolm Wilson was converted to crack in Beverly Powell's kitchen. Powell also bought cocaine from Henderson.

On December 16, 1988, Flint, Michigan, police stopped the vehicle in which Powell was a passenger. Inside the vehicle in plain view, the officers observed a 9 mm. magazine for a semi-automatic handgun and a white plastic grocery bag subsequently found to contain cocaine. A search of Powell's purse revealed .35 grams of cocaine.

Raymond Williams began working for Henderson in 1985. Henderson sent Williams money in Texas to return to Michigan so that Williams could work at the crack houses in Flint, Michigan. Thereafter, Williams supervised three crack houses in Flint and was responsible for hiring and firing workers at these houses. In addition, Henderson would bring Williams the drugs and money, and Williams would give Henderson the profits and keep Henderson informed about the activities at the crack houses.

Defendants Powell, Williams, and Kevin Wilson along with seven other defendants were indicted under a superceding indictment filed on July 14, 1989. Powell, Williams, and Wilson were charged under Count I with conspiring to distribute cocaine and cocaine base in violation of Title 21 U.S.C. §§ 846 and 841(a)(1). The two remaining counts did not name appellants in this case. The case proceeded to jury trial on May 11, 1990, against five of the defendants named in the superceding indictment including defendants. On June 1, 1990, the jury convicted defendants Powell, Williams, and Kevin Wilson of conspiring to distribute cocaine and cocaine base.1 These timely appeals followed.

Defendant Powell argues that the district court erred in denying her motion to suppress evidence when police stopped the vehicle in which she was a passenger and subsequently searched her purse. A district court's factual findings made in consideration of a motion to suppress evidence are to be upheld unless they are clearly erroneous. See United States v. Coleman, 628 F.2d 961, 963 (6th Cir.1980). However, the district court's conclusions of law are subject to de novo review on appeal. See Whitney v. Brown, 882 F.2d 1068, 1071 (6th Cir.1989). The reviewing court is to review the evidence "in the light most likely to support the district court's decision." United States v. Gomez, 846 F.2d 557, 560 (9th Cir.1988).

The facts concerning the seizure of evidence at issue are largely undisputed. Rather, the legal significance of these facts is the primary concern. On December 16, 1988, at approximately 8:00 a.m., Lt. Koger, who was conducting a surveillance in an unrelated drug investigation, observed a black Chrysler limousine pulling out of the driveway at 4708 Fleming Road in Flint, Michigan. Lt. Koger knew that this vehicle was owned by Cicero Bullock. The vehicle had tinted windows on the sides and rear in violation of Michigan Compiled Laws § 257.709. Because he could see through the clear front windshield, Lt. Koger was able to identify Cicero Bullock as the driver. A short time later, while Lt. Koger was still engaged in surveillance of the unrelated matter, he observed the same vehicle driven by Cicero Bullock traveling north on Fleming Road. Lt. Koger discussed his observations over the police radio with Lt. Barksdale and Officer Johnny Goodman. At that time, each officer had reliable information implicating Bullock as a drug trafficker. The following is only a portion of the information known to these officers on December 16, 1988.

On November 28, 1988, an anonymous individual called the Flint Police Department Special Operations Bureau and identified Bullock and Beverly Powell as drug traffickers involved in the sale of large quantities of cocaine in the Flint, Michigan area. This informant indicated that cocaine was stored at the Fleming Road address used by Bullock and that Bullock and Powell made deliveries of cocaine in the morning hours. Bullock had been arrested in the early 1980s more than once for discharging a firearm, and, on one occasion, he was involved in a shootout and was arrested with a shotgun in his car. Another informant considered "very reliable" also indicated that Bullock was involved in trafficking large quantities of drugs. J.A. 88. Further, police officers had seen Bullock's limousine within the preceding two weeks at addresses where the traffic pattern was consistent with narcotics activity.

Johnny Henderson, who had been convicted for a drug offense in Flint on August 1, 1988, indicated that Powell was selling cocaine at the Chevrolet plant in Flint, Michigan, where she worked and that she was making deliveries of cocaine. He also informed the police that she carried a firearm. Another informant advised the police that Powell was involved with "dropping off dope." J.A. 88. Finally, as of December 16, 1988, Bullock, who had several narcotics convictions, was on parole on one of his convictions.

Based on this information, the officers decided to follow Bullock's limousine which pulled into the driveway at Powell's residence, at approximately 9:00 a.m. Powell came out of her house carrying a large black purse and joined Bullock in his limousine. After following Bullock's vehicle for a short time, the officers decided to stop the vehicle. The district court found that the officers stopped the vehicle for two reasons, namely, (1) the officers believed that Bullock might be immediately involved in delivering drugs, and (2) the tinted windows violated Mich.Comp.Law § 257.709.

After the officers stopped the limousine, they asked Bullock and Powell to exit the vehicle because Lt. Barksdale was concerned about what he believed to be Bullock's violent tendencies. After Bullock and Powell left the vehicle, Barksdale saw white plastic grocery bags protruding from under the driver's seat. As Lt. Barksdale had previously arrested Bullock with paper grocery bags containing marijuana, he ordered that the plastic grocery bags underneath the seat be searched. He discovered that white plastic grocery bags were wrapped around a clear plastic bag with white powder in it. The white powder in the bag was determined to be cocaine.

Lt. Koger testified that he was concerned Powell might have a weapon in her purse. This concern was based on the empty 9 mm. magazine for a semi-automatic handgun found in the car, the fact that a semi-automatic handgun had not been found, and that Powell was known to be involved in drug trafficking and to carry a weapon. Lt. Koger asked Powell to open her purse, but she refused. He informed her he was just looking for a weapon and asked her if he could feel or squeeze her purse. She also refused this request. Lt. Koger later testified that when he attempted to touch her purse, she became "wild and boisterous" and "obnoxious and belligerent, swearing like crazy." J.A. 546-47. At this point, Lt. Koger placed Powell under arrest for disorderly conduct. He then opened her purse and discovered .35 grams of cocaine.

Defendant Powell argues that the stop of the vehicle in which she was riding and the subsequent search of her purse were both unlawful, and therefore all evidence obtained from the stop and search should have been suppressed. However, the magistrate judge who conducted the suppression hearing found and the district court agreed that the stop was justified as an investigative stop under Terry v. Ohio, 392 U.S. 1, 88 S. Ct. 1868, 20 L. Ed. 2d 889 (1968). In the alternative, they found that the stop was justified on the ground that the police had probable cause to believe that Bullock violated state law with regard to the tinted windows on his limousine.

It is well settled that police officers may stop a person for investigative purposes where, considering the totality of the circumstances, the officers have a reasonable and objective basis for suspecting that particular person is engaged in criminal activity. Terry v. Ohio, 392 U.S. 1, 21-22, 88 S. Ct. 1868, 1879-80, 20 L. Ed. 2d 889 (1968); United States v. Cortez, 449 U.S. 411, 418, 101 S. Ct. 690, 695, 66 L. Ed. 2d 621 (1981).

Clearly, the officers had a reasonable and objective basis for believing that Bullock and defendant Powell were engaged in criminal activity on the morning that they were stopped. The officers had reliable information from a number of sources that Bullock and Powell were engaged in heavy drug trafficking and that Powell often made deliveries early in the morning. The stop was made at 9:00 a.m. Additionally, during the two weeks preceding the stop, the police had seen Bullock's black Chrysler limousine at addresses where the traffic patterns were consistent with narcotics activity. Moreover, the fact that the vehicle's windows violated Michigan law also justified the officers' decision to stop the vehicle.

Defendant Powell argues that the officers did not consider the tinted windows as a basis for stopping Bullock's vehicle, and that it was only after the stop that they noted that the windows of the limousine were heavily tinted in violation of Mich.Comp.Law § 257.709. In support of this argument, Powell refers to Lt. Koger's answer at the suppression hearing to a question inquiring about the "things going through your head" when he decided to make the stop. J.A. 537. In response, Lt. Koger stated that he believed Bullock and Powell were engaged in a delivery of drugs; however, Lt. Koger did not mention the tinted windows. Nevertheless, later in the hearing, Lt. Koger testified that at the time he detained Bullock and Powell, he knew the tinted windows violated Michigan law. Therefore, the district court's determination that the police officers stopped Bullock and Powell, in part, because the tinted windows violated Michigan law is not clearly erroneous.

The next question to consider concerns Lt. Koger's search of Powell's purse revealing .35 grams of cocaine. It is well established that an officer may legally search for weapons if a reasonably prudent officer in the same circumstances would be justified in believing that his safety or that of others was threatened. Terry, 392 U.S. at 27, 88 S.Ct. at 1883; U.S. v. Paulino, 935 F.2d 739, 746 (6th Cir.), cert. denied, --- U.S. ----, 112 S. Ct. 315, 116 L. Ed. 2d 257 (1991). The magistrate judge determined and the district judge agreed that, under the circumstances at the time of the stop, the police officers were justified in believing that their safety might be in danger and that it was necessary to search Powell's purse for a firearm. Defendant Powell argues that the officers' belief that their safety was in jeopardy was unreasonable. Specifically, she refers to the fact that the 9 mm. magazine found in the back of the car was empty, that she had not attempted to open her purse after exiting the vehicle, that there were at least four police officers on the scene, and that the information the officers had concerning her possessing a firearm was at least ten months old. Her argument is meritless. As the magistrate judge succinctly and correctly stated:

Lt. Koger's belief that defendant might be armed was also reasonable--he had information that she acted as a drug courier, and in so doing often carried a weapon. Although this information was not recent, he had also discovered drugs and a magazine for a 9 mm. automatic weapon in the car in which defendant was riding. His request that he be allowed to feel defendant's purse was a reasonable one, tailored to the discovery of potentially dangerous weapons. Defendant's vehement refusal to allow Lt. Koger to touch the purse also raised legitimate suspicion of its potentially dangerous contents. The search of the purse for weapons was thus justified as a reasonable self-protective search by Lt. Koger.

J.A. 99. Lt. Koger's search of defendant Powell's purse did not violate her Fourth Amendment guarantees against unreasonable searches. Consequently, the district court did not err in denying Powell's motion to suppress evidence of the .35 grams of cocaine found in her purse.2

The second issue that Powell raises on appeal is whether the district court erred in refusing to order the production of Special Agent Dodson's handwritten notes made from interviews with the government's witnesses. Powell argues that Agent Dodson's handwritten notes, which were used by him to prepare reports of government witnesses' interviews, are statements as defined by the Jencks Act, 18 U.S.C. § 3500(e), and, therefore, failure to produce these notes violated the Jencks Act. The district court's ruling on factual determinations relating to production of documents is reviewed under a clearly erroneous standard. United States v. Sturman, 951 F.2d 1466, 1485 (6th Cir.1992), petition for cert. filed, (Feb. 26, 1992) (No. 91-1367); United States v. Arnold, 890 F.2d 825, 830 (6th Cir.1989); United States v. Nathan, 816 F.2d 230, 237 (6th Cir.1987).

The Jencks Act, 18 U.S.C. § 3500(b), provides that a government witness' statement shall be the subject of discovery or inspection after the witness has testified on direct examination. In section 3500(e), a statement is defined as:

(1) a written statement made by said witness and signed or otherwise adopted or proved by him;

(2) a stenographic, mechanical, electrical, or other recording, or a transcription thereof, which is substantially verbatim recital of an oral statement made by said witness and recorded contemporaneously with the making of such oral statement....

According to the "Adoption Test" set forth in Nathan, 816 F.2d at 236-37, and Arnold, 890 F.2d at 829, a government report or notes of a witness' statement must be produced "if the notes from the interview were read back to and verified by the witness and if the report summarized the notes without material variation." Arnold, 890 F.2d at 829, citing Nathan, 816 F.2d at 237. The purpose of this test is to determine whether the witness adopted the notes as being "substantially verbatim to the statement given." Arnold, 890 F.2d at 829. As we stated in Arnold,

[t]he reasoning behind the rule is that "it would be grossly unfair to allow the defense to use a statement to impeach a witness which could not fairly be said to be the witness' own rather than a product of the investigator's selections, interpretations and interpolations."

Arnold, 890 F.2d at 829 (quoting Nathan, 816 F.2d at 236).

Powell's argument that the district court erred in failing to order the production of Special Agent Dodson's notes is meritless. At trial, Agent Dodson was cross-examined at length regarding the manner in which he took notes from interviews of the government witnesses. He stated that the notes were his own interpretations of what the witnesses told him. Further, he testified that at no time did he allow the witnesses to read his notes nor did he read his notes to the witnesses and allow them to adopt them as their own. Therefore, the district court was not in error in determining that Special Agent Dodson's handwritten notes were not "statements" as defined by the Jencks Act. In addition, both parties agreed that Agent Dodson's notes would be submitted to the district court for review overnight to determine if the notes contained any exculpatory evidence. The district court did so and found nothing exculpatory. No objection was made to this procedure.

Defendant Williams argues that he was denied a fair trial by the government's failure to timely file a bill of particulars and by a prejudicial variance between the bill of particulars and the proof offered at trial. On December 19, 1989, all defendants filed a motion for a bill of particulars arguing that a four-page letter submitted by the government setting forth its theory against defendants was not sufficiently detailed. The motion was heard before the magistrate judge and granted on January 26, 1990. The government appealed the magistrate judge's ruling to the district judge, and the request for a bill of particulars was affirmed on April 24, 1990. The district judge held that

the government shall promptly serve upon the defendants a Bill of Particulars detailing with regard to its case in chief, what specific acts each defendant is alleged to have done making him or her liable under the indictment.

J.A. 101-102. On May 8, 1990, on the second day of jury selection, defendant Williams received the government's bill of particulars. The bill of particulars consisted of the four-page letter plus a list of receipts for discovery material which the government had submitted to defendants. All defendants objected to the bill of particulars as being inadequate. The district court, however, overruled their objections and deemed the bill of particulars to be sufficiently detailed to have complied with its order. It does not appear from the record, nor does Williams argue, that he asked for additional time to review the bill of particulars.

At trial, the government introduced evidence of two incidents which defendant Williams alleges were not mentioned in the bill of particulars and thus constitute a prejudicial variance. The first incident involved the alleged violent beating of an individual at a drug house by Williams. The second incident concerned Williams' arrest in 1985 at a crack house where one rock of crack cocaine was found in his back pocket. The police also found $900 hidden under the sofa where Williams was arrested and a stash of firearms in another room of the crack house. This second incident was elicited from testimony given on May 21, 1990.

We must first consider whether defendant Williams has properly preserved this issue for appeal. Williams' counsel moved for a mistrial the following day on May 22, 1990, arguing that the testimony about Williams' alleged participation in a beating constituted a prejudicial variance from the bill of particulars. In regard to the testimony of Williams' 1985 arrest at a crack house, Williams admits he did not raise the issue of a prejudicial variance from the bill of particulars until after trial when he filed a motion for a new trial.

Because Williams failed to object at trial to the evidence concerning his 1985 arrest, the government argues that defendant Williams has not preserved this issue for appeal. We agree. An objection to an alleged variance between a bill of particulars and proof offered at trial must be made when the evidence is offered in order to allow the court to consider an amendment to the bill of particulars, as well as to preserve the error for appeal. United States v. Linn, 889 F.2d 1369, 1373, n. 4 (5th Cir.1989), cert. denied, --- U.S. ----, 111 S. Ct. 43, 112 L. Ed. 2d 19 (1990); Jackson v. United States, 359 F.2d 260, 263, n. 1 (D.C.Cir.), cert. denied, 385 U.S. 877, 87 S. Ct. 157, 17 L. Ed. 2d 104 (1966).

Williams argues that it is unnecessary to object at trial in order to preserve this issue for appeal. In support of his argument, he cites United States v. Beeler, 587 F.2d 340, 343 (6th Cir.1978), cert. denied, 454 U.S. 860, 102 S. Ct. 315, 70 L. Ed. 2d 158 (1981), in which we held that an objection at trial was unnecessary to preserve for appeal the issue of an alleged variance from an indictment. However, our holding in Beeler is not applicable to an alleged variance from a bill of particulars. The purpose of an objection is to allow the court to correct its mistakes. Federal Rule of Criminal Procedure 7(f) provides that a bill of particulars may be amended "at any time subject to such conditions as justice requires." Indictments, however, may not be amended because doing so would "substitute the prosecutor's judgment for that of the constitutional body, the Grand Jury, in framing the charge against a defendant." United States v. Beard, 436 F.2d 1084, 1087 (5th Cir.1971). However, a bill of particulars is drawn by the prosecutor only. Thus, an objection at trial to an alleged variance from a bill of particulars serves a useful function and must be made at trial in order to preserve the issue for appeal.

Next we address the issue of the alleged variance in the bill of particulars arising from the testimony concerning Williams' alleged participation in a beating of an individual. In the four-page letter supplied by the government to defendant Williams, the government stated that it sought to prove Williams was an "enforcer" of the conspiracy. Defendant Williams states that while the discovery material provided by the government notified him of an alleged beating by members of the conspiracy, the discovery material did not notify him that he was believed to be involved in the beating. Defendant Williams contends that failure to specifically state he was involved in the beating constitutes a prejudicial variance because the testimony regarding Williams' participation went beyond the scope of the bill of particulars. However, such testimony actually conformed to the assertion in the bill of particulars that defendant Williams was an enforcer in the conspiracy. Defendant Williams' argument appears to be more accurately described as one alleging that the government failed to comply with the district court's order to provide specifics regarding alleged acts committed by the defendant. In any event, error, if any, was harmless in light of the overwhelming evidence against defendant Williams. United States v. Haskins, 345 F.2d 111, 114 (6th Cir.1965) ("variance between the proof and the bill of particulars is not grounds for reversal unless the defendant was prejudiced by the variance."). Finally, at oral argument counsel for Williams stated that he did not accuse the government of bad faith, and counsel for the government stated that he believed the government had provided a full report of the alleged beating in the voluminous discovery materials which were incorporated into the bill of particulars.

Both defendants Williams and Wilson object to the district court's finding that they were organizers, leaders, managers, or supervisors in the conspiracy. Pursuant to United States Sentencing Guidelines, § 3B1.1 ("U.S.S.G."), this finding enhanced defendants' base offense levels, four points for Wilson and two points for Williams.³ Additionally, defendant Wilson argues that the district court erred in determining he was responsible for 50 kilograms of cocaine and 500 grams of cocaine base (crack). Based on this finding, Wilson received a base offense level of 36 pursuant to U.S.S.G. § 2D1.1(c).4 A district court's findings of fact pursuant to the guidelines are reviewed for clear error. 18 U.S.C. § 3742; United States v. Alvarez, 927 F.2d 300, 303 (6th Cir.), cert. denied, --- U.S. ----, 111 S. Ct. 2246, 114 L. Ed. 2d 487 (1991).

Defendants' arguments are meritless. The evidence clearly shows that Wilson was a leader and that Williams supervised others within a conspiracy of five or more persons. Additionally, sufficient evidence exists to show that defendant Wilson was involved in a conspiracy which acquired over 400 to 500 kilograms of cocaine, 90 percent of which was distributed as crack. Under U.S.S.G. § 1B1.3, the district court must consider all quantities of drugs involved in the same conspiracy. United States v. Smith, 887 F.2d 104, 107 (6th Cir.1989). Finally, Wilson relies upon United States v. Metcalf, 898 F.2d 43 (5th Cir.1990), to support his assertion that crack is not cocaine base. However, the Fifth Circuit in Metcalf determined that "crack cocaine is one type of cocaine base." Id. at 46; see also United States v. Levy, 904 F.2d 1026, 1033 (6th Cir.1990) (Congress intended the term "cocaine base" to include crack), cert. denied, --- U.S. ----, 111 S. Ct. 974, 112 L. Ed. 2d 1060 (1991). Therefore, the district court's findings that defendant Wilson was a leader in the conspiracy, that defendant Williams was a supervisor in the conspiracy, and that defendant Wilson was responsible for 50 kilograms or more of cocaine and 500 grams of cocaine base are not clearly erroneous.

Finally, defendant Wilson makes two constitutional challenges to his conviction and sentence. First, Wilson argues that the treatment of cocaine base for purposes of sentencing as the equivalent of 100 times the same amount of cocaine powder under 21 U.S.C. § 841(b) is arbitrary and capricious and thus violates Equal Protection Standards under the Fifth Amendment. Second, he argues that the failure of Congress to define "cocaine base" in 21 U.S.C. § 841(b)(1)(B)(iii) renders the statute void for vagueness. These challenges are meritless. In Levy, 904 F.2d at 1032-33, we held that 21 U.S.C. § 841(b)(1)(B) which provides penalties for offenses involving 500 grams or more of cocaine or 5 grams or more of cocaine base is not unconstitutionally vague.

To date, we have not addressed the issue of whether the penalty scheme under 21 U.S.C. § 841(b), which treats 1 gram of crack as the equivalent of 100 grams of cocaine, violates the Equal Protection Standards under the Fifth Amendment. However, in upholding the one to one hundred ratio set forth in 21 U.S.C. § 841(b) in the face of Substantive Due Process and Eighth Amendment challenges, we have held that the penalty scheme bears a reasonable relation to a legitimate end. See United States v. Pickett, 941 F.2d 411, 418 (6th Cir.1991) (One to one hundred ratio of crack to cocaine does not violate Substantive Due Process standards or constitute cruel and unusual punishment under the Eighth Amendment). In Pickett, we held that the one to one hundred ratio of crack to cocaine established by Congress was not irrational for two reasons. First, Congress was concerned that crack is a purer drug than cocaine and the speed with which it progresses to the brain "produces a significantly different effect that increases the likelihood of addiction." Id. Second, we stated that

Congress was clearly concerned that the special attributes of crack--its small size and cheap price per dose--could create other societal problems that required remedying. Senators noted that because crack is sold in small doses (called "rocks") it is easier to transport and use, thereby increasing the difficulty of suppressing addiction. The cheap price of each "rock" also permits children to afford cocaine for the first time, thereby exposing another segment of American society to drug addiction.

Id.; see also United States v. Avant, 907 F.2d 623, 627 (6th Cir.1990) ("In enacting stiffer sentences for crack cocaine, Congress apparently intended to combat what it perceived to be the greater danger of crack cocaine."). Similarly, the one to one hundred ratio of crack to cocaine does not violate Equal Protection Standards because, for the same reasons, the ratio is reasonably related to a legitimate end. Moreover, every circuit which has addressed this issue has upheld the ratio as comporting with Equal Protection Standards of the Fifth Amendment. See United States v. Galloway, 951 F.2d 64, 66 (5th Cir.1992) (per curiam); United States v. Lawrence, 951 F.2d 751, 753-56 (7th Cir.1991); United States v. Thomas, 900 F.2d 37, 39-40 (4th Cir.1990); United States v. Cyrus, 890 F.2d 1245, 1248 (D.C.Cir.1989). Today, we join those circuits in holding that 21 U.S.C. § 841(b) does not violate the Equal Protection Standards of the Fifth Amendment.

For the reasons stated, the defendants' convictions and sentences are AFFIRMED in all respects.