Whenever the council of any incorporated city or town in this state shall be of the opinion that there has been a substantial increase or decrease in the population of such city or town since the last preceding census of such city or town, taken under the authority of the state, or of the United States, said council may, by resolution, declare that it is deemed advisable and necessary that a special census be taken in said city or town, and request the governor to order a special census to be taken therein. Upon such a resolution being passed by the council of any incorporated city or town and a certified copy thereof, certified to by the city clerk of such city or town, being presented to the governor, the governor shall order a special census to be taken in such city or town and shall immediately appoint a census supervisor, who shall be a resident in and qualified voter of such city or town, to supervise the taking of such special census. Such supervisor shall subscribe to an oath that he will faithfully discharge the duties of such office and cause a true and correct census of the population of such city to be taken, according to his best ability, which oath shall be filed with the secretary of state.