The defendants, Albert Edwards and S. Frank Edwards, were convicted of violating 26 U.S.C. § 7203 by willfully failing to register for and pay the gambling tax as required by 26 U.S.C. §§ 4411, 4412.1 On appeal, this Court by a majority vote reversed the judgments of conviction for lack of proof that the defendants had knowledge of the law. 321 F.2d 324. The case is now before the Court en banc on a petition for rehearing filed by the United States.2
The crucial questions presented are: (1) Was there sufficient evidence that defendants loillfully failed to register for *363and pay the gambling tax? (2) Was the district court’s charge 3 that the defendants are presumed to have known the law erroneous? (3) If the charge as given was erroneous, was it such “plain error” as to call for a reversal?4 We answer the first question in the affirmative, the second in the negative but with a slight reservation on the charge as given, and the third in the negative. The result is that we affirm the judgments of conviction.
The defendants were allegedly engaged in a lottery operation, called Cuba or bolita, conducted from a house admittedly owned by defendant Frank Edwards. A search of the house under a search warrant disclosed the paraphernalia used in such lottery operations: memo pads, adding machine tapes, tally sheets or recap sheets of sellers or pickup men, cards used to notify buyers of the winning number, a short-wave radio, and a telephone listed in the name of Frank Edwards. A qualified expert on bolita operations testified to the necessity of keeping on hand a large amount of cash. When Frank Edwards was arrested at the Green Palace Bar, which is in front of the house from which the lottery was conducted, he had in his pocket $71.47 and in a bag on his person $1,091.47. There was considerable testimony about a five-gallon can which Frank Edwards had on occasions carried. The can filled with various lottery paraphernalia was found under the house next door to that from which the operations were conducted. Frank Edwards had been observed meeting various persons in the parking lot behind the Green Palace Bar and accepting packages from them; he had been observed going in and out of the house where the lottery was conducted. He was also seen carrying paper sacks under his shirt and retrieving sacks left for him in the mail box.
Two paid informers had purchased bo-lita tickets from Albert Edwards in the Green Palace Bar, and had seen other persons making similar purchases from him. Frank Edwards at the time of his arrest admitted ownership of the house, but claimed that it was rented out, although he refused to reveal to whom it was rented. Frank had been arrested for a bolita offense in 1949. Both defendants testified at the trial and denied being in the bolita business. Neither of the defendants stated whether or not he was *364aware of the duties imposed by the gambling tax.
The majority of the original panel took the Government’s position to be that ignorance of the law is no defense in a prosecution for willful failure to register for and pay the federal wagering tax. Accordingly, the majority opinion was primarily concerned with showing that “willfulness” requires knowledge of the law. The concurring opinion 5 and footnote 3 of the majority opinion 6 indicated that the Government has the burden of proving knowledge and that there is no presumption that the defendants knew of the wagering tax requirements. The dissent7 contended that some presumption of knowledge does exist.
On petition for rehearing the Government has conceded that since the misdemeanor includes the element of willfulness ignorance of the law is a defense, but contends that there was no evidence of such ignorance and there was sufficient evidence that the defendants knew the law so as to support the jury verdicts. In reviewing the sufficiency of the evidence, this Court must view the evidence in the light most favorable to the prosecution and permissible inferences supporting its case must be so drawn. Accordingly, the first issue to be decided is whether there is evidence from which the jury could have inferred beyond a reasonable doubt8 that the defendants had knowledge of the duties imposed upon them by the wagering tax statutes. If so, since the evidence eon.clusively establishes that the defendants failed both to register for and to pay the tax, the test of willfulness is met. As said in Spies v. United States, 1943, 317 U.S. 492, 497, 498, 63 S.Ct. 364, 367, 87 L.Ed. 418:
“The difference between willful failure to pay a tax when due, which is made a misdemeanor, and willful attempt to defeat and evade one, which is made a felony, is not easy to detect or define. Both must be willful, and willful, as we have said, is a word of many meanings, its construction often being influenced by its context. United States v. Murdock, 290 U.S. 389 [54 S.Ct. 223, 78 L.Ed. 381], It may well mean something more as applied to nonpayment of a tax than when applied to failure to make a return. Mere voluntary and purposeful, as distinguished from accidental omission to make a timely return might meet the test of willfulness. But in view of our traditional aversion to imprisonment for debt, we would not without the clearest manifestation of Congressional intent assume that mere knowing and intentional default in payment of a tax where there had been no willful failure to disclose the liability is intended to constitute a criminal offense of any degree. We would expect willfulness in such a case to include some element of evil motive and want of justification in view of all the financial circumstances of the taxpayer.” (Emphasis supplied.)
In the instant case there is no direct proof that the defendants knew of the duties imposed by the federal gambling tax statute — they neither admitted nor denied such knowledge, and there was no evidence that they had been warned of their obligation or that they had previously paid the tax. But knowledge of the law, a state of mind, may be proved by circumstantial evidence.9
What circumstantial evidence will permit an inference of knowledge in wagering tax cases? We believe the answer lies in Ingram v. United States, 1959, 360 U.S. 672, 79 S.Ct. 1314, 3 L.Ed.2d 1503. In that case two defendants, Ingram and *365Jenkins, were convicted of conspiring to evade and defeat the wagering tax and of willfully failing to register for and pay the tax. Two other defendants, Smith and Law, although not required by law to pay the tax since they were neither “writers” nor “bankers,” were nevertheless convicted of conspiracy to attempt to evade or defeat the tax. The defendants had been engaged in a closely organized and large-scale operation of a numbers game in violation of state law from 1954 to 1957. They made every effort to conceal the operation — e. g., they used false license plates, evasive routes, and false names and even attempted bribes. The Supreme Court noted: “There was no direct evidence to show that any of the petitioners knew of these taxes.” 10 The Court held that there was sufficient evidence to support the convictions of Ingram and Jenkins. As to Smith and Law, the Court held that there was no evidence to indicate that they knew that Ingram and Jenkins had not paid these taxes, and without such knowledge Smith and Law could not have conspired to evade the tax. A minority of the Court dissented as to Ingram and Jenkins, being of the opinion that mere concealment should not be enough to infer knowledge that a tax is imposed.11
In the instant case, the defendant Frank Edwards was arrested for a bolita offense as far back as 1949.12 He purportedly had rented the house to someone else; whereas, in fact, he used it to carry out his gambling operation. He accepted packages at night in the parking lot behind the bar, hid the can containing lottery paraphernalia under the house next door, carried paper sacks under his shirt, and retrieved paper sacks left for him in the mail box.13 This long experience in the lottery business and concealment of operations is enough under the Ingram case to allow the jury to infer that Frank Edwards was aware of the wagering tax.14
While the circumstantial evidence against Albert is not as strong as that against Frank, Albert was a “writer” and is Frank’s son, so that the jury could reasonably infer that Albert knew of the law himself or that Frank passed this knowledge on to him. As to Albert, however, a close question is presented as to whether this inference could be drawn beyond a reasonable doubt as required by Riggs, n. 8, supra, and we prefer to *366base our decision on our holding, hereafter elaborated, that the evidence from which the jury might draw the inference of knowledge of the law is aided or supplemented by a rebuttable presumption that the defendants knew the law.
In determining the correctness vel non of the court’s charge, n. 3, supra, it is important to note the distinction between an “inference” and a “presumption.” Professor Morgan has defined an inference as follows:
“If the court means that when [basic fact] A is established in the action, the existence of [presumed fact] B may be deduced by the operation of the ordinary rules of reasoning, it sometimes says that the trier of fact may presume the existence of B if it finds A. The presumption is said to be one of fact, and careful judges and writers insist that the proper term is ‘inference’ rather than ‘presumption.’ ” 15
On the other hand, he defines a rebutta-ble presumption as follows:
“Thayer, Wigmore, the American Law Institute, and commentators generally have argued, and many courts have agreed, that the term ‘presumption’ should be used only to mean that when A is established in an action, the existence of B must be assumed unless and until a specified condition is fulfilled.” 16
“Presumption” itself is a word of several meanings. It is often stated that every person is “presumed” to know the law. This “conclusive presumption” is merely a restatement of the substantive rule that ignorance of the law is not a defense; accordingly, many writers object to treating this as a rule of evidence.17 Of course, in cases such as the instant one, where ignorance of the law is a valid defense, the rule has no application.18 Here, the defendants are charged with the violation of a statute which makes criminal the willful failure to comply with specific duties imposed by statute. The problem is whether the jury should have been instructed in terms of an inference or a rebuttable presumption.
Where knowledge of certain facts is an essential element of a crime, the burden of going forward with the evidence on this issue is sometimes placed on the defendant if the matter is peculiarly within his own knowledge. See Crapo v. United States, 10 Cir. 1939, 100 F.2d 996, 1001; 1 Wharton, Criminal Evidence §§ 109, 14 (12th ed. 1955). This principle was extended in Blumenthal v. United States, 8 Cir. 1937, 88 F.2d 522, so as to hold that there was a presumption that the defendant had knowledge of a statute imposing a duty to act. The offense charged was knowingly transporting alcohol which was not labeled in ac*367cordance with the statute. The court said:
“It is elementary that every one is presumed to know the law of the land, whether that be the common law or the statutory law, and hence, one’s ignorance of the law furnis"hes no defense for criminal acts, and this rule applies whether the crime charged is malum prohibitum or malum in se. * * *
“Assuming, without deciding, that the presumption was a rebuttable one, it is to be observed that the defendants introduced no evidence in an attempt to rebut the presumption. The corpus delicti having been established, and the government having thus proved a prima facie case, the burden of adducing evidence to rebut the presumption shifted to the defendants. The matter was peculiarly within their knowledge. Agnew v. United States, 165 U.S. 36, 17 S.Ct. 235, 41 L.Ed. 624.” 19
The Blumenthal case was followed in Cruz v. United States, 10 Cir. 1939, 106 F.2d 828, 830, where Judge Phillips said:
“Furthermore, if there was a want of knowledge as to the existence of Section 12 on the part of the defendants, that was a fact peculiarly within their knowledge, and when the government established a prima facie case, the burden of adducing evidence to rebut the presumption of such knowledge rested on the defendants. Blumenthal v. United States, supra [8 Cir. 1937, 88 F.2d 522, 530]; Crapo v. United States, 10 Cir., 100 F.2d 996, 1001, and cases cited in note 4.”
Professor Perkins has agreed:
“But in those exceptional situations in which ignorance of the law is an excuse, the case will still be decided as if the law had been known unless the defendant comes forward with evidence to show that he did not know. Stated differently, knowledge of the law is presumed; in most cases this presumption is conclusive but under exceptional circumstances it is disputable.” 20
Professor Hall has stated:
“It seems necessary to retain the presumption that there was such knowledge [of the law], allowing the defendant to introduce evidence tending to prove his ignorance or mistake of the law, but placing the final burden of proving mens rea, in the above sense, upon the state.” 21
Where the law is plain, definite, and well settled, and any want of knowledge of its requirements is a fact resting peculiarly within the knowledge of the defendants, when the Government has established its case in all other respects, the burden of adducing some evidence to rebut the presumption of such knowledge rests on the defendants. A mental state being involved, the presumption of knowledge of the law is analogous to the presumption of sanity as to which the Supreme Court said in Davis v. United States, 1895, 160 U.S. 469, 487, 488, 16 S.Ct. 353, 358, 40 L.Ed. 499.
“ * * * In a certain sense it may be true that where the defence is insanity, and where the case made by the prosecution discloses nothing whatever in excuse or extenuation of the crime charged, the accused is bound to produce some evidence that will impair or weaken the force of the legal presumption in favor of sanity. But to hold that such presumption must absolutely control the jury until it is overthrown or impaired by evidence sufficient to es*368tablish the fact of insanity beyond all reasonable doubt, or to the reasonable satisfaction of the jury, is in effect to require him to establish his innocence by proving that he is not guilty of the crime charged.
“ * * *
“Strictly speaking, the burden of proof, as those words are understood in criminal law, is never upon the accused to establish his innocence or to disprove the facts necessary to establish the crime for which he is indicted. It is on the prosecution from the beginning to the end of the trial and applies to every element necessary to constitute the crime. Giving to the prosecution, where the defence is insanity, the benefit in the way of proof of the presumption in favor of sanity, the vital question from the time a plea of not guilty is entered until the return of the verdict, is whether, upon all the evidence, by whatever side adduced, guilt is established beyond reasonable doubt. If the whole evidence, including that supplied by the presumption of sanity, does not exclude beyond reasonable doubt the hypothesis of insanity, of which some proof is adduced, the accused is entitled to an acquittal of the specific offence charged.” 22
The charge of the district court as given, n. 3, supra, as applied to the plain, definite and well-settled law here involved, would have been more accurate if, instead of the phrase, “unless and until outweighed by evidence to the contrary,” it had used some such expression as “unless the defendants produce some evidence to the contrary.” 23 If the failure. so to word the charge was error, it was not such plain error as to require a reversal (see n. 4, supra); because, in the light of the fact that the defendants produced no evidence whatever to the contrary, the failure to use the more accurate expression did not affect the defendants’ substantial rights.
For the reasons stated, the judgments of conviction are
Affirmed.
. Ҥ 4411. Imposition of tax
“There shall be imposed a special tax of $50 per year to be paid by each person who is liable for tax under section 4401 or who is engaged in receiving wagers for or on behalf of any person so liable.”
Ҥ 4412. Registration
“ (a) Requirement. — Each person required to pay a special tax under this subchapter shall register with the official in charge of the internal revenue district _* *
Ҥ 7203. Willful failure to file return, supply information, or pay tax
“Any person required under this title to pay any estimated tax or tax, or required by this title or by regulations made under authority thereof to make a return (other than a return required under authority of section 6015 or section 6016), keep any records, or supply any information, who willfully fails to pay such estimated tax or tax, make such return, keep such records, or supply such information, at the time or times required by law or regulations, shall, in addition to other penalties provided by law, be guilty of a misdemeanor and, upon conviction thereof, shall be fined not more than $10,000, or imprisoned not more than 1 year, or both, together with the costs of prosecution.”
. Judge Hays, the organ of the Court on the original opinion, is a judge of the Second Circuit who was sitting by designation. Judge Cameron, who concurred with Judge Hays, died on April 5, 1964, after a rehearing en banc was ordered but before the ease was orally argued and submitted on rehearing. Thereafter I asked the advice of my brothers, stating to them that “since neither Judge Hays nor Judge Cameron can participate in the en banc rehearing on Monday, May 11, it seems to me that to insure complete fairness to both sides, and especially the appearance of fairness to the appellants, I should recuse myself and let this ease be considered and decided by the remaining active judges of the Circuit.”
Chief Judge Tuttle and Judges Jones, Brown and Gewin advised that I should sit, and Judge Bell advised that he agreed with my tentative view but did not think it inappropriate for me to sit. I did not hear from Judges Hutcheson and Wisdom.
After such study as I could give the matter, I reached the conclusion that whether a judge should recuse himself in a particular case depends not so much on his personal preference or individual views as it does on the law, and that, under the law, I have no choice in this case.
It is a judge’s duty to refuse to sit when he is disqualified but it is equally his duty to sit when there is no valid reason for recusation. Banco Nacional de Cuba v. Sabbatino, 2d Cir. 1962, 307 F.2d 845, 860, reversed on the merits by Supreme Court on March 23, 1964, 376 U.S. 398, 84 S.Ct. 923, 11 L.Ed.2d 804; United States v. Valenti, D.C.N.J.1954, 120 F.Supp. 80, 92 ; 48 C.J.S. Judges § 93a. If a party is dissatisfied and makes timely objection, a judge’s decision to refuse to act on a case is subject to review. Medlin v. Taylor, 1893, 101 Ala. 239, 13 So. 310; 48 C.J.S. Judges § 93b. The only two statutes on disqualification which I found are §§ 47 and 455 of Title 28, United States Code, neither of which would appear to have any application to my situation. Judges sit as a matter of *363course on reliearings of their own decisions. See 30A Am.Jur. Judges, § 185. If either or both of the other judges who participated in the original decision could sit on the en banc rehearing there could be no question that I must also sit. While their absence makes me prefer not to sit, I have not found that it furnishes me any legal excuse.
A court en bane consists of “all active circuit judges of the circuit,” 28 U.S.C. § 46(c). In the absence of a valid legal reason,. I have no right to disqualify myself and must sit.
. In its oral charge, the district court instructed the jury as follows:
“Now, you will note that the omission or failure to act charged in the information is alleged to have been willfully done. A failure to act is willfully done if done voluntarily and purposely and with a specific intent to fail to do wdiat the law requires to be done. That is to say, with that purpose either to disobey or disregard the law.
“It is not necessary for the prosecution to pz'Ove knowledge of the accused that a particular act or failure to act is a violation of law unless and until outweighed by evidence to the contrary. The presumption is that every person knows what the law forbids and what the law requires to be done.”
. See Rule 52(b), Fed.R.Crim.P. The district court, at the conclusion of its oral charge, complied strictly with Rule 30, Fed.R.Crim.P., as shown by the following colloquy:
“THE COURT: In the absence of the Jury and at the conclusion of the Court’s Oral Charge to the Jury, does the Government have any objections or exceptions to the Oral Charge as given?
“MR. HANLON: No, Your Honor. The Government has no objections or exceptions.
“THE COURT: In the absence of the Jury and at the conclusion of the Court’s Oral Charge to the Jury, do the defendants have any objections or exceptions to the Oral Charge as given?
“MR. LEE: No, sir.”
. 321 F.2d at 327.
. 321 F.2d at 326-327, n. 3.
. 321 F.2d at 327.
. See Riggs v. United States, 5 Cir. 1960, 280 F.2d 949, 955.
. Cf. Gaunt v. United States, 1 Cir. 1950, 184 F.2d 284, 290; Battjes v. United States, 6 Cir. 1949, 172 F.2d 1, 5; 10 Mertens, Federal Income Taxation § 55A.-09 at n. 13 (1958).
. 360 U.S. at 674, 79 S.Ct. at 1317.
. 360 U.S. at 682, 79 S.Ct. at 1321.
. On cross-examination, Frank Edwards testified:
“Q. Is it your testimony here today that you have never engaged in the bolita business ?
“A. That’s right.
“Q. Ever; is that correct?
“A. (No response.)
“Q. Is that your testimony today, Mr. Edwards ?
“A. I am trying to think back.
“Q. You are under oath, and I want you to take your time and reflect.
“A. Yes. Back in ’49, I think it was.
“Q. You were in the bolita business?
“A. I got arrested.
“Q. You were here in the Courtroom and heard various witnesses testify that you were delivered sacks of I don’t know what. What is your statement with respect to those sacks that they discussed as being delivered to you by various people?
“A. My s tatement is that I didn’t receive any sacks from no one.”
. It is interesting to note that in 1953 the Florida Legislature passed a statute making the possession of or payment for a federal wagering tax stamp prima facie evidence of violation of the Florida gambling law. In 1954, however, the Florida Supreme Court held this statute to be unconstitutional. Jefferson v. Sweat, 1954 Fla., 76 So.2d 494, 498-501 (opinion on rehearing).
. In United States v. McGonigal, D.Del. 1963, 214 F.Supp. 621, the court entered a judgment of acquittal for lack of proof that the defendant knew of the necessity of purchasing a gambling tax stamp; but the court carefully pointed out that this defendant had not engaged in the activity for a persistent or long-drawn-out time, associated frequently with known gamblers, nor engaged in deliberate acts of concealment.
. 1 Morgan, Basic Problems of Evidence 31 (1961).
. 1 Morgan, Basic Problems of Evidence 32 (1961). Professor Wigmore has warned against confusing a presumption with an inference:
“So long as the law attaches no legal consequences in the way of a duty upon the opponent to come forward with contrary evidence, there is no propriety in applying the term ‘presumption’ to such facts, however great their probative significance.” 9 Wigmore, Evidence 288 (1940).
The distinction between inference and presumption was recognized by this Court in Barfield v. United States, 5 Cir. 1956, 229 F.2d 936, 940, and Mann v. United States, 5 Cir. 1963, 319 F.2d 404, 409.
. See 1 Jones, Evidence § 11 (5th ed. 1958); 1 Wharton, Criminal Evidence § 107 at 215 (12th ed. 1955); 1 Wharton, Criminal Law & Procedure § 162 (Anderson ed. 1957). Professor Hall has stated: “In such cases, which include the common law felonies and the more serious misdemeanors, instead of asserting that knowledge of law is presumed, it would be much more to the point to assert that knowledge of law (equally, ignorance or mistake of law) is wholly irrelevant.” Hall, Ignorance and Mistake in Criminal Law, 33 Ind.L.J. 1, 20 (1957).
. See Hargrove v. United States, 5 Cir. 1933, 67 F.2d 820, 90 A.L.R. 1276; Wardlaw v. United States, 5 Cir. 1953, 203 F.2d 884, 885.
. 88 F.2d at 530.
. Perkins, Ignorance and Mistake in Criminal Law, 88 U.Pa.L.Rev. 35, 38-39 (1939).
. Hall, Ignorance and Mistake in Criminal Law, 33 Ind.L.J. 1, 36-37 (1957). See also Ford v. United States, 9 Cir. 1926, 10 F.2d 339, 349, aff’d 1927, 273 U.S. 593, 47 S.Ct. 531, 71 L.Ed. 793; Underhill’s Criminal Evidence, 4th ed., sec. 45, p. 57.
. See also Howard v. United States, 5 Cir. 1956, 232 F.2d 274, 276; Carter v. United States, 5 Cir. 1963, 325 F.2d 697.
. In cases of this kind where the defendant produces some evidence of ignorance of the law no charge on presumption of knowledge of the law would ordinarily be needed, and it might then contribute to clarity simply to charge the jury on the usual burden of proof.