BAUER, Circuit Judge.
Defendants-appellants Ralph Read, Ronald E. Spiegel, and Howard Swiger appeal their convictions for conspiracy, mail fraud, and securities fraud. We affirm the judgments of conviction entered for Ralph Read and Howard Swiger in Nos. 80-1017 and 80-1019. We reverse Ronald Spiegel’s conviction for conspiracy in No. 80-1018 and remand for a new trial. We affirm Spiegel’s conviction on the substantive counts.
I
The indictment charged a scheme to artificially inflate the year-end inventory of Cenco Medical Health Supply Corporation (“CMH”) and thus increase its reported profits. The defendants-appellants were officers of CMH and Cenco, CMH’s parent corporation. Ralph Read was president of Cenco and a member of its board of directors; Ronald Spiegel was a vice-president of Cenco, and president of CMH; Howard Swiger was also a vice-president of Cenco and comptroller of CMH. Other defendants — Russell Rabjohns, Bernard Mag[1229]*1229dovitz, and Jack Carlson — pled guilty to two counts and testified for the government. Another defendant, Robert Smith, was acquitted.
We need only briefly outline the evidence at trial showing defendants’ massive manipulation of CMH’s finances from 1970 to 1975. The greatest amount of the fraud was accomplished by overstating CMH’s inventory. During annual inventory, each CMH branch recorded the amount of every item in stock on computer cards. When the cards were returned to the central Chicago office for processing, some of the defendants, at Spiegel’s direction, increased the numbers on the cards. Thousands of cards were altered in this fashion; defendants made additional changes in the computer listings of the inventory that CMH submitted to its auditors. In 1970, defendants increased the reported inventory of CMH by 3.5 million dollars. In each succeeding year, defendants increased the inventory by several millions more and carried the previous years’ inflation forward. The overstatement of inventory decreased CMH’s cost of sales, which in turn produced greater reported profits, dollar-for-dollar. This practice continued until 1975. Estimates of the total fraud ranged from 20 to 25 million dollars.
Other methods included inflating profits by accruing sales in one year and deferring expenses for those sales until the next fiscal year. The defendants also increased reported sales by listing the sales from August 1972 on computer printouts for March 1973 sales. They also created fake documents showing hundreds of thousands of dollars of non-existent inventory to be in transit between warehouses so that it could not be physically counted.
In 1974, Curtiss-Wright Corporation, a large conglomerate, purchased five percent of Cenco’s shares. Curtiss-Wright’s accountants, while examining Cenco’s finances for a possible loan,-found discrepancies in Cenco’s inventory records. Alarmed, the defendants sought to create the appearance of $10 million of non-existent inventory should Curtiss-Wright’s auditors physically check the inventory. In order to do so, they ordered the repacking of obsolete inventory in boxes of expensive products. Finally, in 1975, the defendants implemented an inventory destruction program to cover up the fraud. The defendants persuaded Cenco’s board of directors to approve the destruction of $16 million of obsolete inventory as part of a supposed tax savings program. Almost all of the “destroyed” inventory existed only on paper.
The ultimate result of the fraud was to overstate the profitability of Cenco, thereby defrauding its board, its stockholders, and the SEC. The prosecution also showed that Read’s compensation was linked to the company’s profits.
The indictment charged the defendants with conspiracy, mail fraud, and securities fraud.1 On September 6, 1979, the case proceeded to trial against Read, Spiegel, Swiger, and Smith. On October 29, 1979, following almost eight weeks of testimony, the jury returned guilty verdicts on all counts as to Read, Spiegel, and Swiger. Smith was acquitted. Read, Spiegel, and Swiger appeal their convictions.
II
All appellants charge that the evidence at trial proved multiple conspiracies, not the single conspiracy charged in the indictment. They claim they were prejudiced by this variance between the indictment and proof. [1230]*1230We find that the evidence showed a single conspiracy.
The problem of single or multiple conspiracies relates to the scope of the conspiracy in which the defendant is involved. “If there is one overall agreement among the various parties to perform different functions in order to carry out the objectives of the conspiracy, the agreement among all the parties constitutes a single conspiracy.” United States v. Varelli, 407 F.2d 735, 742 (7th Cir. 1969).
On the other hand, if the evidence shows more than one agreement, directed at different goals, a single conspiracy has not been shown. If a single conspiracy is alleged but several conspiracies are proven, a variance between the indictment and proof is shown. If the variance prejudices the substantial rights of a defendant — for example by surprise, transference of guilt by substantial evidence of crimes unrelated to the defendant, or double jeopardy — the defendant must be acquitted. Kotteakos v. United States, 328 U.S. 750, 774, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946); Berger v. United States, 295 U.S. 78, 82, 55 S.Ct. 629, 79 L.Ed. 1314 (1935). If the evidence, however, shows that one of the conspiracies proven is the conspiracy alleged in the indictment, the defendant’s conviction can stand. United States v. Papia, 560 F.2d 827, 838-39 (7th Cir. 1977). The jury here was cautioned, as we recommended in Papia, id. at 838, that it could not convict a defendant of conspiracy if it found that the proof did not show the single conspiracy charged in the indictment.
Each appellant claims that he was not involved in one or more parts of the conspiracy to manipulate Cenco’s finances. The manufacturing and inventory destruction schemes were planned and executed after Spiegel and Swiger left Cenco, and, they claim, after they left the conspiracy. Since they did not agree to or condone the operations, Spiegel asserts these “cover-up” plans were a separate conspiracy among the remaining defendants. Read, in contrast, claims he cannot be held liable for the inventory inflation scheme because he learned of it only in 1974, after it was almost over. The evidence also showed that several defendants received kickbacks from Rose Packaging Company, the firm which packaged the bogus inventory. None of the appellants received kickbacks, and they claim the kickback scheme constituted a separate conspiracy. We disagree.
Appellants do not dispute their agreement to the common goal charged in the indictment — to “manipulate and falsely report and cause to be manipulated and falsely reported financial information, including profit figures, of Cenco and its subsidiaries.” Indictment H14. Appellants’ objections concern only their participation in the various activities of the conspiracy. Each defendant, however, need not agree to or participate in every step of the conspiracy. Each conspirator is liable for overt acts of every other conspirator done in furtherance of the conspiracy, whether the acts occurred before or after he joined the conspiracy. United States v. Hickey, 360 F.2d 127, 140 (7th Cir.), cert. denied, 385 U.S. 928, 87 S.Ct. 284, 17 L.Ed.2d 210 (1966). He need not be a member of the conspiracy at its inception or throughout the conspiracy. Id. at 138. Read entered the conspiracy late, but he was responsible for the prior actions of all the conspirators once he knowingly contributed his efforts in furtherance of it. Id. at 140. Even if Spiegel and Swiger did not participate in the later events of the conspiracy, they were still responsible for its actions in furtherance of the initial goal.2
We must view the evidence relating to the kickbacks in the light most favorable to the government. Glasser v. United States, 315 U.S. 60, 62 S.Ct. 457, 86 L.Ed. 680 (1942). The evidence showed that the packaging scheme cost CMH less than expected. The jury could have easily inferred that the kickbacks were arranged so as to avoid suspicion should money be returned to CMH from Rose Packaging. There was also testimony that the kickbacks were for attor[1231]*1231neys fees should the fraud be discovered. See tr. 790-91. Further, the jury was instructed that it could find that a defendant was a member of the conspiracy only with evidence of his own acts and declarations. None of the appellants took kickbacks. Evidence of this collateral activity was harmless in light of the overwhelming evidence that the appellants joined in a single conspiracy. United States v. Bastone, 526 F.2d 971, 980 (7th Cir. 1975), cert. denied, 425 U.S. 973, 96 S.Ct. 2172, 48 L.Ed.2d 797 (1976).
The evidence at trial amply supported the jury’s verdict that the one conspiracy charged in the indictment existed. The government showed a common scheme, plan, or purpose among the defendants to manipulate Cenco’s finances. United States v. Dalzotto, 603 F.2d 642, 644 (7th Cir.), cert. denied, 444 U.S. 994, 100 S.Ct. 530, 62 L.Ed.2d 425 (1979). Since we hold that the evidence amply supported the jury’s finding of one conspiracy, there was no variance between the indictment and proof. It follows that none of the appellants were entitled to separate trials on the grounds of prejudicial variance. The trial court correctly denied each appellant’s motion for severance.
Ill
Ronald Spiegel’s main defense at trial was that he withdrew from the conspiracy more than five years before the indictment was filed. He argued that his prosecution therefore was barred by the statute of limitations. 18 U.S.C. § 3282. Spiegel argues on appeal that the trial court gave erroneous instructions on the issue of withdrawal.
The trial court instructed the jury:
Now, we talked about withdrawal. How does a person withdraw from a conspiracy? A person can withdraw from a conspiracy, and in such a case he is not liable for the acts of his former co-eonspirators after his withdrawal. A defendant may withdraw by notifying co-conspirators that he will no longer participate in the undertaking. A defendant may also withdraw from a conspiracy by engaging in acts inconsistent with the objects of the conspiracy. These acts or statements need not be known or communicated to all other co-conspirators as long as they are communicated in a manner reasonably calculated to reach some of them. To withdraw from a conspiracy there is no requirement that a conspirator try to convince the other co-conspirators to abandon their undertaking or that he go to public authorities or others to expose the conspiracy or to prevent the carrying out of an act involved in the conspiracy. But a withdrawal defense requires that a defendant completely abandon the conspiracy and that he do so in good faith. If you find that a defendant completely withdrew from the conspiracy before the 24th of April, 1974, you should acquit him. If you find that he was a member on April 24, 1974, and that an overt act was committed while he was still a member, his later withdrawal, if any, standing alone, is not a defense.
Why. do we pick the date “April 24th, 1974”? We do that because the indictment in this case, as you will see, bears a stamp, the Clerk’s stamp that it was filed on April 24th, 1979. There is a five year statute of limitations for criminal conspiracy and the charge — and the five year statute of limitations runs from the date of the last overt act in the indictment to the date of the filing of the indictment. Accordingly, if you find that an overt act was committed within five years before April 24, 1979 — another way of saying that is that if you find that an overt act was committed between April 24th, 1974 and August of 1975, the conspiracy count in its entirety may be considered by you, going all the way back to 1970 or earlier.
Tr. 5621-23.
Spiegel objected to the above instructions. He claimed before the trial court, and here, that the instructions put the burden of proving withdrawal on Spiegel and failed to put the burden of disproving withdrawal beyond a reasonable doubt on the government. He also attacks the propriety of instructing the jury that the withdrawal [1232]*1232must be in good faith. He further asserts that the instruction erroneously allowed the jury to find that he participated in the conspiracy after the limitations date by proof of overt acts not alleged in the indictment.
Spiegel also claims he withdrew before commission of the securities and mail fraud crimes. He complains that the jury was not instructed that his withdrawal was effective if it occurred before the dates of the sales or mailings charged in the indictment.
We agree that the instructions concerning withdrawal were erroneous and require a remand for a new trial on the conspiracy charge. We disagree, however, that withdrawal is a defense to the substantive crimes, and affirm Spiegel’s conviction on those counts.
A
Due process requires that the prosecution prove beyond a reasonable doubt every fact necessary to constitute the crime charged. In re Winship, 397 U.S. 358, 364, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970); Mullaney v. Wilbur, 421 U.S. 684, 685, 95 S.Ct. 1881, 44 L.Ed.2d 508 (1975); Patterson v. New York, 432 U.S. 197, 97 S.Ct. 2319, 53 L.Ed.2d 281 (1977). The prosecution’s burden often includes disproving defenses because they bring into question facts necessary for conviction. This rule has been well-settled with regard to some defenses. See, e. g., Davis v. United States, 160 U.S. 469, 488, 16 S.Ct. 353, 358, 40 L.Ed. 499 (1895) (insanity).3
Patterson requires us to inquire whether the particular defense negates an essential element of the offense as defined by the legislature. 432 U.S. at 210, 97 S.Ct. at 2327. As held in Holloway v. McElroy, 632 F.2d 605, 625 (5th Cir. 1980), the government “may not place the burden of persuasion on [an] issue upon the defendant if the truth of the ‘defense’ would necessarily negate an essential element of the crime charged.”
18 U.S.C. § 371 provides:
If two or more persons conspire either to commit any offense against the United States, or to defraud the United States, or any agency thereof in any manner or for any purpose, and one or more of such persons do any act to effect the object of the conspiracy, each shall be fined not more than $10,000 or imprisoned not more than five years, or both.
The statute, as long construed, requires the prosecution to prove (1) that the alleged conspiracy existed; (2) that an overt act was committed in furtherance of the conspiracy; and (3) that the defendant knowingly and intentionally became a member of the conspiracy.
Prosecution for conspiracy is also subject to a five-year statute of limitations, 18 U.S.C. § 3282, which runs from the date of the last overt act. Fiswick v. United States, 329 U.S. 211, 216, 67 S.Ct. 224, 227, 91 L.Ed. 196 (1946). In practice, to convict a defendant the prosecution must prove that the conspiracy existed and that each defendant was a member of the conspiracy at some point in the five years preceding the date of the indictment. Grunewald v. United States, 353 U.S. 391, 396, 77 S.Ct. 963, 969, 1 L.Ed.2d 931 (1957); United States v. Borelli, 336 F.2d 376, 389 (2d Cir. 1964), cert. denied, 379 U.S. 960, 85 S.Ct. 647, 13 L.Ed.2d 555 (1965).
Withdrawal marks a conspirator’s disavowal or abandonment of the conspiratorial agreement. Hyde v. United States, 225 U.S. 347, 369, 32 S.Ct. 793, 803, 56 L.Ed. 1114 (1912). By definition, after a defendant withdraws, he is no longer a member of the conspiracy and the later acts of the conspirators do not bind him. The defendant is still liable, however, for his previous agreement and for the previous acts of his co-conspirators in pursuit of the conspiracy. United States v. Hickey, 360 [1233]*1233F.2d at 140. Withdrawal is not, therefore, a complete defense to the crime of conspiracy. Withdrawal becomes a complete defense only when coupled with the defense of the statute of limitations. A defendant’s withdrawal from the conspiracy starts the running of the statute of limitations as to him. If the indictment is filed more than five years after a defendant withdraws, the statute of limitations bars prosecution for his actual participation in the conspiracy. He cannot be held liable for acts or declarations committed in the five years preceding the indictment by other conspirators because his withdrawal ended his membership in the conspiracy. United States v. Borelli, 336 F.2d at 388. It is thus only the interaction of the two defenses of withdrawal and the statute of limitations which shields the defendant from liability.4
Withdrawal, then, directly negates the element of membership in the conspiracy during the period of the statute of limitations. Under Patterson, Mullaney, and Winship, the government should disprove the defense of withdrawal beyond a reasonable doubt.
The government, however, insists that Hyde v. United States, 225 U.S. 347, 32 S.Ct. 793, 56 L.Ed. 1114 (1912), a long-established Supreme Court case, placed the burden of proving withdrawal on the defendant. Indeed, Hyde has often been cited for that proposition in the courts of appeals. Almost every case we researched holds that the burden is on the defendant to “prove” establish” withdrawal.5 Within this Circuit, we recently held that it “is well-settled [that] this burden of establishing withdrawal lies on the defendant.” United States v. Dorn, 561 F.2d 1252, 1256 (7th Cir. 1977).
We have, however, reexamined Hyde. Our research convinces us that the cases, including our own, have misinterpreted Hyde. According to our interpretation, Hyde placed only the burden of going forward on the defendant. To understand what Hyde did hold, however, it is important to understand the law of conspiracy as it existed pre-Hyde.
Turn-of-the-century law held that the crime of conspiracy was complete with the agreement. United States v. Owen, 32 F. 534 (D.Or.1887). Under old law, the statute of limitations ran from the first overt act. United States v. Britton, 108 U.S. 199, 204, 2 S.Ct. 531, 534, 27 L.Ed. 698 (1883). To prove that a conspiracy was still “live,” the government had to prove each defendant’s membership in the conspiracy with evidence from within the statute of limitations. Ware v. United States, 154 F. 577, 580 (8th Cir.), cert. denied, 207 U.S. 588, 28 S.Ct. 255, 52 L.Ed. 353 (1907). Put another way, the government had to prove that each defendant had not withdrawn prior to the running of the statute of limitations.
In Hyde v. United States, 225 U.S. 347, 32 S.Ct. 793, 56 L.Ed. 1114 (1912), the Supreme [1234]*1234Court reacted to the problems of proving membership in a conspiracy that did not end with one agreement, but rather was a continuous series of agreements, such as gambling or liquor and drug smuggling. See United States v. Kissel, 218 U.S. 601, 31 S.Ct. 124, 54 L.Ed. 1168 (1910). The old rule envisioned a static conspiracy, with the relation of the conspirators fixed at one moment in time. The Hyde Court rejected that image. It held that if a conspiracy may continue, “it would seem necessarily to follow [that] the relation of the conspirators to it must continue, being to [the conspiracy] during its life as it was to it the moment it was brought into life.” 225 U.S. at 369, 32 S.Ct. at 803. Since liability for conspiracy is predicated on the responsibility of the participants for each other’s acts, “[i]f each conspirator was the agent of the others” at one time, “he remains an agent during all [other] time[s].” Id. Thus, the Court held, the government need only prove a defendant’s membership in the conspiracy at one point in time.
The Court next responded to debate that its new theory of group responsibility would make conspirators perpetually liable. The Court stated that its new theory would not “take from a conspirator the power to withdraw from the execution of the offense or to avert a continuing criminality.” Id. The Court stated the defense of the statute of limitations was viable in a continuing conspiracy, but that its “application” was “different.” Id. Withdrawal from a conspiracy, the Court held, “requires affirmative action, but certainly that is no hardship. Having joined in an unlawful scheme ... to be continuous until full fruition be secured, until he does some act to disavow or defeat the purpose he is in no situation to claim the delay of the law.” Id. (emphasis added). The Court justified its new requirement of affirmative proof of withdrawal by saying:
As the offense has not been terminated or accomplished he is still offending. And we think, consciously offending, offending as certainly ... as at the first moment of his confederation, and consciously through every moment of its existence .... As he has started evil forces he must withdraw his support from them or incur the guilt of their continuance.
Id. at 369-70, 32 S.Ct. 803.
Hyde made one definite change in the law — the prosecution no longer had to show each defendant’s participation in the conspiracy during the statute of limitations. Instead, the prosecution could prove a defendant’s membership at any time during the life of the conspiracy. It was then up to the defendant to show that he did “some act to disavow or defeat the purpose” of the conspiracy to mark his withdrawal. If his withdrawal predated the statute of limitations, he could then “claim the delay of the law.”
Hyde said nothing explicit about the amount of evidence the defendant must offer to show “some act to disavow or defeat the purpose” of the conspiracy. As one commentator noted, the Hyde language “might have been interpreted as merely shifting the production burden on the issue of withdrawal to the defendant, and leaving the persuasion burden with the state.” Developments in the Law-Criminal Conspiracy, 72 Harv.L.Rev. 920, 958 (1959). Two early cases interpreted Hyde in this manner. Mansfield v. United States, 76 F.2d 224, 229 (8th Cir.), cert. denied, 296 U.S. 601, 56 S.Ct. 117, 80 L.Ed. 425 (1935), flatly held that the burden of persuasion was on the government. The court, citing Hyde, held that the jury need only
find some evidence that would create a doubt in their minds as to whether or not the appellants remained in the scheme or conspiracy to defraud before they would be justified in acquitting them of the conspiracy on the basis of [withdrawal]. It does not relieve the government of the burden of establishing their guilt beyond a reasonable doubt.
Id. at 230. Another case, Buhler v. United States, 33 F.2d 382, 385 (9th Cir. 1929), held that implicit in the guilty verdict was a finding “beyond reasonable doubt that appellant continued to participate in the al[1235]*1235leged conspiracy” within the statutory period. Accord, United States v. Ames, 39 F.Supp. 885, 886 (S.D.N.Y.1941) (“the conscious participation of the defendant . . . within three years before the filing of the indictment [is] indispensable to the maintenance of the prosecution”).
Other cases, however, reached strikingly different conclusions. Coates v. United States, 59 F.2d 173, 174 (9th Cir. 1932), drew from Hyde’s requirement of an affirmative showing a presumption that a “conspiracy once established is presumed to continue until the contrary is established.” (Emphasis added). Accord, Marino v. United States, 91 F.2d 691, 695 (9th Cir. 1937), cert. denied, 302 U.S. 764, 58 S.Ct. 410, 82 L.Ed. 593 (1938). That Hyde set up a presumption that membership in the conspiracy continued with the conspiracy was probably a reasonable interpretation of the decision. As a slightly later case held, “abandonment will not be presumed” by lack of evidence of a defendant’s participation within the statute of limitátions period. Local 167, Int’l Bro. of Teamsters v. United States, 291 U.S. 293, 298, 54 S.Ct. 396, 398, 78 L.Ed. 804 (1934). The “some act to disavow” standard suggests that Hyde set up a rebuttable presumption. Mansfield and Buhler correctly interpreted the presumption to require the defendant to produce some evidence of withdrawal; the prosecution was then required to prove the contrary beyond a reasonable doubt. Cf. United States v. Davis, 160 U.S. at 487-88, 16 S.Ct. at 358 (requiring this order of proof in insanity defense cases). Coates and Marino, however, loosely used the term “established” to describe the defendant’s burden, although in both cases the defendant produced no evidence of withdrawal at all. Slightly later decisions built on this shakey foundation. For example, United States v. Rollnick, 91 F.2d 911, 918 (2d Cir. 1937), cited Coates for the “presumption” point and then repeated the Hyde affirmative act requirement. Again, the defendant had put on no evidence of withdrawal. Then, six years later, United States v. Cohen, 145 F.2d 82, 90 (2d Cir. 1944), cert. denied, 323 U.S. 799, 65 S.Ct. 553, 89 L.Ed. 637 (1945), cited Rollnick and the same language in Hyde but held that the defendant has “the burden of satisfying [the jury] that he had withdrawn.”
At the same time, courts grappled with the issue of what acts constituted withdrawal. Mansfield and Buhler both recognized that evidence showing the defendant’s severing of relations with the companies involved in the conspiracies created a jury issue of withdrawal. United States v. Dubrin, 93 F.2d 499, 504 (2d Cir. 1937), cert. denied, 303 U.S. 646, 58 S.Ct. 644, 82 L.Ed. 1107 (1938), ruled on similar evidence that the defendant had not shown any evidence of withdrawal. Although the defendant left the brokerage firm involved in the conspiracy more than three years prior to indictment (the then applicable statute of limitations), his departure was not sufficient to raise the withdrawal issue because it was not an affirmative act. Eldredge v. United States, 62 F.2d 449, 451 (10th Cir. 1932), went even further. It held that the defendant must show not only affirmative acts of disassociation with the conspiracy but also that these acts effectively nullified all the consequences of his previous participation. This was a requirement definitely not set forth in Hyde. Eldredge’s requirement of an effective withdrawal, however, was repeated by later cases in dicta, lending support to the idea that the defendant must create more than a doubt about his withdrawal from the conspiracy. See Note, 29 N.Y.U.L.Rev. 1470, 1473 (1954) (criticizing Eldredge as shifting the burden of proof to the defendant).
A subtle, but important, change was occurring. Within decades, the Hyde rule that a defendant show some “affirmative action” to trigger the withdrawal defense was transformed into a rule that the defendant must meet “rigorous requirements” to show his withdrawal. United States v. Borelli, 336 F.2d at 388. The Mansfield case was ignored; Buhler was distinguished on its facts. Present law now states the burden of establishing withdrawal lies on the defendant. See cases cited at n.5.
[1236]*1236The withdrawal rule is based on a misinterpretation of Hyde’s requirement that the defendant do “some act to disavow or defeat the purpose” of the conspiracy to withdraw. We have traced back the citation of authority in our own cases; they lead back to only the same language in Hyde.6
As withdrawal negates the essential element of membership, it must be disproved beyond a reasonable doubt by the government. We therefore overrule those cases imposing the burden of proving withdrawal on the defendant.7 We hold today that the burden of going forward with evidence of withdrawal and with evidence that he withdrew prior to the statute of limitations remains on the defendant. However, once he advances sufficient evidence, the burden of persuasion is on the prosecution to disprove the defense of withdrawal beyond a reasonable doubt. As in the cases of other defenses, once the jury has been instructed on the withdrawal defense, the jury should be instructed that the government bears the burden of disproving withdrawal beyond a reasonable doubt.8
B
The government argues that the failure to specifically instruct the jury of its burden to disprove withdrawal beyond a reasonable doubt was harmless error because the government’s burden was adequately [1237]*1237explained in other instructions. The trial court in fact justified his refusal of Spiegel’s instruction on this basis.9
In some circuits, failure to specifically instruct on the government’s burden of disproving defenses is reversible error per se, notwithstanding a general instruction on the government’s burden of proof. See e. g., United States v. Wolffs, 594 F.2d 77, 83 (5th Cir. 1979); Notaro v. United States, 363 F.2d 169, 176 (9th Cir. 1966); United States v. Booz, 451 F.2d 719, 723-24 (3d Cir. 1971). The newly-recommended instructions of the Seventh Circuit suggest that the jury be explicitly instructed of the burden as one of the elements of the offense in the “issues” instruction,10 or in some cases, with the instruction on the defense itself. See, e. g., Instruction 4.04, “Entrapment,” Committee on Federal Criminal Jury Instructions of the Seventh Circuit, Federal Criminal Jury Instructions of the Seventh Circuit (approved in principle by the Judicial Council of the Seventh Circuit, 1980) [West], Nevertheless, this Circuit does not impose a per se rule; we review all the instructions and the facts and circumstances of the case. United States v. Johnson, 605 F.2d 1025, 1028 (7th Cir. 1979) (en banc), cert. denied, 444 U.S. 1033, 100 S.Ct. 706, 62 L.Ed.2d 670 (1980). Our review of the evidence and the instructions convinces us that the failure to instruct here was reversible error.
The statute of limitations ran on April 24, 1974, five years before the return date of the indictment. 18 U.S.C. § 3282. The indictment charges no overt act of Spiegel after that date; the indictment alleges several “parts” of the conspiracy in April 1974, but without specific dates.11
[1238]*1238The evidence conflicted on Spiegel’s withdrawal from the conspiracy, thus making the burdens of proof more dispositive. Russell Rabjohns testified that Spiegel told him to destroy the cards used to inflate inventory and that Spiegel said there would be no inventory inflation in 1974. Tr. 1149, 1161. At trial Rabjohns placed the conversation seven to ten days before May 11, 1974; at an earlier deposition Rabjohns said this conversation took place before April 10, 1974. Tr. 628. Spiegel’s counsel impeached Rabjohns at trial by showing him that the conversation in May took place at a restaurant different from the one Rabjohns remembered and that there was an earlier lunch with Spiegel in April. Tr. 1159. Counsel also elicited testimony that the government told Rabjohns that the date of the conversation was very important. Tr. 967. All this certainly created a jury issue on the statute of limitations.
Spiegel claimed that he instituted a computer program which would improve, not worsen, inventory control. Tr. 1116. He also put on evidence that he refused to meet Read’s projections for CMH by inflating inventory. Tr. 1116-17. Bernard Magdovitz testified that he told Spiegel in early May not to destroy the cards, but Spiegel said it was none of his business. Tr. 3997. He also testified that Spiegel was terminated because he was not going to go along with more inflation. Tr. 4263.
The prosecuting attorneys put on evidence controverting Spiegel’s claims. They attempted to show that Spiegel did not withdraw, but that he was fired in May 1974 because of his role in the scheme. Tr. 3733. They showed that Spiegel’s severance agreement with Cenco was the largest in its history. Tr. 3881-83. The government claimed that the agreement was reached so that Spiegel would not destroy the phony inventory cards. Tr. 1419. The testimony at trial, however, revealed that Magdovitz was surprised when he found out, after Spiegel’s resignation, that the cards had not been destroyed. Tr. 4009, 4273. The jury could have believed no blackmail was involved.
The government further showed that Spiegel met with some of the defendants after he left Cenco. Tr. 1404. At one of the meetings, Spiegel discussed the inventory destruction plan. Tr. 4107-08. Finally, in June 1975, Spiegel appeared before the Cenco board of directors and denied any knowledge of the falsification of the financial figures within Cenco. Tr. 2255.12
The conflicting evidence demonstrates, that the erroneous instruction may have prejudiced Spiegel. The jury might have believed that Spiegel’s evidence of withdrawal had to convince them, not merely create a reasonable doubt. Bihn v. United States, 328 U.S. 633, 638, 66 S.Ct. 1172, 1174, 90 L.Ed. 1484 (1946).
The other jury instructions may have also led the jury to infer that Spiegel bore the burden of proof as to withdrawal. Although the trial court indicated that he did not wish to give instructions on the burden of proof several times, he did repeat the burden of proof as to other defendants’ defenses. For example, after summarizing the indictment, the trial court stated:
The defendants have pleaded not guilty to the charges in the indictment, and this plea puts in issue each of the essential elements of the offenses I’ll describe to you in the instructions, and imposes upon the government the burden of establishing each of these elements of proof beyond a reasonable doubt.
Tr. 5612. After briefly summarizing each defendant’s theory of defense, the court said that the jury must find “beyond a reasonable doubt” that each element of the offense challenged by the particular defendant existed.13 After describing Spie[1239]*1239gel’s defense of withdrawal, he said nothing about the burden of persuasion. Compare tr. 5615 and 5617.
Although the trial court referred to the government’s burden of proof many times in the charge, it was never mentioned in connection with withdrawal. Moreover, the withdrawal instruction itself said that the jury must find (“If you find”) that Spiegel withdrew. It did not state that the jury should acquit if they had a reasonable doubt as to his membership in the conspiracy on April 24, 1974. Tr. 5622. The “if you find” language has been found to be misleading in cases involving other defenses. See, e. g., Notaro v. United States, 363 F.2d at 173. Finally, since the jury received a copy of the instructions (a practice we endorse) they could compare and see that they were not told that the government bore the burden to disprove withdrawal.
In sum, the circumstances here demonstrate that the erroneous instruction on withdrawal was prejudicial to Spiegel. A new trial on the conspiracy count is required. Since this opinion represents a change in the law of the Circuit on the subject of withdrawal instructions, its application is prospective only.
C
We reject Spiegel’s other objections to the withdrawal instructions. Acts not alleged in the indictment may be proved to show his participation within the statute of limitations. United States v. Harris, 542 F.2d 1283, 1300 (7th Cir. 1976), cert. denied, 430 U.S. 934, 97 S.Ct. 1558, 51 L.Ed.2d 779 (1977); Worthington v. United States, 1 F.2d 154, 155 (7th Cir.), cert. denied, 266 U.S. 626, 45 S.Ct. 125, 69 L.Ed. 475 (1924). The jury was properly instructed that Spiegel had to withdraw before any act committed within the statute of limitations period. United States v. Nowak, 448 F.2d 134, 140 (7th Cir. 1971), cert. denied, 404 U.S. 1039, 92 S.Ct. 714, 30 L.Ed.2d 731 (1972).
Good faith may also be required to withdraw. The defendant must put forth some evidence of good faith, although the burden of persuasion is always on the government. United States v. Dorn, 561 F.2d at 1256; United States v. Nowak, 448 F.2d at 139.
D
Spiegel also attacks the court’s instruction on withdrawal from the securities and mail fraud charges. The judge instructed the jury on the mail fraud counts that “one can withdraw from a scheme to defraud the same way one withdraws from a conspiracy, and you know what has to be shown before you can establish that withdrawal.” Tr. 5625. Spiegel complains that the jury should have been instructed that his withdrawal was effective if he withdrew before the date of the mailings or securities transactions. We reject Spiegel’s contention for the more fundamental reason that Spiegel was not entitled to an instruction on withdrawal for the substantive offenses.
A scheme to defraud and conspiracy embrace analogous, but not identical, concepts. The primary analogy between the two crimes is evidentiary. The evidentiary rule that statements and acts of co-conspirators are relevant and admissible against other conspirators applies in mail and securities fraud cases in which an overall scheme to defraud is charged. United States v. Serlin, 538 F.2d 737, 743 (7th Cir. 1976).14
[1240]*1240The elements of the offenses are, however, different. The predicate for liability for conspiracy is an agreement, and a defendant is punished for his membership in that agreement. Mail and securities fraud, on the other hand, punish the act of using the mails or the securities exchanges to further a scheme to defraud. No agreement is necessary. A party’s “withdrawal” from a scheme is therefore no defense to the crime because membership in the scheme is not an element of the offense. Spiegel is liable for mail fraud as a principal or as an aider and abettor, not a conspirator. As an aider and abettor, Spiegel need not agree to the scheme. He need only associate himself with the criminal venture and participate in it. United States v. Beck, 615 F.2d 441, 448-49 (7th Cir. 1980).
The evidence here overwhelmingly showed Spiegel’s association and participation in the mail and securities frauds. He directed the inventory inflation scheme which largely contributed to the false statements contained in the mailings and disclosure statements. The mailings and sales were an inevitable consequence of his actions. Spiegel “could properly be found to be jointly responsible .. . for setting the scheme in motion . . . and thus causing the mailings by third parties.” United States v. Brighton Building and Maintenance Co., 598 F.2d 1101, 1104 (7th Cir.), cert. denied, 444 U.S. 840, 100 S.Ct. 79, 62 L.Ed.2d 52 (1979).
Nor is the statute of limitations implicated here. The statute of limitations begins to run from the date of the mailings or stock sales. Like a person who sets a bomb with a timed fuse, Spiegel is responsible from the moment the bomb explodes, even though all his actions occurred before the statutory period. United States v. Ashdown, 509 F.2d 793, 797-98 (5th Cir.), cert. denied, 423 U.S. 829, 96 S.Ct. 48, 46 L.Ed.2d 47 (1975). All the mailings and sales occurred within five years of the indictment, as required by 18 U.S.C. § 3282. Accordingly, the prosecution was timely. Of course, as in any prosecution, proof of conduct prior to the statute of limitations is admissible to show the scheme and intent.
Since we hold that withdrawal is not an available defense to the substantive counts, Spiegel was not entitled to an instruction regarding withdrawal. Although the court erred, Spiegel could not have been prejudiced by the giving of an instruction favorable to him. His conviction on the securities and mail fraud counts was therefore proper.
IV
Appellants’ other contentions of trial error require slight attention. No prejudicial variance arose from the government’s proof that the inventory inflation resulted in a reduction of Cenco’s loss in 1974 rather than a profit, as alleged in one paragraph of the indictment. Testimony at trial demonstrated that Cenco’s loss for 1974 would have been far greater but for the inventory inflation. Tr. 4508. The difference between a true “profit” and a reduction of loss, under the circumstances, was immaterial.
Read also complains of pre-indictment delay. He has failed, however, to prove actual prejudice from the delay. The trial court also recognized that the fraud at Cenco was vigorously pursued once uncovered and that the delay was not caused merely “to gain tactical advantage over the accused.” United States v. Marion, 404 U.S. 307, 324, 92 S.Ct. 455, 465, 30 L.Ed.2d 468 (1971).
We reject Spiegel’s challenge to the trial court’s instruction on the securities fraud counts. The language employed in the instructions properly informed the jury that the fraud had to be in connection with a securities transaction. The court instructed the jury that the third element of the offense was that “while he was a participant in the scheme he used or caused to be used the facilities of the National Securities [1241]*1241Exchange in connection with the purchase or sale of stock.” Tr. 5629-30. The judge also instructed the jury that an act done with the knowledge that the national securities exchange would be used in the ordinary course of business is one which knowingly causes the exchange to be used. Since every purchase or sale of a stock listed on an exchange is effected through the exchange, the defendants’ fraud, which was in connection with the exchange, was also in connection with the purchase or sale of stock.
The court also properly refused to instruct the jury that the defendants must have intended that their actions would influence a securities transaction. No such intent is required. United States v. Charnay, 537 F.2d 341, 352 (9th Cir.), cert. denied, 429 U.S. 1000, 97 S.Ct. 527, 50 L.Ed.2d 610 (1976).
Spiegel also complains that the court restricted his cross-examination of Bernard Magdovitz by excluding evidence allegedly showing that Magdovitz had committed improprieties at Cenco before he claimed to know about the problems at CMH. We agree that the district court correctly exercised its discretion in refusing the evidence. The judge ruled that the proffered evidence was irrelevant to the issues in the case of Magdovitz’ credibility. Magdovitz was carefully cross-examined, and the jury was given ample opportunity to test his memory truthfulness, perception, and bias. United States v. Fitzgerald, 579 F.2d 1014, 1021 (7th Cir.), cert. denied, 439 U.S. 1002, 99 S.Ct. 610, 58 L.Ed.2d 677 (1978).
E
Read contends that he was subjected to an overly broad cross-examination. He particularly objected to a line of questioning in which the government asked him whether he believed, in light of all the testimony Read heard in the trial, that there was no inventory fraud at Cenco.
Our review of the record convinces us of the propriety of the cross-examination. Read flatly denied any knowledge of any impropriety at Cenco and denied implicating conversations by other witnesses. The government’s cross-examination was aimed at testing the credibility of Read’s testimony, and Judge Crowley properly ruled the cross-examination was proper on that basis. Tr. 5101. The cross-examination was within the scope of the direct examination. Cf. Brown v. United States, 356 U.S. 148, 154-55, 78 S.Ct. 622, 626, 2 L.Ed.2d 589 (1958).
F
Spiegel and Read also contend that juror misconduct requires reversal. Before the jury began its third day of deliberations, a juror delivered a letter to the district court. According to the letter, most of the jurors made up their minds by the second week of trial (the trial lasted at least seven weeks); many completely disregarded the judge’s instructions that the jurors not look in the newspaper financial sections and made a point of examining Cenco stock; many of these jurors refused to deliberate or discuss the case, claiming “all these guys are guilty,” and instead worked on crossword puzzles, and several of the jurors thought the whole trial was hilarious and laughed at the attorneys.
Judge Crowley denied defendants’ motion for mistrial based on the alleged misconduct. Instead, Judge Crowley read the jury an additional cautionary instruction after receipt of the letter. He also interviewed the juror who wrote the letter after the verdict was delivered. She said that “the change was incredible [after the judge gave the additional instruction] . . . the people that were so irate actually, you know, started to come around and everything.” Tr. Oct. 29, 1979 at 3.
Judge Crowley properly exercised his discretion in responding to. the allegations. He was in “the best position to sense the atmosphere of the courtroom as no appellate court can on a printed record.” United States v. Barnes, 604 F.2d 121, 144 (2d Cir. [1242]*12421979), cert. denied, 446 U.S. 907, 100 S.Ct. 1833, 64 L.Ed.2d 260 (1980). It was not error to deny the motion for a mistrial.
G
Since a new trial is necessary for Spiegel, we need not address Spiegel’s contentions regarding Rabjohns’ alleged change in testimony.
We affirm the judgment of convictions of Read and Swiger entered in numbers 80-1017 and 80 — 1019. We reverse Spiegel's conviction on Count I in 80-1018 and remand for a new trial; we affirm his conviction on the remaining counts.
No. 80-1017 — Affirmed;
No. 80-1018 — Affirmed In Part, Reversed And Remanded In Part;
No. 80-1019 — Affirmed.