Any town or city within this state, now incorporated under and by virtue of any special or local law, and in which the citizens thereof desire incorporation as a city of any special class under the general laws of this state, and believe that since the taking of the last census, state or national, there has been sufficient increase in population to entitle it to be incorporated as a city of a higher class than they would be entitled to under said last census, may, by authority of an ordinance, and at the expense of such town or city, cause to be taken a census of its population; and should such census, when so taken, show that the town or city taking the same has the requisite population to entitle it to become a city of the class desired, then such town or city may proceed to secure such incorporation as its population may entitle it to under and by authority of the provisions of chapter 72.