If any county probation officer, after having been retired on one-half pay, shall die, leaving him surviving a widow, who was his wife at the time of his retirement, such widow, so long as she shall remain unmarried, shall receive a pension equal to one-half the amount of the annual salary of such county probation officer at the time of his retirement; and upon the death of such widow, or in the event there be no widow, 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.