To entitle anyone to be retired because of time of service only, the time served by the person upon the regularly constituted police force, fire department, or band on which the person shall then be serving, or of the Territory or the Republic of Hawaii, its predecessor, shall be computed, but all times so served by the person before, as well as after May 2, 1917, shall be included in the computation. No time served by any person as a special police officer or a police officer solely paid by any private person, or as a merchant police officer, shall be considered in computing the length of service of the person in the police force.