Armstrong, J.

This bill in equity was brought by the owner of 4.5 acres of vacant land on Alfred Street near its intersection with Main Street in Woburn, against the Woburn city council, appealing the council’s denial of a special permit to erect on that land 144 one-bedroom apartment units in nine buildings, with parking facilities for 156 automobiles. The plaintiffs application to the city council was filed pursuant to a city ordinance requiring a special permit issued by the council for the construction of apartment buildings in a residential zone. 1 The ordinance sets forth standards to govern the council’s exercise of its discretion in granting or denying special permits. 2

*310 After hearing, the council voted on the application, which failed to receive the two-thirds vote required for approval. Three reasons were cited for denial of the special permit in the lengthy and detailed findings and decision adopted by the members who so voted: (1) the proposed apartment complex with adjacent parking areas would aggravate a periodic flooding problem in nearby residential areas by eliminating a natural, soft-peat holding area for the Middlesex canal waterway and the surrounding area, and the members were not persuaded that the plaintiffs proposed drainage system would provide an adequate substitute; (2) the Woburn water supply system is insufficient to meet the existing residential and industrial demands as well as to maintain sufficient pressure for fire protection, and “future construction of this magnitude would create a public safety hazard for the North Woburn area”; and (3) due to the narrow, S-curve construction of Alfred Street at its junction with Main Street, neither those streets nor the intersection would be equipped to handle an increased traffic load without creating a “serious [traffic] safety problem.”

On appeal under G. L. c. 40A, § 21, the trial judge made independent findings of facts which are set out in the margin. 3 On the basis of these findings, the judge con- *311 eluded that the council did not act arbitrarily in denying the special permit, that it had to deal with serious problems of traffic congestion, water drainage, and high population density, and that its action in denying the permit was therefore within the scope of its authority. From a final decree to that effect, the plaintiff appealed.

The plaintiffs principal contention is that the judge’s findings of fact are not sufficiently detailed to comply with the standard of review required by G. L. c. 40A, § 21, as construed (with reference to a predecessor statute) in Pendergast v. Board of Appeals of Barnstable, 331 Mass. 555, and a line of cases following it. The plaintiff relies principally on Josephs v. Board of Appeals of Brookline, 362 Mass. 290.

The Josephs case, however, was an appeal from a decision granting, not denying, a variance and several special permits. In such a case not only must a board of appeals make an affirmative finding as to the existence of each condition of the statute or by-law required for the granting of the variance or special permit (Planning Bd. of Springfield v. Board of Appeals of Springfield, 355 Mass. 460, 462), but the judge in order to affirm the board’s decision on appeal must find independently that each of those conditions is met. Blackman v. Board of Appeals of Barnstable, 334 Mass. 446, 449. In the Josephs case the judge’s findings were not detailed enough to support a decree sustaining the grant of certain of the special permits. “The pertinent by-law provisions require the specific application of mathematical formulae. The judge’s findings did not comply with these requirements.” 362 Mass, at 299.

The present case, however, is an appeal from the council’s denial of a special permit. Such a denial is within the *312 discretion of a board of appeals. Pendergast v. Board of Appeals of Barnstable, 331 Mass. 555, 559-560. Gulf Oil Corp. v. Board of Appeals of Framingham, 355 Mass. 275, 277-278. MacGibbon v. Board of Appeals of Duxbury, 356 Mass. 635, 638. The discretion must not be exercised arbitrarily, however. “The board must act fairly and reasonably on the evidence presented to it” (MacGibbon v. Board of Appeals of Duxbury, 356 Mass. 635, 638-639), and must set “forth clearly the reason or reasons for its decisions.” G. L. c. 40A, § 18. On appeal under § 21 the nature of the findings of fact the judge is required to make must be governed by the nature of the reasons a board gives for its decision. The council here did not purport to base its decision on lack of authority to grant the permit because a legally essential prerequisite was absent. Rather, the council denied the permit as an act of discretion, and set forth its reasons for exercising its discretion in the manner it did. The judge’s function on appeal was to ascertain whether the reasons given by the council had a substantial basis in fact, or were, on the contrary, mere pretexts for arbitrary action or veils for reasons not related to the purposes of the zoning law. If formal requirements have been met, the council’s decision cannot “be disturbed unless it is based on a legally untenable ground, or is unreasonable, whimsical, capricious or arbitrary. Gulf Oil Corp. v. Board of Appeals of Framingham, 355 Mass. 275, 277, and cases cited.” MacGibbon v. Board of Appeals of Duxbury, 356 Mass. 635, 639.

On the basis of the evidence before him the judge made independent findings which were appropriate to the type of review required in this case. Although the judge did not make a finding concerning the water supply problem, he did find that the flooding danger and the traffic congestion were substantial problems, and not mere pretexts. These findings justify his conclusion that the council did not exercise its discretion arbitrarily.

Decree affirmed.

A zoning ordinance may authorize the city council, rather than the board of appeals, to act on applications for special permits. G. L. c. 40A, § 4.

“Section 9.08 — Permit for Special Exceptions (Chapter 40A, Section 4). Certain uses, structures, or conditions are designated as Special Exceptions in Section 4.03 — Table of Use Regulations, and elsewhere in this Ordinance. Upon application duly made to the Building Inspector and forwarded to the City Council, the Council may, in appropriate cases and subject to appropriate conditions and safeguards, grant a permit for such Special Exception and no others.

“1. In acting upon an application for a Special Exception, the Council shall take into consideration; whether the specific site is an appropriate location for the use or structure; the use developed will adversely affect the neighborhood; there will be undue nuisance or serious hazard to vehicles or pedestrians; and adequate and appropriate facilities will be provided to ensure the proper operation of the proposed use, structure, or condition. It shall permit the Special Exception only when it finds that, in view of these considerations, such exception is consistent with the spirit of this Ordinance.

“2. The Council shall also impose such additional conditions to those specified in this Ordinance as it finds reasonably appropriate to safeguard the neighborhood or otherwise serve the purpose of this Ordinance, including but not limited to, the following; front, side or rear yards greater than the minimum required by this Ordinance, screening, buffers or planting strip, fences, or walls, as specified by the Council modification of the exterior appearance of the structure; limitation upon the size, number of occupants, method and time of operation, or extent of facilities; regulation of number and location of drives, accessways, or other traffic features; and off-street parking or loading, or other special features beyond the minimum required in this Ordinance.

“3. The Council may not authorize as a Special Exception a change from one nonconforming use to another, or the extension or enlargement of a nonconforming use” (emphasis in original).

“I find as a fact that the locus, due to the fact that it was located in close proximity to the old Middlesex Canal, was subject to water infiltration from that canal, and at certain times of the year a portion of the locus was flooded. Part of the subsoil of the locus consisted of peat and the peat acted as retention material with respect to water infiltrating the area. The plan submitted by the plaintiff indicated that the plaintiff would install a drainage system for the purpose of eliminating any water problems due to the location of the site and the nature of the land itself. The proposed apartment complex would front on Alfred Street. Alfred Street is a two-lane street having a 25-foot hot-topped surface. The portion of the street in front of the locus is in the shape of a relatively sharp S-curve. The erection of the apartment complex would have the effect of increasing the traffic flow on Alfred Street and at the intersection of Main and Alfred Streets. At that intersection, in a westerly direction, there is located a shopping center which has a tendency to create congestion and traffic problems at the intersection. The area in the vicinity of the locus has, at various times, been subject to flooding, and opposition to the construction of the apartment complex was voiced by some of the neighbors on the ground that the construction of the apartment complex might result in further flooding of the adjacent area.

“I do not find that the City Council acted arbitrarily, whimsically or capriciously in denying the plaintiffs application. I find that in fact, the Council had to deal with a serious problem of traffic congestion and safety as well as a *311 potential water drainage problem and the question of subjecting the locus to a high density of population. The City Council could, acting as rational members, concerned with the public interest, comé to the conclusion that it would not be in the public interest to grant the permit. I cannot say that their action rested on a legally tenable ground. I therefore rule as a matter of law on the basis of the above findings that the City Council, in denying the application for the special permit, did not exceed its authority.”