
585 P.2d 197 (1978)
In the Matter of Jeff Clements, pupil.
Jeff CLEMENTS, Appellant (Petitioner below),
v.
BOARD OF TRUSTEES OF SHERIDAN COUNTY SCHOOL DISTRICT NO. 2, IN the COUNTY OF SHERIDAN, State of Wyoming, Appellee (Respondent below).
No. 4920.
Supreme Court of Wyoming.
September 6, 1978.
*198 Timothy S. Tarver and Kim D. Cannon, of Burgess & Davis, Sheridan, for appellant.
William K. Archibald, of Holstedt & Archibald, Sheridan, for appellee.
Before GUTHRIE, C.J., and McCLINTOCK, RAPER, THOMAS and ROSE, JJ.
*199 ROSE, Justice.

NATURE OF THE CASE
This is an appeal from an order of the District Court for the Fourth Judicial District, Sheridan County, Wyoming, which was entered January 19, 1978, affirming an order dated December 21, 1977, made and entered by the Board of Trustees of Sheridan County School District No. 2, Sheridan County, Wyoming. The Board's order, affirmed by the district court, directed that appellant, Jeff Clements, be suspended from Sheridan High School for a period of ten days and that he be placed on probation for the remainder of the 1978-1979 school year. We will affirm.

DISPOSITION BY THE BOARD AND DISTRICT COURT
The appellant was charged by the School Board with harassing a school bus. Shortly after the incident occurred, the Wyoming Highway Patrol issued traffic citations charging Sheridan High School students Chris Sutton and appellant-Jeff Clements with reckless driving.
Sutton and Clements were tried separately on reckless-driving charges in the Justice of the Peace Court, with Sutton being convicted and Clements acquitted. Following this, the Board of Trustees notified Clements that there would be a public hearing held for the purposes of determining whether or not he should be expelled from school on account of
"behavior clearly detrimental to the safety of other pupils, in that he did on or about the 2nd day of September, 1977, purposely operate a vehicle to hazard and harass School Bus No. 15, of Sheridan County School District No. 2, while it was proceeding from Story, Wyoming, to Sheridan, Wyoming, transporting students to school; and that the said student [Clements] did operate a motor vehicle in such manner as to pass in front of the school bus and prevent it from proceeding at a normal speed, prevent it from passing, and did otherwise purposely distract the driver, thereby endangering the students aboard said bus, and did impede the normal progress of said bus."
Clements moved to vacate the Notice of Hearing, but this motion was denied and a public hearing was held.
The statutory authority for disciplining a student is § 21-4-305(a)(d) and (e), W.S. 1977, which, in part, provides:
"(a) The board of trustees of any school district may delegate authority to disciplinarians chosen from the administrative and supervisory staff to suspend any student from school for a period not to exceed ten (10) school days.
* * * * * *
"(d) The board of trustees of any school district may suspend a student for a period exceeding ten (10) school days or may expel a student for a period not to exceed one (1) school year, provided the student is afforded an opportunity for a hearing in accordance with the procedures of the Wyoming Administrative Procedure Act [§§ 9-4-101 to 9-4-115]:
"(e) Suspension or expulsion shall not be imposed as an additional punishment for offenses punishable under the laws of the state, except where the offense was committed at a school function or is of such nature that continuation of the child in school would clearly be detrimental to the education, welfare, safety or morals of other pupils. No suspension or expulsion shall be for longer than one (1) school year.",
and § 21-4-306(a)(iii), W.S. 1977, which provides in part:
"(a) The following shall be grounds for suspension or expulsion of a child from a public school during the school year:
* * * * * *
"(iii) Any behavior which in the judgment of the local board of trustees is clearly detrimental to the education, welfare, safety or morals of other pupils;"
The tapes from the Justice of the Peace proceeding were erased and the tapes from the Board hearing are inaudible; therefore, *200 the only evidence of record for our consideration comes from depositions and stipulation. When the evidence had been presented, the Board of Trustees convened in executive session where it authored findings of fact and conclusions of law, which, in relevant part, are:
"1. That Jeff Clements is a student at Sheridan High School, School District No. 2.
"2. That on the 2nd day of September, 1977, the said Jeff Clements, while driving a Jeep vehicle did pass School Bus No. 15 of Sheridan County School District No. 2 at the stop sign at the Highway 87-Story Road Junction without stopping himself; and did operate said Jeep vehicle just ahead of School Bus No. 15 from said junction to just South of the `Maverick Road' turn-off at a speed of from 35 to 40 miles per hour, so as to purposely impede the progress of said School Bus on said highway in a 55 mile per hour zone.
"3. That in concert with one Chris Sutton, who was driving a pickup truck, the said Jeff Clements did by his actions create a dangerous situation for the pupils aboard said bus in that the slow driving of Jeff Clements resulted in disruption to to [sic] the environment on the bus, and his driving conduct created a distraction to the bus driver, which was conducive to a situation hazardous to the normal well-being of the students on the bus."
As matters of law, the Board concluded:
"That Jeff Clements had been guilty of behavior which in the judgment of the Board is clearly detrimental to the welfare and safety of other pupils who were passengers on the bus [§ 21-4-306(a)(iii) language] and without punishment therefor his continuation in school would be clearly detrimental to the welfare and safety of other pupils." [§ 21-4-305(e) language] [Bracketed material ours]
On December 21, 1977, the Board ordered appellant-Clements suspended from school for ten days and placed on probation for the remainder of the school year. On December 22, 1977, the student filed a petition for review with the District Court for the Fourth Judicial District, seeking review of the Board of Trustees' order. Clements again raised the double-jeopardy and due-process issues and, in addition, questioned whether the Board's Findings of Fact and Conclusions of Law were supported by substantial evidence. The district court affirmed the decision of the Board of Trustees, and timely appeal has been taken, pending which the district court has stayed the Board's suspension order.
Appellant identifies for us these following issues on appeal:
I. "Did the Board of Trustees violate Appellant Clements' rights under the Double Jeopardy Clause of the Fifth Amendment to the United States Constitution?"
II. "Is W.S. 1957, § 21.1-62(c) (Cum. Supp. 1975) [§ 21-4-306(a)(iii), W.S. 1977] void for vagueness under the Due Process Clause of the Fourteenth Amendment to the United States Constitution?"
III. "Did the Board of Trustees err in suspending Appellant Clements from school for ten days placing him on probation for the remainder of the school year when there was no evidence that his continuation in school would clearly be detrimental to the welfare, safety and morals of other pupils?"

FACTS
The relevant facts gleaned from the only evidence of record, which appear in the form of depositions taken of the two school employees and the stipulation of the parties, are these: Highway 87 runs north and south between Buffalo and Sheridan, Wyoming, and there is a minimum of four rather long, steep hills on this particular stretch of highway, and eight hills altogether with double lines on each side of and including their crests.
In this area, on the morning of September 2, 1977, appellant, Jeff Clements, with David Teigland as his passenger, was driving his Jeep vehicle from his home in Story *201 to High School in Sheridan, where both boys are students. School Bus No. 15, carrying its usual load of student passengers, and being operated by Mr. Glen Canfield and monitored by Jerry Willette, employees of School District No. 2, was also proceeding from Story to Sheridan, as was a pickup truck driven by High School student Chris Sutton and carrying an unidentified passenger (or passengers).
Where the Story highway and Highway 87 intersect, the School bus had stopped at a stop sign when, without stopping, Clements drove his Jeep around the left side of the bus at a speed approximating 30 miles per hour. The three vehicles thereafter proceeded onto Highway 87, traveling north toward Sheridan. Appellant Clements was in the lead in his Jeep; School Bus No. 15 was second; and the Sutton pickup brought up the rear. The evidence most unfavorable to the appellant  and that which the Board had a right to consider  was given by Howard Willette, the monitor-employee of School District No. 2, who was that morning riding in the rear of the bus. His testimony included such assertions as:
"Ralph (Clements) slowed right up and almost brought us to a stop." [Parenthetical matter supplied]
Willette also testified that going up one of the hills:
"I wouldn't say he was going over fifteen or 20 miles an hour there."[1]
At one point, Willette says the Jeep slowed down, then speeded up, then slowed down, and then speeded up  "[J]ust about drove you out of your mind the way they were doing it." Further, the witness says that in reaction to the Jeep's slowing down and speeding up, the bus driver was having to apply his brakes pretty hard. Willette also testified as follows:
"Q. Did the bus try to pass the Jeep there while the pickup was still behind?
"A. There was one place along there that he tried to pass and the Jeep would speed up and wouldn't let him pass, but I can't remember if that was on this side of the fourth hill or back between the third and fourth, I can't recall that.
"Q. Did he pull over into the left lane or did he just pull up behind and try to catch up?
"A. No, he pulled out in the left lane to pass and then the Jeep would just speed up, so he would just fall back behind."

SUFFICIENCY OF THE EVIDENCE
It was Clements' burden to prove the insufficiency of the evidence to sustain the Board's decision. Board of Trustees, Laramie County School District No. 1 v. Spiegel, Wyo., 549 P.2d 1161. See, also, Adams v. Campbell County School District, 10 Cir.1975, 511 F.2d 1242; Smith v. Losee, 10 Cir.1973, 485 F.2d 334; and Fluker v. Alabama State Board of Education, 5 Cir.1971, 441 F.2d 201.
Upon review, the district court was charged with the duty of determining whether there was sufficient evidence to support the Board's findings and conclusions of law. § 9-4-114(c)(iv), W.S. 1977 [§ 9-276.32(c)(iv), W.S. 1957, 1975 Cum. Supp.].
In Board of Trustees v. Spiegel, supra, we asked the question,
"What, then, is `substantial evidence' ...?",
and answered it this way:
"It was said in Bortz Coal Co. v. Air Pollution Commission, 2 Pa.Cmwlth. 441, 279 A.2d 388, 397, 48 A.L.R.3d 311, 322:
"`... "Substantial evidence" is such relevant evidence as a reasonable mind might accept as adequate to support a conclusion, and more is required than a mere scintilla of evidence or suspicion of the existence of a fact to be established. See Pennsylvania State Board of Medical Education and Licensure v. Schireson, 360 Pa. 129, 61 A.2d 343 (1948); Erie Resistor Corporation *202 v. Unemployment Compensation Board, 194 Pa.Super. 278, 166 A.2d 96 (1960).'
"The test as to whether or not there is substantial evidence has been said to be
"`... whether the administrative decision finds reasonable support in substantial evidence, whether the evidence reasonably tends to support the findings, or, it has been indicated, whether the decision is not clearly contrary to the overwhelming weight of the evidence.' 2 Am.Jur.2d Administrative Law § 688. `What constitutes substantial evidence.', p. 574. (With extensive footnote citations)
"In interpreting the term `substantial evidence' as contemplated by the Federal Administrative Procedure Act the United States Supreme Court, in Consolo v. Federal Maritime Commission, 383 U.S. 607, 86 S.Ct. 1018, 1026, 16 L.Ed.2d 131, said:
"`... We have defined "substantial evidence" as "such relevant evidence as a reasonable mind might accept as adequate to support a conclusion." Consolidated Edison Co. of New York v. National Labor Relations Board, 305 U.S. 197, 229, 59 S.Ct. 206, 217, 83 L.Ed. 126. "[I]t must be enough to justify, if the trial were to a jury, a refusal to direct a verdict when the conclusion sought to be drawn from it is one of fact for the jury." National Labor Relations Board v. Columbian Enameling & Stamping Co., 306 U.S. 292, 300, 59 S.Ct. 501, 505, 83 L.Ed. 660. This is something less than the weight of the evidence, and the possibility of drawing two inconsistent conclusions from the evidence does not prevent the administrative agency's finding from being supported by substantial evidence. National Labor Relations Board v. Nevada Consolidated Copper Corp., 316 U.S. 105, 106, 62 S.Ct. 960, 961, 86 L.Ed. 1305; Keele Hair & Scalp Specialists, Inc. v. FTC, 5 Cir., 275 F.2d 18, 21.'" 549 P.2d at 1178.
We said in Howard v. Lindmier, 67 Wyo. 78, 214 P.2d 737, 740:
"... [T]he term `substantial evidence' does not include the idea of weight of evidence, although it is more than a mere scintilla and means such relevant evidence as a reasonable mind might accept as adequate to support a conclusion... ."
We hold that on the basis of this record there was substantial evidence  regardless of the failure to show concert of action with the pickup[2]  which would permit the Board to conclude that Clements operated his vehicle so as to "purposely impede the speed" of the bus. There was also uncontradicted testimony that he drove the Jeep around the bus, at a speed of 30 miles per hour, while it was stopped at a stop sign.
Appellant seems to place primary reliance on the absence of evidence that his continuation in school would clearly be detrimental to the welfare, safety and morals of the other pupils. While we agree with this conclusion, it is, nevertheless, true that an inquiry into the presence of such evidence is appropriate only if the provisions of § 21-4-305(e), supra, are applicable to this case. In order to trigger the need to satisfy the exceptions contained in § 21-4-305(e), supra, the suspension or expulsion envisioned must fall within the parameters of "additional punishment for offenses punishable under the laws of the state." Clements' *203 conduct potentially fell within the category of "offenses punishable under the laws of the state." For example, § 31-5-304(a), W.S. 1977, provides
"No person shall drive a motor vehicle at such a slow speed as to impede the normal and reasonable movement of traffic... ."
The record discloses, however, that Clements was found not guilty of charges connected with this incident. There was, therefore, no punishment for offenses punishable under state laws. We are unable to conclude  under the clear language of § 21-4-305(e), supra  that the appellant's suspension was imposed as additional punishment. The statute does not apply and, therefore, there is no need to search the record for evidence to support an exception to the statutory bar of multiple punishments.

DOUBLE JEOPARDY
Appellant concedes in his brief that "the double jeopardy clause only prohibits imposition of two sanctions if both sanctions are punitive," but contends that the disciplinary suspension herein was punitive and not remedial. We find that appellant's contention is satisfactorily answered by the discussion in Paine v. Board of Regents of the University of Texas System (W.D.Tex. 1972), 355 F. Supp. 199, aff'd, 5 Cir., 474 F.2d 1397. See, Kister v. Ohio Board of Regents, S.D.Ohio, 365 F. Supp. 27, aff'd, 414 U.S. 1117, 94 S.Ct. 855, 38 L.Ed.2d 747. In Paine, the University of Texas Regents had imposed a regulation providing for automatic suspension of any student placed on probation or convicted of the illegal use, possession or sale of narcotics. While the students suspended under this regulation prevailed in their argument that the regulation violated the tenets of procedural due process and equal protection, the court rejected the double-jeopardy clause, saying:
"... Through two separate governmental organs, the legislative branch and the Board of Regents, the State does indeed impose two successive sanctions for the same offense: judicially imposed punishment and automatic suspension from the University of Texas System. However, the state laws defining criminal conduct and authorizing its punishment are intended to vindicate public justice in regard to the individual offender while, as plaintiffs recognize in their Trial Brief, the Regents' Rule mandating automatic suspension of student drug or narcotic offenders is intended to protect the university community and the educational goals of the institution from such adverse influence as the offender may wield if he is allowed to remain a student. Thus the two sanctions imposed by the state upon plaintiffs have sufficiently different underlying purposes to permit characterization of the first as `criminal' or `punitive' and the second as `civil', `remedial' or `administrative.' Since the Double Jeopardy Clause operates only upon sanctions of the first type successively imposed for the same offense, plaintiffs may not avail themselves of its protection here. United States ex rel. Marcus v. Hess, 317 U.S. 537, 63 S.Ct. 379, 87 L.Ed. 443 (1943); Helvering v. Mitchell, 303 U.S. 391, 58 S.Ct. 630, 82 L.Ed. 917 (1938); see, Mullican v. United States, 252 F.2d 398 (5th Cir.1958); General Order on Judicial Standards of Procedure and Substance in Review of Student Discipline in Tax Supported Institutions of Higher Education, 45 F.R.D. 133 (W.D.Mo. 1968); McKay, The Student as Private Citizen, 45 Denver L.J. 558 (1968)." [Emphasis supplied] 355 F. Supp. 199, 203.
It is apparent that throughout these proceedings the Board was primarily concerned with the safety of pupils being transported in its school buses. While it cannot be denied that the imposition of a suspension from school has certain punitive effects, the underlying purpose of the Board's action and the provisions of § 21-4-306(a)(iii), supra, is the protection of other students  not the vindication of public justice. We hold that appellant's double-jeopardy claim is without merit.

DUE PROCESS  VAGUENESS
Appellant contends that § 21-4-306(a)(iii), supra, is void for vagueness  at *204 least insofar as it was applied to him. He primarily relies on the fact that there was no specific Board regulation prohibiting the conduct involved in this case, and he questions how far a school board may go in regulating student conduct on the public highways.
First, we are satisfied that § 21-4-306(a)(iii), supra, is constitutional on its face. In upholding a statute substantially similar to the one here in question, the Colorado Supreme Court, in People in the Interest of K.P., 182 Colo. 409, 514 P.2d 1131, stated:
"When applied to the challenge presented in this case, and as we interpret C.R.S. 1963, 123-20-7(1)(d), the legislature has provided factors in sufficiently clear and definite language to apprise students of the type of conduct which is prohibited. In so deciding, we particularly note that the standard of conduct set forth in the statute is distinguishable in two decisive respects from comparable statutory language which has been held to be void. First, the statute focuses its prohibition only on conduct which is directed toward other pupils  a narrowed class of individuals. Second, the conduct proscribed is strictly limited to conduct which is hostile to welfare, safety, or morals and could not be utilized to prohibit all forms of socially unacceptable conduct."
This analysis provides a sufficient distinction between § 21-4-306(a)(iii), supra, and the statutes held void in the cases cited by appellant.
Second, students may be reasonably disciplined by a school administration without a prior published rule specifically prohibiting the conduct in question. Karp v. Becken, 9 Cir., 477 F.2d 171, 173; Shanley v. Northeast Independent School District, Bexar County, Tex., 5 Cir., 462 F.2d 960, 970-971; Eisner v. Stamford Board of Education, 2 Cir., 440 F.2d 803, 808; Richards v. Thurston, 1 Cir., 424 F.2d 1281, 1282; and Hasson v. Boothby, D.Mass., 318 F. Supp. 1183, 1187. Such authority, however, is not limitless, and the imposition of sanctions without a specific promulgated rule might well be constitutionally deficient under certain circumstances. Hasson v. Boothby, supra. That students are entitled to a public education as a property interest, protected by the due-process clause, which may not be taken away without some measure of procedural due process is no longer questioned. Goss v. Lopez, 419 U.S. 565, 95 S.Ct. 729, 42 L.Ed.2d 725. The deprivation of procedural due process is not questioned in this appeal  rather the primary inquiry here has to do with substantive due process and whether or not the dictates thereof were abridged through the application to the appellant of § 21-4-306(a)(iii), supra.
Having determined that § 21-4-306(a)(iii), supra, is not impermissibly vague on its face, we become principally concerned with whether the statute was reasonably applied in this case  that is  for a purpose consonant with the purpose of the legislation itself. See, 16 Am.Jur.2d, Constitutional Law, § 550. We have already indicated that the primary purpose for Clements' suspension was the protection of other students from potentially unsafe conditions during their transit to and from school. Such a purpose clearly falls within the object of § 21-4-306(a)(iii), supra. It is no answer to say that there was no specific regulation directed towards Clements' conduct. Students should know, and are chargeable with the knowledge, that interference with the school's transportation of other students to and from school is wrong and unacceptable. School districts are, in fact, obligated under state law to provide transportation for certain pupils resident within the district. § 21-4-401, W.S. 1977. An inherent part of that obligation is to provide safe transportation. The sanctions imposed herein to assist in the fulfillment of such obligations represent a reasonable exercise of the authority which is vested in local school boards.
It matters little that the proscribed conduct occurred on a public highway. It is generally accepted that school authorities may discipline pupils for out-of-school conduct having a direct and immediate effect *205 on the discipline or general welfare of the school. Annot., "Discipline of Pupil for Nonschool Conduct," 53 A.L.R.3d 1124, 1132. See, 68 Am.Jur.2d, Schools, §§ 256 and 266; and 79 C.J.S. Schools and School Districts § 496. This is particularly true where the discipline is reasonably necessary for the student's physical or emotional safety and well-being of other students, teachers or public school property. R.R. v. Board of Education of Shore Regional High School District, 109 N.J. Super. 337, 263 A.2d 180, 184. Cf., Bunger v. Iowa High School Athletic Association, Iowa, 197 N.W.2d 555, 53 A.L.R.3d 1110, where sanctions imposed for the mere occupation of a car containing beer with knowledge of the presence of the beer were found to be unreasonable given the lack of a direct effect upon the school. We hold that the provisions of § 21-4-306(a)(iii), supra, were not unreasonably applied in this case, nor was there a derogation of appellant's right to substantive due process.
While we do not find the absence of a specific promulgated rule fatal in this case, it should be noted that the desirability of written rules regulating serious disciplinary actions in an academic setting is growing in recognition. See, Wilson, Campus Freedom and Order, 45 Denver L.J. 502; and Van Alstyne, The Student as University Resident, 45 Denver L.J. 582. The ultimate limits of the relatively new frontiers represented by the field of student rights are still being tested  and we make no attempt to define them here. Suffice it to say that the area is fraught with difficulty of which we should all be aware.
Affirmed.
THOMAS, Justice, concurring, with whom RAPER, Justice, joins.
I concur in the result reached by the Court in this case. I am concerned about an apparent construction of § 21-4-305(e), W.S. 1977, which makes the application of its provisions dependent upon whether the student actually was punished under the laws of the state. I believe that construction to be too narrow. If correct, it broadens the possibility of a delegation or transfer of the public prosecution function from the prosecutor and the court system to the school board. Such action would be improper and unwarranted, but there could be situations in which criminal charges would not be filed on the assumption that punishment for the same conduct would be forthcoming in the form of suspension or expulsion from the school. Conversely, under more recent concepts of double jeopardy prompt action by the school board might be asserted as a bar to further prosecution under state law. That result would be even less satisfactory. If the statute applies whenever the grounds asserted by the school board for suspension or expulsion also describe an offense potentially punishable under state law, and not only those which are actually punished, then the school authorities are on notice to proceed with caution and to at least confer with the public prosecutor. Further, there would be no temptation to trade off statutory punishment for school discipline.
In resolving this case I would conclude that the provisions of § 21-4-305(e), W.S. 1977, are not applicable because I can find no offense described in the laws of the state which matches the conduct for which the school board disciplined Clements. Alternatively, the justification of the Court's conclusion relative to the absence of double jeopardy resolves this issue as well because we hold that the Board did not suspend Clements for the purpose of punishment, and that even though the suspension has punitive effects a claim of double jeopardy is without merit. It follows that the discipline imposed by the School Board was not "additional punishment" under § 21-4-305(e), W.S. 1977.
NOTES
[1]  While Canfield testified that the bus would only go up the hills at about 25 to 30 miles per hour, and that the Jeep proceeded at about 35 to 40 miles per hour, we must still recognize the support which Willette's testimony gave to the Board's decision.
[2]  On the question of "boxing in the bus," the parties stipulated as follows:

"(a) David Teigland was the passenger in the Appellant's Jeep on the morning of the alleged incident.
"(b) David Teigland, without the prior consent or knowledge of the Appellant, stuck his head out of Appellant's Jeep window and asked the passenger in the Sutton vehicle if the people in the Sutton vehicle wanted to box in the bus. The people in the Sutton vehicle stated they did not want to box in the bus.
"(c) David Teigland only proposed boxing in the bus once and Appellant did not consent, at that time or at any time prior to or subsequent to that time, to boxing in the bus. The parties further agree that David Teigland's testimony that Appellant at no time consented to Teigland's proposal to boxing in the bus was unimpeached."
