Hennessey, J.

The plaintiffs appeal from a final decree in the Superior Court sustaining a decision of the board of appeals of Brookline (board) granting a variance and four special permits to a developer, B & L Associates (B & L). The judge heard evidence, took a view of the locus, and filed a report of material facts. The evidence is not reported.

The facts are here stated. B & L seeks to construct a high rise building at 1550 Beacon Street. As modified to comply with conditions imposed by the board, the proposed building is to be fifteen stories high and will contain 203 units of low and moderate income apartments for the elderly, medical offices for not more than fifteen physicians or dentists, and automobile parking stalls for the apartments and the medical offices. The locus, a vacant parcel consisting of 37,103 square feet, forms a triangle, bounded by Lancaster Terrace on the north, Beacon Street on the south, and the boundary of a lot occupied by Temple Beth Zion on the west. The area in which the building is to be erected is composed primarily of multistory apartment dwellings.

Subject to certain conditions, the board granted B & L one variance and four special permits, all of which are challenged in this proceeding. The judge entered a final decree that the board’s decision did not exceed its authority. Since the evidence is not reported, the only issues presented are whether the board and the judge made specific findings demonstrating that the statutory and by-law prerequisites had been met. Goldston v. Randolph, 293 Mass. 253, 255. Bottoms v. Carlz, 310 Mass. 29, 32. Planning Bd. of Springfield v. Board of Appeals of Springfield, 355 Mass. 460, 462. We conclude that the final decree was correct only as to the variance, and was in error as to the special permits.

variance. General Laws c. 40A, § 15, cl. 3, as amended, authorizes local boards of appeal to grant variances from the terms of the zoning-by-law “where, owing to conditions especially affecting such parcel . . . but not affecting generally the zoning district in which it is located, a literal enforcement of the provisions of the . . . by-law would involve substantial hardship, financial or otherwise to the appellant, and where desirable relief may be granted without substantial detriment to the public good and without nullifying or substantially derogating from the intent or purpose of such . . . by-law.”

This court has repeatedly emphasized the stringency of the requirements set out in § 15, cl. 3. Zinck v. Zoning Bd. of Appeals of Framingham, 345 Mass. 394. Russell v. Zoning Bd. of Appeals of Brookline, 349 Mass. 532. McNeely v. Board of Appeal of Boston, 358 Mass. 94. Damaskos v. Board of Appeal of Boston, 359 Mass. 55, 60-61. Furthermore, we have stated that “a decision of the board of appeals granting a variance cannot stand unless the board specifically finds that each statutory requirement has been met.” Planning Bd. of Springfield v. Board of Appeals of Springfield, 355 Mass. 460, 462, and cases cited. On appeal from the board’s decision, it is the judge’s duty to determine the facts for himself, to apply the governing principles of law, and then to inspect the decision of the board and enter such decree as justice and equity may require. Blackman v. Board of Appeals of Barnstable, 334 Mass. 446, 449. The judge, like the board of appeals, may uphold the variance only if he finds that the prerequisites of § 15, cl. 3, have been met. Coolidge v. Zoning Bd. of Appeals of Framingham, 343 Mass. 742. Planning Bd. of Springfield v. Board of Appeals of Springfield, 355 Mass. 460, 462. With these principles in mind, we conclude that the final decree was correct in so far as it ruled that the board had not exceeded its authority in granting the variance.

Section 6.21 (a) of the Brookline zoning by-law requires that a loading bay fourteen feet in height be provided in all buildings containing offices. In this case, the

variance granted by the board permits B & L to construct a loading bay with a height of ten feet. Although the findings of the board as to the loading bay were meager, we conclude that they were legally sufficient in that they found compliance with § 15, cl. 3, both in terms of the statutory language and in a recitation of the applicable facts concerning the property here concerned.

In ruling that the board did not exceed its authority in granting the variance, the judge concluded that all the requirements of § 15, cl. 3, had been met. His findings on the issue are here summarized. The locus is roughly triangular in shape and slopes downward north to south and from west to east. While much of the zoning district in which the locus is situated is hilly and sloping, the locus involved is the only parcel of comparable size in the area which is now vacant and which is not essentially rectangular in shape. Because of the peculiar topography of the locus, it will be necessary to construct the off street loading bay on Lancaster Terrace. If a loading bay of fourteen feet in height is required, the judge found that it would be necessary “either to depress the level of the roadway in relation to the record grade or to maintain record grade and extend the height of the bay into the story above.” The first alternative would create an excessively steep access ramp from the bay to the street and present hazards to persons using the ramp. The second alternative would interfere with the use of the space within the building and would result in an economic loss. On these findings, the judge was warranted in concluding that a “hardship, financial or otherwise” would result from literal enforcement of the fourteen foot bylaw requirement and that the hardship is due to “conditions especially affecting such parcel . . . but not . . . generally the zoning district in which it is located.” G. L. c. 40A, § 15, cl. 3. Kairis v. Board of Appeal of Cambridge, 337 Mass. 528, 530-532. Planning Bd. of Springfield v. Board of Appeals of Springfield, 338 Mass. 160, 165-166, Shacka v. Board of Appeals of Chelmsford, 341 Mass. 593, 595, Broderick v. Board of Appeal of Boston,

361 Mass. 472-477. The judge also justifiably found that because trucks using the bay will be off the street entirely and because of the bay’s location and design, a reduction in height “will have no effect upon the abutting properties and, hence, this reduction will not nullify or derogate from the intent or purpose of the by-law.” Reading his findings fairly in their entirety, we conclude that he also found that the variance here was granted without substantial detriment to the public good, and this finding was wararnted by the evidence.

2. We turn now to a consideration of the special permits granted by the board.

General Laws, c. 40A, § 4, as amended, provides the statutory authority for the granting of special permits. That section states, in part, “[a] zoning ordinance or by-law may provide that exceptions may be allowed to the regulations and restrictions contained therein, which shall be applicable to all of the districts of a particular class and of a character set forth in such ordinance or by-law. Such exceptions shall be in harmony with the general purpose and intent of the ordinance or by-law and may be subject to general or specific rules therein contained. The board of appeals . . . may, in appropriate cases and subject to appropriate conditions and safeguards, grant to an applicant a special permit to make use of his land or to erect and maintain buildings or other structures thereon in accordance with such an exception” (emphasis added).

We have on numerous occasions stated that in granting special permits under § 4 the board’s power is discretionary. Gulf Oil Corp. v. Board of Appeals of Framingham, 355 Mass. 275, 277, and cases cited. Zaltman v. Board of Appeals of Stoneham, 357 Mass. 482, 484-485. Strazzulla v. Building Inspector of Wellesley, 357 Mass. 694, 698. That discretion, however, is not without limits. The Zoning Enabling Act and the local by-laws must provide adequate standards for the guidance of the board in deciding whether to grant or withhold special permits. MacGibbon v. Board of Appeals of Duxbury, 356 Mass.

635, 638. Furthermore, as is the case where the granting of a variance is involved, the board, when granting a special permit, must set forth “clearly the reason or reasons for its decisions” that the applicable statutory and by-law standards have been met. G.L. c. 40A, § 18, as amended. Gaunt v. Board of Appeals of Methuen, 327 Mass. 380, 381-382. Cities Serv. Oil Co. v. Board of Appeals of Bedford, 338 Mass. 719, 728. Otherwise, “zoning regulations can become a matter of administrative whim.” Damaskos v. Board of Appeal of Boston, 359 Mass. 55, 62.

On appeal to the Superior Court, the judge is required to hear the matter de nova and determine the legal validity of the decision of the board upon the facts found by him. G. L. c. 40A, § 21. Lawrence v. Board of Appeals of Lynn, 336 Mass. 87, 89, and cases cited. In making his findings, the judge is not allowed to give the board’s findings or decision evidentiary weight (Devine v. Zoning Bd. of Appeals of Lynn, 332 Mass. 319, 321-322), nor may he make findings which, in substance, constitute a “mere repetition of the statutory words.” Brackett v. Board of Appeal of the Bldg. Dept, of Boston, 311 Mass. 52, 54. Wolfson v. Sun Oil Co. 357 Mass. 87, 89, and cases cited. With the above principles in mind, we examine the findings of both the board and the judge concerning the four special permits involved herein.

The standards governing the board’s action, in this case, are contained in G. L. c. 40A, § 4, and in the by-law under which the permits were granted. Section 9.5 of the Brookline zoning by-law1 provides certain conditions for the approval of special permits.

A. The Board’s Decision.

Section 5.43 of the by-law authorizes the board to reduce by special permit the minimum setback requirements, provided that the result “shall assure the same standard of amenity to nearby properties as would have been provided by compliance with the regulations of the By-law.” In attempting to determine the “regulations of the By-law” the board stated that it was “completely frustrated.” The frustration may have been due to the irregular shape of the locus and to the fact that the applicant “offered no evidence or argument on the point.” Nevertheless, the board stated that “[although we would like to know what the yard requirements are in this case, it seems that we will have to resort to granting a special permit without knowing exactly how much of a deviation we are approving.” The board then stated that on the basis of certain plans, not now before this court, “no set-back is less than 5.3 ft.” and that “[t]he other places where the corners of the building are fairly near the lot lines appear to be not less than 10 feet from the line.” The board concluded that, in its judgment, “all of the criteria for a special permit found in Sec. 9.5 (a) are satisfied, and the amenities are better preserved than they would be by a conventional building in the shape of an oblong.”

Under § 5.21 (a) of the zoning by-law,2 the board

granted a special permit allowing an increase in the floor area ratio from the permissible 4.0:1 to 4.4:1. With respect to this permit, the board stated that “[a]ll members . . . agreed that an exception to maximum floor area ratio regulations could be granted without violating Sec. 9.5 (a), especially since the desired ratio is only 4.4 while the applicant is eligible to apply for as much as 4.77. We accept the findings on page 2 of the Report in this regard.” At this point, we observe that the report referred to is not incorporated into the board’s decision nor is it a part of the record before us.

Under § 6.11 (b) (4) of the zoning by-law3 the board granted a special permit to reduce the number of parking spaces required for residents from 179 to 58, the maximum allowable reduction. The board also required that at least two parking spaces be provided for every doctor having an office in the building. In granting the special permit, the board specifically found that since the proposed building will be occupied by low and moderate income elderly persons, the parking needed for the intended type of occupancy will be below that otherwise required. The board further found that the number of spaces otherwise required could be provided on the site should the building ever be changed to another kind of occupancy.

The fourth special permit was granted under § 5.314 and authorized an increase in height as to certain por

tians of the building. Under the applicable provision of the by-law, the maximum height of buildings on the locus is 120 feet above “record grade,” but special permits authorizing an increase of up to 25 % may be granted for those segments of the building which, among other things, are more than 200 feet from an S, SC or T zoning district. In this case, the board divided the building into six segments and used as the heights of those segments the figures contained in the planning board report. The board’s decision noted, however, that “[a]t least one member of the Board is not in agreement with all of those figures.” The board then proceeded to grant a special permit as to three segments of the building which it found are more than 200 feet from an S, SC or T zoning district. As to one of those segments, however, the board observed that “[t]he Planners did not measure the height in segment 5 from the record grade of the street, as seems to be required by [the by-law].” The board concluded “that this special permit is warranted because all the conditions of Sec. 9.5 (a) are met, and no adverse effect will be created.”

Reviewing the board’s findings on each of the special permits granted and having in mind the applicable statutory and by-law standards, we conclude that, with the exception of the findings on the special permit relating to off street parking, the board’s findings are inadequate. In some instances, they amount to little more than a mere recitation of the statutory and by-law standards and, in others, they indicate that the board did not have sufficient evidence before it to make the necessary findings.

B. The Judge’s Decision.

The judge, hearing the matter de nova, found affirmatively with respect to each of the special permits granted that the conditions set forth in the by-law had been established by the board. The issue before us is whether the final decree ruling that the board did not exceed its

authority in granting the special permits is supported by the material facts found by him. Goldston v. Randolph, 293 Mass. 253, 255.

With respect to the floor area ratio, the judge found that the locus is a corner lot, that it adjoins a street which is more than 100 feet in width and that it exceeds 24,000 square feet in area. Solely on the basis of these findings and applying the three applicable by-law provisions, §§ 5.21 (a) (3), 5.21 (a) (4), 5.21 (a) (5), the judge concluded that granting the special permit for a floor area ratio of 4.4:1 was permissible since it was less than the maximum allowable. Upon examining the by-law provisions, however, we are of opinion that his findings are not adequate to support his conclusion that the special permit was properly granted. The pertinent by-law provisions require the specific application of mathematical formulae. The judge’s findings did not comply with these requirements.

With respect to the special permit concerning height, the judge found that “[t]he portions of the building to which this special permit relates are more than two hundred feet from an S, SC or T district, thus under § 5.31 (b) the Board is authorized to grant a maximum height increase up to 25 % greater than the allowed one hundred and twenty (120) feet or up to one hundred and fifty (150) feet.” The judge then seems to have relied exclusively on the figures which were before the board and concluded that the statutory and by-law provisions had been met. There is no finding as to how the figures were computed or, if adopted from the board’s decision, whether they were, in fact, properly calculated.

With respect to the special permit concerning the setback requirement, the judge made no finding as to the application of the by-law formula to the locus nor did he find as required by § 5.43 that the setback permitted by the board assures “the same standard of amenity to nearby properties as would have been provided by compliance with the regulations of the By-Law.”

Further, the judge made no specific findings relative

to the granting of the special permit for off street parking. The mere description of the proposed project as being one for low income elderly persons is not a sufficient finding under the applicable by-law.

Finally, an examination of all of the judge’s findings indicates that he made no specific findings of fact concerning compliance with the requirements of § 9.5 (a) (see footnote 1).

3. In summary, we conclude that the findings of the board and the judge were sufficient as to the variance. With the exception of its finding concerning the off street parking special permit, the findings of the board as to the special permits were inadequate. The findings of the judge were inadequate as to all of the special permits. There is an indication here that these deficiencies resulted from an inadequate presentation of evidence by B & L. There is probably nothing inherent in the physical circumstances at the locus that will require a denial of these special permits. If it is the board’s decision to grant the special permits, the deficient findings discussed above will probably be remediable at a further hearing. Accordingly, the final decree is reversed and a new decree is to be entered providing (1) that the decision of the board of appeals as to the variance was not in excess of its authority, (2) that the decision of the board of appeals in granting the special permits was in excess of its authority and is annulled, (3) that the case is remanded to the board of appeals for further proceedings consistent with this opinion, and (4) that the Superior Court shall retain jurisdiction of the case.