Sec. 13. PENSION TO DEPENDENTS, WHEN. When any member who has been retired upon pension, whether retirement pension or disability pension, or when any member who has a pension certificate shall thereafter die from any cause, his pension of Seventy-five Dollars ($75) per month shall be payable to his dependents, if any, as is provided in the next preceding Section hereof, but only for the unexpired portion of ten (10) years. In computing said ten (10) years, such length of time as a pension may have been paid to said member during his lifetime shall be deducted from such ten-year period, and such dependents shall receive said payment only for the unexpired term of ten (10) years.