
72 N.J. Super. 60 (1962)
178 A.2d 85
B. FRANKLIN WILBERT, AUGUST KOFOET AND WALTER HOLM, MEMBERS OF THE TOWNSHIP COMMITTEE OF THE TOWNSHIP OF LACEY; TOWNSHIP OF LACEY AND JOHN C. PARKER, PLAINTIFFS,
v.
ELIZABETH DeCAMP, SECRETARY OF THE CENTRAL REGIONAL BOARD OF EDUCATION, AND CHARLES S. WHILDEN, OCEAN COUNTY SUPERINTENDENT OF SCHOOLS, DEFENDANTS.
Superior Court of New Jersey, Appellate Division.
Argued January 15, 1962.
Decided January 16, 1962.
*61 Before Judges GOLDMANN, FREUND and FOLEY.
Mr. Edward W. Haines argued the cause for plaintiffs (Messrs. Haines & Schuman, attorneys).
Mr. Alfred Abbotts, Deputy Attorney General, argued the cause for defendant Charles S. Whilden (Mr. David D. Furman, Attorney General, attorney).
The opinion of the court was delivered by GOLDMANN, S.J.A.D.
Plaintiffs seek judgment setting aside the reapportionment of the membership of the Board of Education of the Central Regional School District in Ocean County made by defendant Charles S. Whilden, Ocean County Superintendent of Schools, pursuant to the provisions of N.J.S.A. 18:8-5; directing him to apportion the membership to provide for a representation of two members for Lacey Township; and ordering defendant Elizabeth DeCamp, secretary of the board of education, to accept for *62 filing the nominating petition of plaintiff John C. Parker and to place his name upon the ballot to be used in the school board election to be held February 6, 1962.

I.
Plaintiffs, who are the members of the Lacey Township Committee, Lacey Township itself, and Parker, instituted this action in the Law Division by a verified complaint in lieu of the prerogative writ of mandamus. An order issued calling upon defendants to appear before the Law Division on January 12, 1962 and show cause why judgment should not be entered granting the relief sought by plaintiffs, and further, restraining them from taking any action with respect to the printing of ballots for the school board election pending final determination of the matter. Defendants moved to dissolve the temporary restraint and dismiss the complaint because plaintiffs had failed to exhaust their administrative remedies, as required by R.S. 18:3-14 and 15 and R.R. 4:88-14. Upon the return day of the order to show cause it was suggested that the Law Division might not be vested with jurisdiction since the matter involved the review of action by a state administrative agency under R.R. 4:88-8. The Law Division judge thereupon, on his own motion, transferred the case to the Appellate Division.
Both sides agree that this matter properly belongs in the Appellate Division. A state agency is involved, since all county superintendents of schools are appointed by the State Commissioner of Education with the advice and consent of the State Board of Education, N.J.S.A. 18:4-1, and are directed and supervised by him, N.J.S.A. 18:3-19. A county superintendent of schools exercises general supervision over the public schools of the county in his charge, in accordance with rules and regulations prescribed from time to time by the State Board of Education, N.J.S.A. 18:4-7. He is required to render an annual report to the State Commissioner of Education on such matters *63 relating to the schools under his direction as the Commissioner shall require, R.S. 18:4-8.

II.
In September 1954 the school districts of Berkeley and Lacey Townships, and the Boroughs of Island Heights, Seaside Park, Seaside Heights and Ocean Gate, formed a regional school district known as the Central Regional School District under the provisions of R.S. 18:8-1 et seq., as amended. N.J.S.A. 18:8-4 provides that when such a regional school district is created the county superintendent of schools shall select from among the citizens of the school districts comprising the regional district nine members to constitute the regional board of education. The regional board of education, as originally constituted, was comprised of two members each from Berkeley and Lacey Townships and Seaside Park Borough, and one member from each of the remaining school districts of the Boroughs of Seaside Heights, Island Heights and Ocean Gate. This apportionment continued until the results of the 1960 federal census were promulgated and became effective in New Jersey on May 6, 1961. N.J.S.A. 52:4-2. It then became necessary for defendant County Superintendent of Schools Whilden to recompute and reapportion the membership of the regional board of education in accordance with N.J.S.A. 18:8-5, which provides:
"The membership of the regional board of education shall be apportioned by the county superintendent or county superintendents of schools among the several school districts uniting to create a regional school district as nearly as may be according to the number of their inhabitants as shown by the last Federal census officially promulgated in this State, but each constituent school district shall have at least 1 member on the regional board of education. The membership as apportioned shall continue to represent the respective constituent school districts on the regional board of education until changed by reapportionment by the county superintendent or county superintendents of schools of the county or counties in which any part of the regional school district is situated. Such reapportionment shall be made immediately succeeding the official promulgation in *64 this State of each subsequent Federal census or as otherwise required by section 18:5-3 of this Title. Notwithstanding any such reapportionment, the members of the regional board of education, as theretofore apportioned among the constituent school districts, shall continue in office for the terms for which they were elected or appointed, and provision shall be made for election of their successors only to the extent necessary to provide, for each constituent school district, the representation in membership on the regional board of education to which such school district is entitled by reason of any such reapportionment. If by reason of any such reapportionment a constituent school district becomes entitled to increased representation in membership on the regional board of education, such additional members shall be elected from such school district at the next annual regional school district election."
On December 26, 1961 defendant county superintendent of schools announced the reapportionment required under N.J.S.A. 18:8-5. The 1960 federal census figures for the member districts of the Central Regional School District, the original apportionment, and the December 26, 1961 apportionment, follow:


                                          Original       Present
Municipality                Population  Apportionment  Apportionment
Berkeley Twp. ............   4,272            2            4
Lacey Twp. ...............   1,940            2            1
Island Heights Boro. .....   1,150            2            1
Seaside Park Boro. .......   1,054            1            1
Seaside Heights Boro. ....     954            1            1
Ocean Gate Boro. .........     706            1            1
                            ______           __           __
      Total ..............  10,076            9            9

N.J.S.A. 18:7-25 requires that all nominating petitions of candidates for election to a board of education shall be filed with the school board on or before the 40th day preceding the school election date. Although R.S. 18:8-8 formerly called for the election of regional board members on the first Tuesday in February, the section as last amended by L. 1955, c. 159, § 7, eliminates mention of that date. However, section 9 of the 1955 act, now N.J.S.A. 18:8-16, fixes the annual regional school district election as the first Tuesday in February. (We note that R.S. 18:7-14, relating *65 generally to school districts in townships and boroughs, fixes the second Tuesday in February for the election. However, N.J.S.A. 18:8-16 is a much later act and deals specifically with regional boards of education. The filing date for the election in this case was therefore December 28, 1961.)
Plaintiff John C. Parker has been a member of the regional board of education, serving as one of the Lacey Township representatives. His present term of office expires on the first Monday following the forthcoming school board election. N.J.S.A. 18:8-8. Desirous of reelection to the board, he presented his nomination petition to defendant Elizabeth DeCamp, school board secretary, seeking a position on the ballot at the February school board election. She refused to accept it, although it is conceded that the petition is in all respects proper and filed within time.
Plaintiffs contend that the reapportionment method employed by the county superintendent of schools is arbitrary, capricious and unauthorized under N.J.S.A. 18:8-5. They insist that the proper and most equitable method for determining the representation which each of the member school districts shall have on the regional board of education is the so-called method of equal proportions. By this method each municipality would be assigned one member initially, as called for by N.J.S.A. 18:8-5, and the remaining three members allotted so that Berkeley Township would be entitled to a total of three members and Lacey Township to two. It is plaintiffs' claim that as a result of defendants' actions Lacey Township will be deprived of its proper representation on the regional board of education, and plaintiff Parker deprived of his right to stand as candidate for re-election to the board.

III.
Plaintiffs readily agree that N.J.S.A. 18:8-5 does not by its terms establish any particular formula or method to be used in reapportioning membership on the regional board. *66 The only statutory directive is that such membership be apportioned "as nearly as may be" according to the population of each member school district as shown by the latest federal census figures, with the single limitation that each district shall have at least one member on the regional board. Under the statutory directive, say plaintiffs, the county superintendent of schools must use that method of apportionment which the dictates of common sense and justice require in order to assure as equitable a representation as possible. They charge that the method defendant county superintendent has used "patently" does not comply with that requirement.
The method adopted by defendant Whilden is commonly known as the Vinton method. This method is based upon a fixed ratio and operates as follows in the present setting:
1. The total regional school district population (10,076) is divided by the total number of board members (9) to obtain a fixed ratio of 1,119.55, which represents the ideal population per board member.
2. This fixed ratio (1,119.55) is divided into the population of each municipality to obtain the exact quota of board members for each school district. In this case the ideal representation for each district would be:


Municipality                    Population       Ideal Representation
Berkeley Twp. .............        4,272                3.82
Lacey Twp. ................        1,940                1.73
Island Heights Boro. ......        1,150                1.03
Seaside Park Boro. ........        1,054                 .94
Seaside Heights Boro. .....          954                 .85
Ocean Gate Boro. ..........          706                 .63
                                  ______                ____
     Total ................       10,076                9.00

3. One member is assigned to each school district whose exact quota is less than 1. Thus, Seaside Park, Seaside Heights and Ocean Gate would get one member each.
4. Each school district is assigned members equal to whole number in its exact quota, i.e., Berkeley Township 3; Lacey Township 1; and Island Heights 1.
5. The remaining member to be allotted (9 less the number assigned in (3) and (4) above, which total 8) is allotted to the school district having the largest fraction in its exact quota. That school district is Berkeley Township, which thus gets 4 representatives.
*67 The method of equal proportions does not use a fixed ratio, but employs a "priority list," as do the methods of harmonic mean, major fractions, smallest divisors and greatest divisors. Apportionment according to equal proportions would be determined as follows:
1. Each of the school districts would be assigned one representative.
2. A priority list for allocating the remaining three members in this case would be established in the following manner:
a. The population of each municipality would be divided successively by the geometric mean (square root of the product) of each pair of successive integers beginning with 1 and 2, and following with 2 and 3, 3 and 4, etc., until the number of quotients so calculated for each municipality exceeds by at least 1 the number of additional representatives to be allotted to that municipality.
b. All such quotients are then arranged in the order of magnitude, beginning with the largest, to form the priority list.
3. The remaining three members are allotted to the municipalities having the three highest positions in the priority list.
The use of equal proportions would give Berkeley Township three members, Lacey Township two members, and the remaining four municipalities one member each, for a total of nine.
Since no other methods than the Vinton and equal proportions are here involved, and no municipalities other than Berkeley and Lacey Townships challenge their representation, we need consider only the comparative validity of the two reapportionment methods outlined above in the particular setting of this case.

IV.
Before discussing the two methods of apportionment, we consider defendants' argument that the appeal should be dismissed out of hand because of plaintiffs' failure to exhaust their administrative remedies. They point out that under R.S. 18:3-14 the State Commissioner of Education "shall decide * * * all controversies and disputes arising under the school laws * * *." A right of appeal to the State Board of Education is given by N.J.S.A. 18:3-15.
*68 Plaintiffs were not required to exhaust their administrative remedies under R.R. 4:88-14 in the circumstances here present. There is no factual dispute. The question is solely one of law, involving a question of statutory construction. Where the disposition of a matter depends solely on the decision of a question of law, the interests of justice do not require exhaustion of administrative remedies before resort may be had to the courts. Nolan v. Fitzpatrick, 9 N.J. 477, 486-487 (1952); Deaney v. Linen Thread Co., 19 N.J. 578, 581 (1955).

V.
Plaintiffs rely upon Asbury Park Press v. Woolley, 33 N.J. 1 (1960), in support of their argument that the only method that could properly have been used here was equal proportions. That case involved the question of the apportionment of members of the General Assembly among the several counties of the State "as nearly as may be according to the number of their inhabitants," each county at all times being entitled to at least one member. All that the court said was that of the several mathematical formulas which might be used in legislative apportionment, equal proportions "seems generally to be regarded as producing the smallest relative differences in population per assemblyman and the smallest relative difference in the individual share in an assemblyman." However, the court did not decide that the method of equal proportions must be used, the question being reserved for the time being. The court held the case for further argument, awaiting action by the Legislature in reapportioning on the basis of the 1960 federal census. It requested the parties to file additional briefs discussing, among other things, the following:
"(a) Does the language of the Constitution requiring apportionment `as nearly as may be' according to the number of inhabitants of each county circumscribe the discretion of the Legislature to the extent that as a matter of law the formula which is most neutral as *69 between the smaller and larger counties and which, from a mathematical standpoint, most closely approaches the `as nearly as may be' mandate, must be employed?
(b) Are the limits of the `as nearly as may be' test sufficiently broad to permit, in the discretion of the Legislature, adoption of any recognized mathematical formula for apportionment, regardless of whether it in some measure favors the small over the large counties or vice versa?" (33 N.J., at pages 21-22)
The Supreme Court was never called upon to decide these questions because the Legislature reapportioned the General Assembly on February 1, 1961. L. 1961, c. 1. The method used was equal proportions. However, the fact that the method advocated by plaintiffs was adopted by the Legislature does not necessarily lead to the conclusion that any other method is arbitrary, capricious or illegal in the present setting.
Indeed, the Legislature has used other methods of reapportioning the General Assembly since the adoption of the Constitution of 1844. Out of ten reapportionment acts, seven used the Vinton method or a variation thereof. Two used neither Vinton nor a variation. In 1851 the Legislature used a fixed ratio of one Assembly seat for every 8,250 persons, plus one extra seat for every major fraction thereof. See New Jersey Legislative Reapportionment, a summary of legislative proposals for reapportioning General Assembly seats, prepared by the Law and Legislative Reference Bureau in the Division of Education, November 1957, pp. 28-9. We are also informed that the Vinton method has been used to date by the State Department of Education for apportioning regional school districts, and was consistently employed in connection with the recent reapportionments.
Plaintiffs point to the relative populations of Berkeley and Lacey Townships (4,272 as against 1,940) and argue that a 3-2 representation on the regional school board, produced by using the equal proportions method, would be much fairer than the 4-1 proportion produced by the Vinton method. We consider the following table (1,119.55 represents *70 the ideal population which should be represented by a school board member):


                                    Ideal Population
                           Board    Which Should be    Vinton
                          Members   Represented by      Error
Municipality  Population  (Vinton)  Number on Board   (Absolute)
Berkeley Twp. .. 4,272        4       4,478.22          206.22
Lacey Twp. ..... 1,940        1       1,119.55          820.44
                 _____       __       ________        ________
      Total .... 6,212        5       5,597.77        1,026.66
     Board         Ideal Population Which    Equal Proportions
    Members        Should be Represented           Error
(Equal Propor.)    by Number on Board           (Absolute)
      3                  3,358.66                 913.33
      2                  2,239.11                 299.11
     __                  ________               ________
      5                  5,597.77               1,212.44

These figures show the error inherent in each system, the margin of error (absolute values) being greater under the equal proportions method. This error, of course, is explained by the fact that of the remaining four municipalities, three are over-represented (because of the minimum representation provision contained in the statute) and one (Island Heights) slightly under-represented:


                                    Ideal Population
                                   to be Represented
Municipality           Population      by One Member     Error
Island Heights Boro. ... 1,150          1,119.55      +  30.44
Seaside Park Boro. ..... 1,054          1,119.55      -  65.55
Seaside Heights Boro. ..   954          1,119.55      - 165.55
Ocean Gate Boro. .......   706          1,119.55      - 413.55
                         _____          ________      ________
      Total ............ 3,864          4,478.22      - 614.22

In these four municipalities there are 614.22 less residents than the representation warrants. This over-representation must necessarily be reflected in some loss of actual representation in the two larger communities, Berkeley and Lacey Townships.
*71 We may consider the problem from two other points of view: the population represented per school board member, and the individual share of a school district resident in each member:


                                        Individual Share
               Population Per Member       of Member
                            (Equal                   (Equal
Municipality   (Vinton)   Proportion)  (Vinton)    Proportion)
Berkeley Twp. .. 1,068       1,424     .000936       .000702
Lacey Twp. ..... 1,940         970     .000515       .001031

We have already mentioned that ideally each board member should represent 1,119.55 individuals in the school districts making up the regional district, this on the basis of a total population of 10,076. The individual share of each school board member would be.000893. If the above figures were placed on graphs, one dealing with population per member and the other with the individual share of each member, the graphs would show that the Vinton method brings the Berkeley figures much closer to the line than the Lacey figures.
We are compelled to the conclusion that, dealing with the population figures present in this case, it cannot be said that the method adopted by the county superintendent of schools may be described as "patently"  to use plaintiffs' word  arbitrary, capricious and illegal.
As was pointed out by Dr. Anthony Ralston of the University of Leeds, England, Electronic Computing Laboratory, in his report to the New Jersey General Assembly, "A Fresh Look at Legislative Apportionment in New Jersey" (June 1960), the various methods of reapportionment cannot be said to be inherently more or less fair on any objective basis. Within rather wide limits, this is a subjective decision in that each must judge for himself which way the facts seem to point.
A mathematician might prefer the equal proportions method as the one which generally produces the best result. *72 Choice of method is necessarily determined by one's objective; major fractions, harmonic mean, equal proportions, and the other methods each have their virtues in a particular case. Schmeckebier, Congressional Apportionment (Brookings Institution 1941).
We do not find the Vinton method, as employed in the present situation, to be infected with obvious unfairness. That method has sometimes been criticized for producing what is known as the "Alabama Paradox," discussed in some of the above-mentioned authorities and those cited in the Asbury Park Press case, above, 33 N.J., at pages 8-9. We do not find the Alabama Paradox operative in defendant county superintendent's reapportionment under the 1960 federal census figures. Compare the observation by Ralston, op. cit., at page 23, questioning whether the paradox is applicable to the New Jersey reapportionment problem; and see the brief discussion of legislative apportionment in the article by Biunno and Meanor, "Constitutional Law," 15 Rutgers L. Rev. 202 (1961).
Discretion must be exercised by the apportioning authority. We will not interfere with its exercise unless it has plainly and grossly been abused. "As nearly as may be," as used in N.J.S.A. 18:8-5, does not mean that a county superintendent of schools must, in circumstances such as we consider, adopt the equal proportions method. Apportionment involves the exercise of sound judgment and practical wisdom. It is not our function to revise the exercise of the county superintendent's judgment within its legitimate limits, but only to declare void an apportionment so obviously wrong as to trespass upon the statutory direction. See Attorney General v. Secretary of the Commonwealth, 306 Mass. 25, 27 N.E.2d 265 (Sup. Jud. Ct. 1940).
Plaintiffs have failed to show such an abuse of discretion as would invite judicial revision of the apportionment. Their argument seems to come down to this: that in some cases the Vinton method does not, as the court observed in passing in the Asbury Park Press case, above, 33 N.J., *73 at page 9, "presently appear to be regarded as efficient as the so-called modern types."
Finding no clear and palpable violation of the statutory command, defendants must prevail.
