If any county probation officer, after having been retired on one-half pay, shall die, leaving her surviving a widower, who was her husband at the time of her retirement, such widower, so long as he shall remain unmarried, shall receive a pension equal to one-half the amount of the annual salary of such probation officer at the time of her retirement, and upon the death of such widower or in the event there be no widower, the child or children of such probation officer, under the age of sixteen years, shall, until each reaches the age of sixteen years, receive the proportionate amount of such pension; provided, however, that no pension shall be paid to the surviving husband of any deceased probation officer unless such surviving husband was wholly dependent for his income upon such county probation officer at the time of her death, and shall continue to remain so dependent upon the income which such probation officer was receiving at the time of her death; and further provided, that such surviving husband shall be and continue to remain physically or mentally incapable of pursuing some gainful occupation. The question of dependency of surviving husband shall be determined in the same manner as the permanent incapacity of probation officers as provided for in section 43:10-51 of this title.