Upon the death of an employee member from causes which would entitle him if still living to disability retirement or of a member on disability retirement or partial disability retirement there shall be paid to his widow, if living and not remarried, or to his children under eighteen years of age, a monthly pension equal in the aggregate to the monthly total disability benefit said employee member was entitled to receive at the time his disability was caused, subject to Section 18.10 hereof and to the following conditions:
(1) The employee member's widow shall[,] during her lifetime or until she remarries, receive such pension.
(2) Should said employee member so die leaving no widow or upon the remarriage of his widow, his child or children under the age of eighteen years shall receive such pension, share and share alike. When any of such children attain the age of eighteen years or shall die, the share of such child shall be paid to the remaining child or children under the age of eighteen years, share and share alike, until the remaining child or children reach the age of eighteen years respectively whereupon the pension shall cease.