*9 Capotosto, J.

This is a petition for certiorari praying for a review and reversal of the decision of the respondent board denying petitioners’ application for a variance under the zoning ordinance of the town of North Kingstown. Pursuant to the writ the pertinent records have been certified by the board to this court.

The following facts appear therein. In 1938 the petitioners became the owners of an old dilapidated house on Ferry Road in Saunderstown in the town of North Kingstown. Nothing was done with that property until October 1948 when the petitioners applied for and obtained a permit from the building inspector to rebuild the house “on original foundation, 22' x 58'” for a “Residence.” Acting under such permit they tore the house down and began to erect an entirely new one.

According to the zoning ordinance of North Kingstown, which was adopted July 28, 1947, petitioners’ premises were then in an AA zone where a two-family dwelling was prohibited. When work on the building had reached a certain point, residents of the neighborhood complained to the building inspector, through the town solicitor, that apparently the petitioners were erecting a two-family dwelling. Upon ascertaining that such was petitioners’ intent and purpose, the inspector ordered them to stop all further construction, after the building was closed in to protect it from the weather, until they had applied for and received permission from the zoning board to erect such a dwelling. Thereafter on May 10, 1949 petitioners filed an application with the board requesting a variance from the ordinance to erect a two-family dwelling, alleging as grounds for such request that they purchased the property with the understanding that the premises “could be used for two family purposes” and that' if they were restricted to a one-family *10 dwelling it would be unfair to them as they would not be protected in their investment.

At the hearing before the board on June 27, 1949 the petitioners and objectors were represented by counsel. Over fifty property owners in that area opposed the granting of the application either by personal appearance or by remonstrances in writing to the board, while the petitioners alone appeared in support thereof. The latter’s claim that prior to their purchase of the premises in 1938 the house had been used as a two-family dwelling was the subject of conflicting testimony. The record further shows, without denial by the petitioners, that the new building was not located on the “original foundation” as the building permit prescribed, but that the foundation thereof had been considerably extended, at least on one side.

The board denied petitioners’ application on the grounds among others that from the board’s own knowledge the grant of the variance was unsuitable to the character of the district and would depreciate the value of other property; that in securing the building permit the petitioners had failed to inform the building inspector that they intended to construct a two-family house; that the foundation for the new construction had been changed by them without authority; that “the Board was convinced on the testimony that the house had not been used — at least in the past twenty years — as a two-family dwelling”; and that, all circumstances considered, the petitioners had not shown hardship if they were made to comply with the requirements of the zoning ordinance.

Petitioners’ fundamental argument before us is that the zoning ordinance was invalid because of alleged deficient notice and advertisement before its adoption. This point cannot be raised in these proceedings. Before the board petitioners made no claim of their right to construct the house as a two-family dwelling. They invoked only the exercise of the board’s discretion under the ordinance to grant them relief from the requirements thereof. This *11 court has heretofore held in a number of cases that by asking the zoning board to exercise its discretion under an application for an exception or variance the applicant precludes himself from raising any question as to the constitutionality of the enabling act or the validity of a zoning ordinance enacted thereunder, because by filing such an application he necessarily admits the constitutionality or validity of the laws upon which he relies. Heffernan v. Zoning Board of Review, 50 R. I. 26; Allen v. Zoning Board of Review, 75 R. I. 321. See also Caldarone v. Zoning Board of Review, 74 R. I. 196.

Petitioners, citing Harrison v. Hopkins, 48 R. I. 42, further contend that considering the amount expended by them for construction in reliance upon the permit from the building inspector it was an abuse of discretion for the board to deny a variance. This contention is without merit as the Harrison case is clearly distinguishable from the instant one in that there the zoning district was changed after the petitioner had done considerable construction work under a building permit that was in full compliance with the zoning requirements at the time of issue, while here the petitioners obtained a building permit upon an application that failed to disclose their intention to erect a two-family house on premises where such a dwelling was prohibited by the zoning ordinance then in full force and effect. The petitioners attempt to justify such omission by arguing that it was the custom of the building inspector to issue permits upon applications which failed to state specifically the number of dwelling units to be erected. The short answer to this point is that there is no evidence of any such custom in the record before us.

Petitioners' final contention, as we understand it, is to the effect that they were entitled to the variance on the theory of a non-conforming use, arguing that their evidence with reference to the use of the house as a two-family dwelling was of greater weight than that of the objectors. This contention also is without merit. It is well settled *12 that ordinarily we will not pass judgment on the weight of the evidence in a zoning case which is here by certiorari to review the action of a zoning board. Apart from the question whether the non-conforming use might have been considered as abandoned by nonuser and the complete demolishment of the original building, as to which we express no opinion, the evidence of record as to whether the house in question was ever used as a two-family dwelling is in serious conflict. In the usual case, as here, if there is some evidence in the record upon which the board's decision may reasonably rest it cannot be said that they abused their discretion. Costantino v. Zoning Board of Review, 74 R. I. 316. We have consistently held that the decision of a zoning board upon matters within their discretion will not be set aside unless it clearly appears that the board acted arbitrarily or abused its discretion. Spirito v. Zoning Board of Review, 64 R. I. 411; Kent v. Zoning Board of Review, 75 R. I. 64. The petitioners here are not substantially deprived of all beneficial use of their building by a denial of the variance. See Robinson v. Town Council of Narragansett, 60 R. I. 422. Our examination of the record in this case fails to convince us that the board acted arbitrarily or abused its discretion in the matter.

Thomas J. Barry, of Massachusetts Bar, William H. Leslie, Jr., for petitioners. James H. Donnelly, Town Solicitor, for respondent.

The petition is denied and dismissed, the decision of the respondent board is affirmed, and the records heretofore certified to this court are ordered to be returned to the respondent board.